NTSE STAGE-2 Booklet

NATIONAL TALENT SEARCH EXAMINATION STAGE - 2 (LAST FIVE YEAR PAPERS WITH SOLUTIONS )

INDEX TEST PAPERS MENTAL ABILITY TEST -

2013

–

01 - 06

SCHOLASTIC APTITUDE TEST - 2013

–

07 - 17

MENTAL ABILITY TEST -

2014

–

18 - 22

SCHOLASTIC APTITUDE TEST -

2014

–

23 - 32

MENTAL ABILITY TEST -

2015

–

33 - 37

SCHOLASTIC APTITUDE TEST - 2015

–

38 - 47

MENTAL ABILITY TEST -

2016

–

48 - 53

SCHOLASTIC APTITUDE TEST - 2016

–

54 - 63

MENTAL ABILITY TEST -

2017

–

64 - 69

SCHOLASTIC APTITUDE TEST - 2017

–

70 - 79

HINT AND SOLUTIONS MENTAL ABILITY TEST -

2013

–

80 - 81

SCHOLASTIC APTITUDE TEST -

2013

–

82 - 85

MENTAL ABILITY TEST -

2014

–

86

SCHOLASTIC APTITUDE TEST -

2014

–

87 - 91

MENTAL ABILITY TEST -

2015

–

92 - 93

SCHOLASTIC APTITUDE TEST - 2015

–

94 - 98

MENTAL ABILITY TEST -

2016

–

99 - 102

SCHOLASTIC APTITUDE TEST -

2016

–

103 - 107

MENTAL ABILITY TEST -

2017

–

108 - 112

SCHOLASTIC APTITUDE TEST -

2017

–

113 - 120

VIBRANT ACADEMY (India) Private Limited

Roll No.

NTSE 13_MAT

National Talent Search Examination, 2013 (For student Studying in Class-10)

Mental Ability Test Time : 45 minutes

Max. Marks : 50

Instructions to Candidates 1.

Mental Ability Test shall be administered in first 45 minutes. Thereafter scholastic Aptitude Test shall be administered. Answer to Part-I. Mental Ability Test are to be given on the given answer sheet. The Mental Ability answer sheet will be collected after first 45 minutes. After 5 minute Part-II Scholastic Aptitude answer sheet & after 20 minutes Question booklet will be supplied to you which will also be collected after the time is over.

2.

Please write your Roll No. as given on your Admission Card very clearly (only one digit in one box) Please see that no box is left unfilled even zeroes appearing in the Roll No. are correctly transferred to the appropriate boxes on the booklet and the Answer Sheet.

Example : For N.T.S.E.

3.

Mental Ability Test consist of 50 questions. Each question carry one marks.

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[1]

NTSE STAGE_II MENTAL ABILITY PAPER-2013 1.

Here are some words translated from an artificial language mie pie is blue light mie tie is blue berry aie tie is rasp berry Which words could possible mean “light fly” ? (1) pie zie (2) pie mie (3) aie zie (4) aie mie

2.

If in a certain code, STUDENT is written as RSTEDMS, then how would TEACHER be written in the same code ? (1) SZZDGEQ (2) SZDDGEQ (3) SDZDGDQ (4) SDZCGDQ

3.

Which group of letters is different from others ? (1) CBAED (2) IJHGK (3) SRQPT (4) TVWYX

4.

In the following letter sequence, some of the letters are missing. These are given in order as one of the alternatives below. Choose the correct alternative. a b _ a a _ b b b _ a a a a _ b b b ..... (1) abba (2) baba (3) aaab (4) abab

5.

7.

Ramesh started going for regular morning walks for controlling his blood sugar level. He did so for a month and also started taking Yoga lessons, without going for any pathological examination. He underwent pathological test after two months and found that the blood sugar level has come down. Presuming that he had not changed his food habits during these two months, which statement among the alternative given below follows most logically? (1) Blood sugar level comes down after doing regular morning walk. (2) Blood sugar level comes down after doing Yoga. (3) Blood sugar level comes down on doing regular morning walk and Yoga. (4) Regular morning walk, Yoga or both may bring down sugar level despite not changing food habits.

8.

Find the number in the position of ‘?’

Fill in the missing number

- C 2B - 3 A 2A ? -B - 3 C - A - 2B (1) – 3C (3) 3C 6.

(1) 41 (3) 50 (2) – 2C (4) 2B

Vimla used to board the train from Metro Station A for going to her office. Since Station A is a terminus, she had no problem in getting a seat. Ever since she shifted to Locality B she finds it difficult to get a seat, as by the time the train reaches Locality B it becomes crowded. Find the statement among the alternatives which must be true as per the given information. (1) Vimla would prefer to take a bus rather than the metro. (2) Vimla’s travel to office has become less comfortable ever since she has shifted. (3) Commuters staying in and around Locality B would demand metro services originating from station near Locality B. (4) Vimla would look for a job close to her home

9.

(2) 45 (4) 52

Identify the number in the position of ‘?’

(1) 2 (3) 5

(2) 3 (4) 6

10.

Find the next number in the sequence 0, 2, 24, 252, __________ (1) 620 (2) 1040 (3) 3120 (4) 5430

11.

Find the next number in the sequence 6, 24, 60, 120, __________ (1) 180 (2) 210 (3) 240 (4) 360

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12.

Find the letter to be placed in place of ‘?’ in the figure given.

(1) M (3) Q 13.

17.

(2) N (4) R

In this multiplication question the five letters represent five different digits. What are the actual figures ? There is no zero. 18. (1) (2) (3) (4)

14.

M = 3, M = 3, M = 4, M = 4,

E = 9, A = E = 9, A = E = 3, A = E = 9, A =

7, T 7, T 9, T 3, T

= 4, S = 8 = 8, S = 4 = 7, S = 8 = 7, S = 8

Identify which among the pieces given below will not be required to complete the triangular pattern shown below.

(1) q (3) s

(1)

(2)

(3)

(4)

On the basis of the four positions of a dice given below find the colour of the face opposite ‘Yellow’.

(1) Indigo

(2) Red

(3) Pink

(4) Blue

19.

If the given figure is folded to form a box, which among the boxes below will be formed ?

20.

Two positions of a dice are shown. Which number will appear on the face opposite the one having 5 ?

(2) r (4) t

15.

Find the missing number in the series 2, 10, 26, ______ , 242 (1) 80 (2) 81 (3) 82 (4) 84

16.

A pattern is given below. You have to identify which among the following pieces will not be required to complete the pattern.

(1) q (3) s

Which symbol replaces the ‘?’ Figure below represent a balance.

(2) r (4) t

(1) 1

(2) 2

(3) 4

(4) 6

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21.

In the figure, the circle represents youth, the triangle represents footballers and the rectangle represents athletes. Which letter(s) represent(s) athletes among youths who are not footballers ?

(1) g (3) f 22.

28.

Question given below has a problem and two statements I & II. Decide if the information given in the statement is sufficient for answering the problem. K, R, S and T are four players in Indian Cricket team. Who is the oldest among them ? I : The total age of K & T together is more than that of S II : The total age of R & K together is less than that of S (1) Data in statement I alone is sufficient (2) Data in statement II alone is sufficient (3) Data in both statement together is sufficient (4) Data in both statement together is not sufficient

29.

Which of the following diagram/sets indicate the relation between women, mothers and parents?

(2) g and c (4) f and d

(2) B (4) D

Identify the number corresponding to the ‘?’

(1) 3 (3) 7

(2) 5 (4) 8

24.

Which of the given alternative is the mirror image of REASON, if the mirror is placed below the word ? (1) (2) (3) (4)

25.

A sprinter goes off the starting block for 100m run and at that instant the second-hand of a stopwatch had pointed towards North. He touches the finishing line exactly after 12 seconds. In which direction did the second hand point when he just crossed the finishing line ? (1) 18º North of East (2) 18º East of North (3) 72º North of East (4) 82º East of North

26.

Mother was asked how many gifts she had in the bag. She replied that there were all dolls but six, all cars but six, and all books but six. How many gifts had she in all ? (1) 9 (2) 18 (3) 27 (4) 36

Find the odd one out

(1) A (3) C 23.

27.

2 7

(2)

5 7

(3)

3 5

(4)

4 5

(2)

(3)

(4)

30.

In a dairy, there are 60 cows and buffalos. The number of cows is twice that of buffalos. Buffalo X ranked seventeenth in terms of milk delivered. If there are 9 cows ahead of Buffalo X, how many buffalos are after in rank in terms of milk delivered? (1) 10 (2) 11 (3) 12 (4) 13

31.

What is the mirror image of b3k4s I ? b3k4s ? (1) (3)

(2) (4)

32-36

Question 32 to 36 are based on the following information: a, b, g, d , Î ,f , y , h are sitting on a merry-go-round facing at the centre. d is second to the left on h who is third to the left of a. b is fourth to the right of g who is immediate neighbour of h . y is not a neighbour of b or g . f is not a neighbour of b.

32.

Who is third to the left of b. (1) a (2) g (3) f (4) Y

Two candles are of different lengths and thicknesses. The short and the long ones can burn respectively for 3.5 hour and 5 hour. After burning for 2 hour, the lengths of the candles become equal in length. What fraction of the long candle’s height was the short candle initially ? (1)

(1)

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33.

In which of the following pairs is the first person sitting to the immediate right of the second person ? (1) d, Y (2) b, Î (3) h , b (4) Y , h

34.

What is f‘s position with respect to Y ? (1) Third towards right (2) Third towards left (3) Second towards right (4) Second towards left

35.

Who is sitting between a and b ? (1) Both Î and h (2) Both f and g (3) Only Î (4) Only f

36.

How many of them are sitting between g and b ? (1) 0 or 6 (2) 1 or 5 (3) 2 or 4 (4) 3

37.

In a school 120 boys have registered for a singles carrom tournament. Each match eliminates one player. How many matches are to be organized to determine the champion? (1) 60 (2) 61 (3) 119 (4) 120

38.

Amongst five friends, Lata, Alka, Rani, Asha and Sadhana. Lata is older than only three of her friends. Alka is younger to Asha and Lata. Rani is older than only Sadhana. Who amongst them is the eldest? (1) Asha (2) Lata (3) Alka (4) Sadhana

39.

Twenty four teams are divided into 4 group of six teams each. Within each group the teams play each other exactly once. The winners of each group then play in the semifinals. Winners of the semifinals play in the finals and losers for the 3rd place. How many matches are played? (1) 60 (2) 63 (3) 64 (4) 66

40-41. Take the given statement(s) as true and decide which of the conclusion logically follows from the statements. 40. Statement: All Actors are Musicians. No Musician is a Singer. Some Singers are Dancerss. Some Dancers are Musicians.

41.

Statement : All Clocks are Alarms. No Clocks are Cuckoos. All Cuckoos are Alarms. Some Cuckoos are Birds . Conclusion : I. Some Alarms are Birds. II. No Clock is a Bird III. All Birds are Alarms (1) Only conclusion I follows. (2) Only conclusion II follows. (3) Only conclusion III follows. (4) Both conclusion II and III follows.

42.

Two players X and O play a game of “doughts and crosses” on a 3 × 3 grid. The purpose of the game is for a player to get 3 symbols belonging to the player in a straight line (vertically, horizontally or diagonally). Each player marks one symbol on his or her turn. After two moves (1 turn each), the grid looks as follows with X to play next. Where should X put his symbol next so that he will always win this game finally regard less of how well O plays ?

(1) Bottom row right corner (2) Bottom row middle cell (3) Middle row left most cell (4) It is not possible to always ensure X wins if O plays carefully 43.

An electrical circuit for a set of 4 lights depends on a system of switches A, B, C and D. When these switches work they have the following effect on the lights: They each change the state of two lights (i.e. on becomes off and off becomes on). The lights that each switch controls are as follows.

In configuration 1 shown below, switches CBDA are activated in turn, resulting in configuration 2. One switch did not work and had no effect at all. Which was that switch?

Conclusions : I. Some Actors are Singers II. Some Dancers are Actors III : No Actor is a Singer (1) Only conclusion 1 follows. (2) Only conclusion III follows. (3) Exactly one of conclusion I, III follows. (4) Only conclusion II follows. (1) A (3) C

(2) B (4) D

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47.

44.

(1)

(2)

(3)

(4)

48.

I left home for bringing milk between 7am and 8am. The angle between the hour-hand and the minute-hand was 90° I returned home between 7 am and 8 am. Then also the angle between the minute-hand and hour-hand was 90°. At what time (nearest to second) did I leave and return home? (1) 7h 18m 35s & 7h 51 m 24s (2) 7h 19m 24s & 7h 52m 14s (3) 7h 20m 42s & 7h 53m 11s (4) 7h 21 m 49s & 7h 54m 33s I left home at 3:00pm and returned at 3:48pm. The clock was rotated by 45°, so that when I left, the hour-hand of a clock was pointing along the southeast direction. In which direction would the hour-hand point when I returned? (1) 15° East of South (2) 21º East of South (3) 63° South of East (4) 27° South of East

45.

49. (1)

(3)

46.

(2) When the above is folded into a cube, which is the only cube that can be produced amongst the following?

(4)

A, B, C, D and E are sitting on a bench. A is sitting next to B, C is sitting next to D, D is not sitting next to E, who is sitting on the left end of the bench. C is on the second position from the right. A is to the right of B and E. Counting from the left in which position is A sitting? (1) 2 (2) 3 (3) 5 (4) Cannot be determined from the given conditions .

50.

(1)

(2)

(3)

(4)

What will be water image of CHICK? (1) CHIC (2) C (3) K (4)

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[6]

Roll No.

NTSE 13_SAT

National Talent Search Examination, 2013 (For student Studying in Class-10)

Scholastic Aptitude Test Time : 90 minutes

Max. Marks : 100

Instructions to Candidates Read These instructions very carefully before attempting questions 1.

Please write your Roll No. as given on your Admission Card very clearly (only one digit in one box) Please see that no box is left unfilled even zeroes appearing in the Roll No. are correctly transferred to the appropriate boxes on the booklet and the Answer Sheet.

Example : For N.T.S.E.

2.

There are 100 questions in this paper Each question is to be answered.

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[7]

NTSE STAGE_II (SAT) PAPER-2013 1.

An animal cell, a plant cell and a bacterium share the following structural features : (1) Cell membrane, endoplasmic reticulum, vacuoles (2) Cell wall, plasma membrane, mitochondria (3) Cell wall, nucleus, cytoplasm (4) Plasma membrane, cytoplasm, ribosomes

2.

Given below are figures of three kinds of muscle fibres.

(1)

3.

4.

5.

6.

(2)

7.

Photosynthesis in an aquatic plant was measured by counting the number of O2 bubbles coming out of the cut end of the plant . What wiill happen to O2 production if you use a pipe to blow air from your mouth into water in the beaker ?

(1) Air from mouth contains O2 which is being added to the plant. Hence increase in O2 production

(3)

Which one/ones would you find in the grass hopper’s legs? (1) A only (2) B only (3) A and C (4) B and C

(2) Air from mouth contains CO2 which is utilized in photosynthesis. Hence increase in O2 production.

A Plant that has well differentiated body, special tissues for transport of water and other substances, but does not have seed or fruits is a (n) : (1) Bryophyte (2) Angiosperm (3) Gymnosperm (4) Pteridophyte

(4) Water is already in Contact with air. Hence air from mouth will have no effect.

Raju was suffering from severe stomach pain and the doctor diagnosed that he was suffering from peptic ulcers and treated him with antibiotics. He was relieved of pain. What could be the reason for peptic ulcers? (1) Reduced secretion of hormones. (2) Reduced water content (3) Growth of Helicobacter pylori (4) Excess secretion of enzyme The average temperature of the Earth remains fairly steady as compared to that of the moon because of the (1) Atmosphere (2) Lithosphere (3) Biosphere (4) Hydrosphere In flowers which one of the following conditions will increase chances of self-pollination ? (1) Pistil is longer than stamens in a flower (2) Stamens are just above the stigma of pistil in a flower (3) In all flowers of the plant only pistil is present (4) In all flowers of the plant only stamens are present.

(3) Bacteria from mouth will infect plant. Hence reduction in O2 production.

8.

A person with blood group 'A' can donate blood to the persons with blood group 'A' or 'AB' because it (1) has both 'A' and 'B' antigens. (2) has only 'A' antigen and 'B' antibodies. (3) has only 'B' antigen and 'A' antibodies (4) does not have any antigens and antibodies

9.

What would happen to the person if cerebellum of his brain is damaged? (1) He will lose his memory power. (2) He will not be able to swallow food properly. (3) He will be unable to coordinate and stand properly. (4) He will lose his powers of vision and hearing.

10.

Which of the following statements are correct? A.. Tapeworms are hermaphrodites and undergo self-fertilization. B. Earthworms are hermaphrodites and undergo self-fertilization. C. Tapeworms are hermaphrodites but undergo cross-fertiIization. D. Earthworms are hermaphrodites but undergo cross-fertilization (1) A and B (3) C and D

(2) B and C (4) D and A

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11-12

A group of red beetles lives on green leaves of a tree. Beetles multiply through sexual reproduction. One day, some green beetles are seen among the red beetles. Green beetles breed to produce green progeny. Crows on the tree eat beetles.

11.

Some green beetles appear among the red beetle because (1) Beetles become green by accumulating chlorophyll from the green leaves that they eat. (2) Natural variations occur during sexual reproduction. (3) Red beetles mimic green colour of leaves whenever they see crows. (4) Beetles change colour from red to green with change of season.

12.

13.

16.

There is a mixture of three solid compounds A, Band C. Out of' these compounds A and C are soluble in water and compound C is sublimable also. In what sequence the following techniques can be used for their effcctive separation? I. Filtration II. Sublimation Ill. Crystallisation from water extract IV. Dissolution in water (1) (II), (I), (IV), (Ill) (2) (IV), (I), (II), (III) (3) (I), (II), (m), (IV) (4) (II), (IV). (I), (III)

17.

Which of the following is a suitable example for illustrating the law of conservation of mass? (Atomic mass of O = 16; H = l ) (1) 18g of water is formed by the combination of 16g oxygen with 2g of hydrogen. . (2) 18g of water in liquid state is obtained by heating 18g of ice. (3) 18g of water is completely converted into vapour state on heating. (4) 18g of water freezes at 4°C to give same mass of ice.

18.

An element X has 7 electrons in its L shell. What is true about the elemt:nt X? I. It belongs to period 9 of modern periodic table. II. Its atom contains 9 protons. III. It has a valency of 7. IV. Its atoms can accept an electron to acquire noble gas configuration. (1) (I) and (II) (2) (II) and (Ill) (3) (Ill) and (IV) (4) (II) and (IV)

19.

The reaction between carbon and oxygen can be represented as C(S) + O2(g) ¾® CO2(g) + heat

The colour compasItIon of beetle population is likely to change in the following manner: (1) Both red and green beetle survive equally. (2) Only the red beetle survives. (3) More red beetles survive than the green. (4) More green beetles survive than the red. In the following food chain who gets less energy than the tertiary consumer and more than the primary consumer? Grass ® Grasshopper ® Frog ® Snake ® Eagle (1) Grasshopper (2) Frog (3) Snake (4) Eagle

14.

15.

If a non-degradable and fat soluble pollutant, such as DDT enters the food chain, the pollutant (1) magnifies in concentration at each trophic level. (2) degrades at first trophic level. (3) accumulates in the body fat of organism at first trophic level and does not pass to second trophic level. (4) decreases in concentration at each trophic level. A drop each of two non-corrosive and non-irritating liquids A and B at a temperature of 22ºC are placed on the skin. Liquid A gives a more cooling sensation than liquid B.Which of the following can be said about the liquids A and B? (1) Liquid A has higher boiling point than that of liquid B. (2) Liquid A has higher latent heat of vaporisation than that of liquid B. (3) Liquid A has lower latent heat of vaporisation than that of liquid B. (4) The boiling points of liquid A and B are equal.

In which of the following type(s), the above reaction can be classified? I. Combustion reaction II. Displacement reaction III. Endothermic reation IV. Combination reaction (1) (I) and (III) (2) (I) , (III) and (IV) (3) (I) and (IV) (4) (I) only 20.

A metal carbonate X on treatment with a mineral acid liberates a gas which when passed through aqueous solution of a substance Y gives back X. The substance Y on reaction with the gas obtained at anode during electrolysis of brine gives a compound Z which can decolorise coloured fabrics. The compounds X,Y and Z respectively are (1) CaCO3, Ca(OH)2, CaOCI2 (2) Ca(OH)2, CaO, CaOCI2 (3) CaCO3, CaOCl2, Ca(OH)2 (4) Ca(OH)2, CaCO3, CaOCI2

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21.

A salt can be produced by reaction between

26.

A. a weak acid and weak base. B. metal oxide and water. C. metal and a mineral acid.

A. Has 3 valence electrons.

D. metal oxide and a mineral acid. (1) A, Band C (3) C,D and A

An element X combines with hydrogen to form a compound XH3. The element X is placed on the right side of the periodic table. What is true about the element X ? B. Is a metal and is solid.

(2) B,C and D (4) 0, A and B

C. Is a non-metal and is a gas. D. Has 5 valence electrons.

22.

Which of the following is true about the two statements?

E. XH3 reacts with water to form a basic compound.

Statement I : Reactivity of aluminium decreases when it is dipped in nitric acid

(1) A, B and C

(2) B, C and D

(3) C, D and E

(4) E, A and B

Statement II : A protective layer of aluminium nitrate is formed when aluminium is dipped in nitric acid.

27.

An element X (atomic number 12) reacts with another element Y (atomic number 17) to form a compound Z. Which of the following statements are true regarding this compound ? I. Molecular formula of Z is XY2 II. It is soluble in water III. X and Y are joined by sharing of electrons IV. It would conduct electricity in the molten state (1) (II) and (III) (2) (I) and (III) (3) (I),(III) and (IV) (4) (I) and (IV)

28.

A ship sends a sonar wave to the sea bed which is flat and measured several times over a large area. One day the reflected sound wave takes longer time than in previous measurements. The possible reason is : (1) The frequency of the sonar wave, generated by the equipment is lower than previous measurements. (2) There is a solid object of large size in the path of sonar wave. (3) there is a huge air bubble in the path of sonar wave. (4) the loudness of the sonar wave, generated by the equipment is lower than previous measurement.

29.

Which of the following ray diagram is correct?

(1) I is correct but II is incorrect (2) I is incorrect but II is correct (3) Both the statements are correct and II is also the correct explanation of I (4) Both the statements arc correct but II is not correct explanation of I 23.

24.

A silvery white metal X reacts with water at room temperature to produce a water soluble compound Y and a colourless gas Z. The reaction is highly exothermic and the Z catches fire immediately during the reaction. The solution of Y in water on reacting with stoichiometric amount of dilute solution of hydrochloric acid gives a solution of pH = 7.0. The compounds X, Y and Z respectively are : (1) AI, AI(OH)3 and H2

(2) Ag, AgOH and H2

(3) K, KCI and H2

(4) Na, NaOH and H2

A compound X is obtained by the reaction of alkaline KMnO 4 with "mother compound Y followed by acidification. Compound X also reacts with compound Y in presence of few drops of H2SO4 to form a sweet smelling compound Z. The compound X, Y and Z are, respectively

(1)

(1) Ethanol, Ethene, Ethanoic Acid (2) Ethanoic Acid, Ethanol, Ethylethanoate

(2)

(3) Ethanoic Acid, Ethanal, Ethene (4) Ethanol, Ethanoic Acid, Sodium Ethanoate 25.

Which of the following pairs of compounds of carbon will undergo combustion as well as addition reaction ? (1) CH4 and C2H6.

(2) C2H6O and C3H8O

(3) C2H4O2 and C3H6O

(4) C2H2 and C3H6

(3)

(4)

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30.

31.

32.

33.

A concave lens always gives a virtual image. In optical lenses worn by humans which of the following statements is true? (1) The lens can never be concave. (2) In some cases the lens can be concave if the focal length is much larger than 2.5 cm. (3) All focal length concave lenses are possible. (4) All focal length convex lenses are possible. A geo-stationary satellite is orbiting around earth at height of 30,000 km in circular orbit. The radius of the earth is taken as 6000 km. The geostationary satellite comes back to its position after one revolution in exactly 24 hours. Let the acceleration due to gravity (g) be 10 m/s2 and mass of satellite be 1000 kg; calculate the work done in 12 hours when moving under gravitational force. (1) 3.6p × 1014 J (2) 2p × 7.2p 1014 J (3) 1.8p x 1014 J (4) 0 J

34.

235 231 4 92 U ® 90 Th + 2He

(1) Each decay product has the same kinetic energy. (2) The decay products tend to go in the same direction. (3) The thorium nucleus has more momentum than the helium nucleus. (4) The helium nucleus has more kinetic energy than the thorium nucleus. 35.

Consider a simple circuit containing a battery and three identical incandescent bulbs A, B and C. Bulb A is wired in parallel with bulb B and this combination is wired in series with bulb C. What would happen to the brightness of the other two bulbs if bulb A were to burn out? (1) Only bulb B would get brighter. (2) Both A and B would get brighter. (3) Bulb B would get brighter and bulb C would get dimmer. (4) There would be no change in the brightness of either bulb B or bulb C.

Which of the graph below is a possible graph of the position x(t)?

36.

(2) II < III < IIII (4) II > III = IIII

The figure below shows the position of a ball at t = 0, t = 1 s, t = 2 s, t = 3 s and t = 4 s

Position of ball at five successive times

Three different circuits (I, II and III) are constructed using identical batteries and resistors of R and 2R ohm. What can be said about current I in arm AB of each circuit?

(1) III< II < IIII (3) II = III = IIII

A uranium nucleus at rest decays into a thorium nucleus and a helium nucleus, as shown below. Which of the following is true?

(1)

(2)

(3)

(4)

The graph shows position as a function of time for two trains A and B running on parallel tracks. For times greater than t = 0, which of the following statement is true?

(1) At time tB both trains have the same velocity. (2) Both trains speed up all the time. (3) Both trains may have the same velocity at some time earlier than tB. (4) Graph indicates that both trains have the same acceleration at a given time.

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37.

The figure shown below depicts the distance travelled by a body as a function of time.

41.

An open box is made from a square lamina of side 12cm, by cutting equal squares at the corners and folding up the remaining flaps. The volume of this box cannot be (1) 115 c.c. (2) 120 c.c. (3) 125 c.c.

42.

A has a pair of triangles with corresponding sides proportional, and B has a pair of pentagons with corresponding sides proportional. S1 = A's triangles must be similar S2 = D's pentagons must be similar Which of the following statement is correct? (1) S1 is true, but S2 is not true. (2) S2 is true, but S1 is not true. (3) Both S1 and S2 are true. (4) Neither S1 nor S2 is true.

43.

DABC is an equilateral triangle of side 2 3 cms. P is any point in the interior of D ABC. If x, y, z are the distances of P from the sides of the triangle, then x + y + z =

The average speed and maximum speed between 0 and 20 s are (1) 1 m/s, 2.0 m/s respectively. (2) 1 m/s, 1.6 m/s respectively. (3) 2.0 m/s, 2.6 m/s respectively. (4) 1.3 m/s, 2.0 m/s respectively. 38.

39.

A hypothetical planet has density p, radius R, and surface gravitational acceleration g. If the radius of the planet were doubled but the planetary density stayed the same, the acceleration due to gravity at the planet's surface would be : (1) 4g (2) 2g (3) g (4) g/2 Three rings P. Q and R are dropped at the same time over identical hollow magnets as shown below :

Which of the following describes the order in which the ring P, Q and R reach the bottom of the magnet? (1) They arrive in the order P, Q, R. (2) They arrive in the order P, R, Q. (3) Rings P and R arrive simultaneously, followed by Q. (4) Rings Q and R arrive simultaneously, followed by P. 40.

An electron moving with uniform velocity in x direction enters a region of uniform magnetic field along y direction. Which of the following physical quantity(ies) is(are) non-zero and remain constant? I. Velocity of the electron. II. Magnitude of the momentum of the electron. III. Force on the electron. IV. The kinetic energy of electron. (1) Only I and II. (2) Only III and IV. (3) All four. (4) Only II and IV.

(4) 130 c.c.

(1) 2 + 3 cms. (3) 3 cms.

(2) 5 cms. (4) 4 cms.

44.

Which of the following numbers is the fourth power of a natural number? (1) 6765201 (2) 6765206 (3) 6765207 (4) 6765209

45.

The square of an odd integer must be of the form (1) 6n + 1 (2) 6n + 3 (3) 8n + 1 (4) 4n + 1 but may not be 8n + 1

46.

ABCD is a square with side a. With centers A, B, C and D four circles are drawn such that each circle touches externally two of the remaining three circles. Let d be the area of the region In the interior of the square and exterior of the circles. Then the maximum value of d is æ4-pö

(1) a2( 1 – p )

(2) a2 ç 4 ÷ è ø

(3) a2(p – 1)

(4)

pa2 4

47.

The value of tan1º tan2º tan3º......... tan89º is (1) 0 (2) 1 1 (3) 2 (4) 2

48.

ax2 + bx + c = 0, where a, b, c are real, has real roots if (1) a, b, c are integers. (2) b2 > 3ac. (3) ac > 0 and b is zero. (4) c = 0.

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49.

An open box A is made from a square piece of tin by cutting equal squares S at the comers and folding up the remaining flaps. Another open box B is made similarly using one of the squares S. If U and V are the volumes of A and B respectively, then which of the following is not possible? (1) U > V (2) V > U (3) U = V (4) minimum value of U > maximum value of V.

56.

A solid metal sphere of surface area S1 is melted and recast into a number of smaller spheres. S2 is the sum of the surface areas of all the smaller spheres. Then (1) S1 > S2 (2) S2 > S1 (3) S1 = S2 (4) S1 = S2 only if all the smaller spheres of equal radii

57.

Which of the following is an irrational number? (1)

41616

(2) 23.232323 ... 50.

Which of the following statements holds always? (1) Every rectangle is a square. (2) Every parallelogram is a trapezium (3) Every rhombus is a square (4) Every parallelogram is a rectangle

51.

Which of the following polygons are uniquely determined when all the sides are given? (1) Quadrilateral (2) Triangle (3) Pentagon (4) Hexagon

52.

There are several human beings and several dogs in a room. One tenth of the humans have lost a leg. The total numbers of feet are 77. Then the number of dogs is (1) not determinable due to insufficient data (2) 4 (3) 5 (4) 6

53.

All the arcs in the following diagram are semicircles. This diagram shows two paths connecting A to B. Path I is the single large semicircle and Path II consists of the chain of small semicircles.

(1) Path I is longer than Path II (2) Path I is of the same length as Path II (3) Path I is shorter than Path II (4) Path I is of the same length as Path II, only if the number of semi circles is not more than 4 54.

55.

One integer is chosen out of 1, 2, 3, ...,100. What is the probability that it is neither divisible by 4 nor by 6 (1) 0.59 (2) 0.67 (3) 0.41 (4) 0.33 (a - b )2 +

(b - a )2 is

(1) Always zero (2) Never zero (3) Positive if and only if a > b (4) Positive only if a ¹ b

(3)

(1 + 3 )3 - (1 - 3 )3 3

(4) 23.10100100010000 ... 58.

Re.1 and Rs.5 coins are available (as many required). Find the smallest payment which cannot be made by these coins, if not more than 5 coins are allowed. (1) 3 (2) 12 (3) 14 (4) 18

59.

Median of a data set is a number which has an equal number of observations below and above it. The median of 1,9,4,3,7,6,8,8,12,15 is (1) 7·5 (2) 7 (3) 8 (4) any number between 7 and 8

60.

Suppose you walk from home to the bus stand at 4 km/h and immediately return at x km/h. If the average speed is 6 km/h then x is (1) 8 km/h (2) 10 k m/h (3) 12 km/h (4) cannot be detennined unless the distance from home to bus stand is known.

61.

From about 13th century to the time of the French Revolution sumptuary laws were expected to be followed strictly to: (1) regulate the behaviour of the royalty. (2) regulate the income of people by social rank. (3) control the behaviour of those considered social inferiors. (4) provide religious sanctity to social behaviour.

62.

Choose the correct response from the given options. On 3rd March 1933 the famous Enabling Act was passed to: a. establish dictatorship in Germany. b. give Hitler the power to rule by decree. c. ban all trade unions. d. ban all political parties and their affiliates. (1) only a and b are correct (2) only c and d are correct (3) a, band c are correct (4) only d is correct

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63.

Enclosures in England were seen as : (1) hindrance to agricultural expansion and crop rotation. (2) hindrance to commercialization of agriculture. (3) necessary to make long-term investment on land, agriculture and to plan crop rotation to improve the soil. (4) necessary to protect the interests of those who depended on the commons for their survival.

64.

The Balkans, which was a serious source of nationalist tension in Europe after 1871, was a region comprising of : (1) Romaina, Germany, Poland, Bulgaria (2) Romania, Prussia, Bulgaria, Slovakia and Poland. (3) Serbia, Austria, Bulgaria, Slovakia and Poland (4) Serbia, Bulgaria, Greece, Croatia, Romania

70.

Consider the following statements and choose the correct response from the options given thereafter : Statement I : The major cricket tournament of colonial India, the 'Quadrangular' did not represent regions but religious communities. Statement II : The victory of the 'Hindus' in the 'Quadrangular' cricket tournament in 1923 was equated by a cricket fan with Gandhiji's war on 'untouchability'. (1) Statement I is true but statement II is false. (2) Statement I is false but statement II is true. (3) Both statement I and statement II are true and II is correct explanation of statement I. (4) Both statement I and statement II are true but statement II is not the correct explanation of statement l. Match the following columns :

71.

Column A Ambedkar established the Depressed Classes Association Gandhiji began the Civil (II) Disobedience Movement Gandhiji ended the Civil (III) Disobedience Movement (I)

65.

66.

What was Rinderpest? (1) A disease of cattle plagues that spread in Africa in the 1890s (2) Bubonic plague which spread in the region of Maharashtra in the 1890s. (3) A type of cholera that spread in Assam in the 1890s. (4) A devastating bird disease that was imported to Italy from British Asia, through chicken meat. Which of the following is a correct match ? (1) Rashsundari Debi -lstri Dharma Vichar (2) Ram Chadda - Amar Jiban (3) Kashibaba - Chote Aur Bade ka Sawaal (4) Sudarshan Chakra - Gulamgiri

67.

Printing created possibilities of wider circulation of ideas. Who of the following hailed printing as the ultimate gift of God? (1) Martin Luther (2) Menocchio (3) Roman Catholic Church (4) Gutenberg

68.

The Forest Act of 1878 divided forests into : (1) reserved and protected forests. (2) protected and village forests. (3) bio-sphere reserves and wild life sanctuaries. (4) reserved, protected and village forests.

69.

Consider the following statements and identify the correct response from the options given thereafter: Statement I : Hitler said 'In my state the mother is the most important citizen', Statement II : In Nazi Germany while boys were taught to be aggressive, muscular and steel hearted; girls were told that they had to become good mothers. (1) Statement I is true but statement II is false. (2) Both statement I and statement II are true but statement II is not the: correct explanation of statement I. (3) Both the statements are false. (4) Both statement I and statement II are true and statement II is the correct explanation of statement I.

(IV)

Congress adopted the demand for 'Puma Swaraj'

Column B (A) December,1929 (B) August, 1930 (C) March, 1930 (D) March, 1931

(1) (I). (3), (II) - (4), (III) - (2), (IV)· (1) (2) (I) - (2), (II) - (3), (III) - (4), (IV) - (1) (3) (I) -(3), (II) - (1), (III)· (2), (IV) - (4) (4) (I) - (4), (II) - (3), (III) • (2), (IV)· (1) 72.

Consider the following statements and choose the correct response from the options given there after : Statement 1: The Act of Union 1707 led to the formation of the "United Kingdom of Great Britain". Statement II : The British parliament was henceforth dominated by its English members. (1) Both statement I and statement II are false. (2) Both statement I and statement II are true and statement II is the result of statement I. (3) Statement I is true but statement II is false. (4) Both statement I and statement II are true but statement II is not a result of statement I.

73.

Consider the following statements and choose the correct response from the options given thereafter: Statement I : Traders and travellers introduced new crops to the land they travelled. Statement II : Noodles most likely travelled from China through Arab traders to Sicily. Statement III : Potato reached the West through travellers and became the staple diet of the poor. (1) Statement I and statement III are true. (2) Statement II and statement III are true. (3) All three statements are true. (4) Statement I and statement II are true.

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74.

Assertion (A) : Gandhiji’s idea of satyagraha emphasised on the power of truth and the need to search for truth.

78.

Assertion (A) : In India, east coast has more seaports than the west coast. Reason (R) : The east coast is broader and is an example of emergent coast. Select the correct option from the given alternatives.

Reasoning (R) : Gandhiji believed that a satyagrahi could win the battle by appealing to the conscience of the oppressor.

(1) Both (A) and (R) are true, and (R) explain (A)

Select the correct option from the given alternatives.

(2) Both (A) and (R) are true, but (R) does not explain (A)

(1) A is true and R is false.

(3) (A) is true and (R) is false

(2) Both A and R are true but R is not the correct explanation of A.

(4) (A) is false and (R) is true

(3) Both A and R are true and R is the correct explanation of A

79.

W hich pie diagram represents India's age composition in 2001?

(4) Both A and R are false. 75.

(1)

Assertion (A) : The Civil Disobedience Movement was different from the Non-cooperation Movement. Reason (R) : People in the Civil Disobedience Movement were asked not only to refuse cooperation with the British but also to break colonial laws. Select the correct option from the given alternatives.

(3) 80.

(1) Both A and R are true but R is not the correct explanation of A. (2) Both A and R are false (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A 76.

Assertion (A) : Coal is a fossil fuel. Reason (R): It is formed due to compression of inorganic material over millions of years.

81.

(4)

Assertion (A) : The north western parts of India receive rainfall in winter. Reason (R) : The winter rainfall in India occurs due to North East monsoon. Select the correct option from the given alternatives. (1) Both (A) and (R) are true, and (R) explain (A) (2) Both (A) and (R), are true, but (R) does not explain (A) (3) (A) is true and (R) is false (4) (A) is false and (R) is true Which four major ports of India lie on the Golden Quadrilateral?

Select the correct option from the given alternatives.

(1) Chennai, Tuticorin, Mangalore, Marmagao

(1) Both (A) and (R) are true, and (R) explain (A)

(3) Marmagao, Mumbai, Kandla, Mangalore

(2) Both (A) and (R) are true, but (R) does not explain (A)

(4) Kolkata, Mumbai, Vishakhapatanam, Chennai

(3) (A) is true and (R) is false (4) (A) is false and (R) is true 77.

(2)

(2) Kolkata, Chennai, Mangalore, Mumbai

82.

Match the fishing ports indicated on the map of India (I, II, III and IV) with their respective names. A. Kakinada B. Alappuzha C. Porbandar D. Tuticorin

Assertion (A) : The sun rises in Arunachal Pradesh about two hours before Gujarat. Reason (R) : Arunachal Pradesh is on a higher latitude than Gujarat. Select the correct option from the given alternatives. (1) Both (A) and (R) are true, and (R) explain (A) (2) Both (A) and (R), are true, but (R) does not explain (A) (3) (A) is true and (R) is false (4) (A) is false and (R) is true

(1) II-A, (2) I-A, (3) l-C, (4) I-D,

III-B, II-B, II-B, II-B,

I-C, III-D, III-A, III-A,

IV-D IV-C IV-D IV-C

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83.

84.

85.

86.

87.

Which figure relates the trend of population Growth rate of India from 1951-2001?

(1)

(2)

(3)

(4)

Assertion (A) : The Himalayan ranges show change in vegetation from tropical to tundra. Reason (R): In mountainous area with increase in altitude there is corresponding decrease in temperature, which leads to change in vegetation types. Select the correct option from the given alternatives. (1) Both (A) and (R) are true and (R) explain (A). (2) Both (A) and (R) are true but (R) does not explain (A). (3) (A) is true and (R) is false. (4) (A) is false and (R) is true. Which of the following methods are used to restrict soil erosion? A. Ploughing along contour lines B. Strip cropping C. Jhumming D. Mixed farming (1) A and B (2) A and C (3) B and D (4) B and C Assertion (A) : Although only the southern part of India lies in tropical region, the whole of India has tropical climate. Reason (R) : Himalaya mountain ranges protect it from the north cold winds. Select the correct option from the given alternatives. (1) Both (A) and (R) are true and (R) explain (A) (2) Both (A) and (R) are true but (R) does not explain (A) (3) (A) is true and (R) is false. (4) (A) is false and (R) is true.

(1) Advancement of summer monsoon on 1st June. (2) Line dividing tropical evergreen and deciduous forest. (3) Water divide between east and west flowing rivers. (4) Line dividing annual rainfall above and below 100 cm. 88.

W hich of the following feature has similar geological structure with Meghalaya, Karbi Anglong plateau and Cachar Hills? (1) Aravalli Range (2) Purvanchal Hills (3) Siwaliks (4) Chotanagpur Plateau

89.

Assertion (A) : Sex Ratio in India is low. Reason (R):Indian society has been unfavourable to females. Select the correct option from the given alternatives. (1) Both (A) and (R) are true, and (R) explain (A) (2) Both (A) and (R) are true, but (R) does not explain (A) (3) (A) is true and (R) is false (4) (A) is false and (R) is true

90.

A pilot takes off from an airport at 15º S latitude and flies 55º due North. What latitude the pilot has reached? (1) 55º N (2) 40º N (3) 70º N (4) 15º N

91.

Which of the following is not a feature of Indian federalism? (1) The Constitution creates a strong Centre. (2) The Constitution provides for a single judiciary. (3) The Constitution provides for a common All India Services. (4) The Constitution provides equal representation to the States in the Upper House of the Parliament.

92.

Which of these features is not a guiding value of the Indian Constitution? (1) No external power can dictate to the Government of India. (2) The head of the State is a hereditary position. (3) All people are equal before law. (4) Citizens have complete freedom to follow any religion.

93.

According to Dr. B.R. Ambedkar, which of the following is the 'heart and soul' of our Constitution? (1) The Preamble (2) Right to Equality (3) Right against Exploitation (4) Right to Constitutional Remedies

What does the zig-zag line indicate on the map of India?

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94.

Democracy is considered to be better than other forms of government. Which of the following statements support this claim? A. It is a more accountable form of government. B. It improves the quality of decision making. C. It ensures rapid economic development of citizens. D. It enhances the dignity of citizens (1) A,B and D (2) A and C (3) A, B and C (4) B, C and D

95.

The Constitution of India was amended in 1992 to make the third·tier of democracy more effective. As a result, at least one-third of all positions in the local bodies are reserved for women. This is because (1) women are good at managing resources. (2) although women constitute nearly half of the population, they have inadequate representation in decision-making bodies. (3) we have many powerful women leaders. (4) women are obedient and would follow the constitutional provisions well.

96.

In which of the following economies are people more of a resource? (1) Country A with 78% of the working age population illiterate and with very low life expectancy (2) Country B with 10% of the working age population illiterate and with high life expectancy (3) Country C with 60% of people in the working age illiterate, but with high life expectancy (4) Country D with only 10% of population is the working age illiterate, but has very low life expectancy.

97.

Which of the following statements is true of agriculture in Indian economy between 1973 and 2003? (1) The sectorial share of agriculture in employment has decreased far more than its share on total output (2) The sectorial share of agriculture in total output has decreased, but its share in employment has increased. (3) The sectorial share of agriculture in total output has increased, but its share in employment has decreased. (4) The sectorial share of agriculture in output has decreased far more than its share in total employment.

98.

Which of the following considered as Foreign Investment made in India ? A.The TATAs acquire Corus steel plant abroad. B. Mr. Donald, an American citizen, acquires 100 shares of an Indian listed company. C. The remittances sent by an Indian doctor in Dubai back to his hometown in Kerala . D. The US multinational Google opens its fullfledged unit at Gurgaon, Haryana.

99.

(1) (1) and (4)

(2) (1) and (2)

(3) (4) only

(4) (2) and (3)

W e accept paper money as a medium of exchange because (1) it has gold hacking. (2) the law legalizes it. (3) Reserve Bank of India has precious metals against which it prints notes. (4) everyone else accepts it.

100.

Which of the following refers to trade barrier in the context of WTO? I. Restrictions on domestic trade Il. Not allowing companies to do foreign trade beyond specific quantity III. Restrictions on the export and import of goods IV. Restrictions on the price fixed by companies (1) (I), (II) and (III)

(2) (II), (III) and (IV)

(3) (III) and (IV)

(4) (I), (II) and (IV)

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[17]

Roll No.

NTSE 14_MAT

National Talent Search Examination, 2014 (For student Studying in Class-10)

Mental Ability Test Time : 45 minutes

Max. Marks : 50

Instructions to Candidates 1.

Mental Ability Test shall be administered in first 45 minutes. Thereafter scholastic Aptitude Test shall be administered. Answer to Part-I. Mental Ability Test are to be given on the given answer sheet. The Mental Ability answer sheet will be collected after first 45 minutes. After 5 minute Part-II Scholastic Aptitude answer sheet & after 20 minutes Question booklet will be supplied to you which will also be collected after the time is over.

2.

Please write your Roll No. as given on your Admission Card very clearly (only one digit in one box) Please see that no box is left unfilled even zeroes appearing in the Roll No. are correctly transferred to the appropriate boxes on the booklet and the Answer Sheet.

Example : For N.T.S.E.

3.

Mental Ability Test consist of 50 questions. Each question carry one marks.

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NTSE STAGE_II MENTAL ABILITY PAPER-2014 1.

2.

3.

4.

Select the correct number that is missing in the number series given below : 214, 265, 367, ?, 724 (1) 520 (2) 501 (3) 525 (4) 571 Select the correct alphabet number that is missing in the alphabet-number series given below : NAJ31, BEF28, RAM31, ?, YAM31 (1) RPA31 (2) PRA30 (3) RPA30 (4) PAR31

8.

(1) 14 (3) 15 9.

P + Q means P is the father of Q; P – Q means P is thewife of Q; P × Q means P is the brother of Q. Which of the following means A is the materanal uncle of D ? (1) A × B – C + D (2) D × C – B × A (3) A × C + B – D (4) A – C × B + D Select from the alternatives two signs which need to be interchanged to make the following equation correct. 36 ¸ 12 × 6 + 9 – 6 = 38 (1) – and × (2) ¸ and × (3) – and + (4) ¸ and +

5.

According to a certain code, ‘=’ means ‘>’, ‘_’ means ‘+’ and ‘+’ means ‘_’. If a, b and c are positive integers and a = b =c, then which of the following is true ? (1) b = a + c (2) ac = b2 (3) a – c = 2b (4) ab = c2

6.

Find the correct group of letters in place of ‘?’ in the following series. FNHLJ, WOUQS, BNEKH, ?, DTHPL (1) N B K E H (2) N V P T R (3) N F L H J (4) N D R Z V Directions: (Questons 7–8) : Each of the following questions contains three figures in which numbers are written according to a pattern. Find the missing number for each question from among the alternatives.

7.

(1) 13 (3) 12

(2) 14 (4) 18

(2) 16 (4) 11

Two faces of a cube are given below, which number will be opposite 3?

(1) 1 (3) 4

(2) 5 (4) 2

Directions: (Questions 10-11) : Each of the follwoing questions has a problem followed by a few numbered statements. Decide which of the statements are sufficient for answering the problem and choose your answer from the alternatives. 10.

A, B and C together can complete a work in ‘x’ days. How many days would B alone take to complete the work ? Statements : I. C can complete the work in half the number of days taken by A. II. B can complete the work in half the number of days taken by A and C together. III. A and C taken together can complete the work in ‘z’ days. (1) Both I and II and required (2) I alone is sufficient (3) II and III taken together are sufficient (4) Either II or III is sufficient

11.

A boat travels in a stream from A to B and then from B to A. What is the speed of the boat in still water ? Statements : I. The speed of the boat in still water is 2 km/h more than the speed of the current. II. The speed of the current is 1 km/h more than the speed of the boat. III. Boat covers the distance of y kilometres between A and B both downstream and upstream in x hours. (1) All of I, II and III are required (2) Both II and III are required (3) I and III taken together are sufficient (4) Either I and II together or II and III together are sufficient

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12.

How many triangles are there in the following figure?

(1) 20 (3) 22 13.

(2) 18 (4) 17

There are two statements given below as prem ises, which support the conclusion suggested in the answer options. You may select the conclusion that makes the whole argument valid : Statements : I. No film actors are Cricketers. II. Some Cricketers are poets. (1) Therefore, some poets are film actors. (2) Therefore, some poets are not film actors. (3) Therefore, all poets are film actors. (4) Therefore, all film actors are poets.

14.

Find the missing term (?) in the following series 2, 6, 30, 260, ? (1) 470 (2) 510 (3) 630 (4) 3130

15.

One term in the following number series is wrong. Find out the wrong term. 2, 6, 18, 82, 650 (1) 2 (2) 18 (3) 82 (4) 650

16.

If RIR is coded as IRI then MUM is coded as (1) NFN (2) UMU (3) UNU (4) MFM

17.

If FAST is coded as 798 and LAST is coded as 906 then BUSY is coded as (1) 1759 (2) 1431 (3) 952 (4) 948

18.

19.

20.

Six students A, B, C,D, E and F are in a class, A and B are from Town and C, D, E and F are from village. D and F are studious while others are casual. A, C, D are girls and B, E, F are boys. Who is the studious girl from village ? (1) C (2) D (3) E (4) F Read the following information carefully and answer the questions given below it. (A) Gopal is shorter than Ashok but taller than Kunal (B) Navin is shorter than Kunal (C) Jayesh is taller than Navin (D) Ashok is taller than Jayesh Who among them is the tallest ? (1) Gopal (2) Ashok (3) Kunal (4) Navin

Five persons are standing in a line. One of two persons at the extreme ends is a professor and the other is businessman. An advocate is standing to the right of a student. An author is to the left of the businessman. The student is standing between the professor and the advocate. Counting from the left, the advocate is at which place. (1) 1st (2) 2nd rd (3) 3 (4) 5th Directions (Questiosn 21 - 24) : A code language has been used to write the words in capital letters in English in Column I as Greek letters in Column II. Greek letters in Column II do not appear in the same order as letters in Column I. Decode tha language and choose the correct code for the word given in each question from amongst the alternatives provided.

21.

22.

23.

24.

LIVER (1) nhlmp (3) rswen

(2) dgqpe (4) abdgh

TROUBLE (1) nabdghl (3) dghlwen

(2) nswdgqe (4) slrpagq

BROWN (1) wenlw (3) aplhn

(2) wdprn (4) prbne

CYCLE (1) bqgmb (3) prpew

(2) bmbnp (4) plbnp

Direction (Questions 25 - 28) : P, Q, R, S, T, V and W are seven members of a family. Each of them has a different profession-Lawyer, Chartered Accountant (CA), Engineer, Teacher, Doctor, Architect and Pharmacist. There are three female members. No lady is either Pharmacist or Chartered Accountant. Each of them has a different monthly income. The Chartered Accountant (CA) earns the most. S, the engineer, earns less than V, the doctor. R, the teacher earns more than P and less than S. W’s wife earns the least. T is an unmarried lady lawyer and she earns less than P and m ore than only Q. The pharmacist’s income is not the lowest.

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25.

Which of the following pairs of professional represents the professions of hushand and wife? (1) Pharmacist, Architect (2) Chartered Accountant, Architect (3) Engineer, Pharmacist (4) Chartered Accountant, Engineer

26.

Which of the following statements is false ? (1) The Architect earns more than the Lawyer (2) The Teacher earns less than the Engineer (3) The Doctor earns more than the Engineer (4) The Pharmacist earns more than the Lawyer

27.

What is P’s profession ? (1) Pharmacist (2) Lawyer (3) Teacher (4) None of the above

28.

Which of the following represents the three female members of the family ? (1) PTQ (2) TRQ (3) VTQ (4) Data inadequate

29.

Which of the following Venn diagram correctly represents Ocean, Indian Ocean Pacific Ocean and Mariana Trench ?

30.

If RAJASTHAN = 9R17J8L19H13 in a coded language, then what is the encrypted form of the MANIPUR in the same language ? (1) 14R13H11G9 (2) 13M14W11B9 (3) 13R14J11F9 (4) 14M13V11J9

31.

What is the next number in the series 7, 23, 55, 109, ... (1) 199 (2) 189 (3) 191 (4) 209

32.

Find out the missing number in the second figure on the basis of numbers arranged in the first figure.

33.

If urban population is 350 find out the non educated non working urban females ? (1) 13 (2) 10 (3) 9 (4) 20

34.

Find out the urban males who are educated but not working. (1) 110 (2) 40 (3) 30 (4) 7

35.

If rural population is 150, how many non working rural males who are not educated ? (1) 5 (2) 1 (3) 6 (4) 3

36.

Find out total non-working females but educated (1) 80 (2) 79 (3) 51 (4) 19

37.

Find out the total rural male population ? (1) 111 (2) 187 (3) 180 (4) 114

38.

Crime : Police :: Flood : ? (1) Dam (2) River (3) Rain (4) Reservoir

39.

When the given sheet of paper (X) is folded to make a cube, choose the cube that may be formed.

(1) 1 only (3) 2 and 3 only 40.

(1) 30 (3) 160

(2) 58 (4) 32

(2) 1,2 and 3 only (4) 1, 2, 3 and 4

In the following diagram, there are four inter locked figures of a circle, a square, a triangle and a rectangle representing number of students passing in English, Maths, Science and Hindi, respectively. Different regions of the diagrams are also lattered form A through Q.

Direction: (Questions 33-37) : In the Venn diagram given below, sample data of a small town having total population of 500, the square represents persons form urban areas, the triangle represents women, the circle represents persons who are working and the rectangle represents the persons who are educated. Number given are number of persons.

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Now consider the following statements : statements : I. There is no letter that represents a student who passed in all the four subjects. II. There are only two letters that represent a student who passes on three subject only. Which of the above statements is/are correct ? (1) I only (2) II only (3) Both I and II (4) Neither I and II 41.

What is ‘X’ in the following table ?

(1) 16 (3) 18 42.

(2) 17 (4) 21

Consider the question and two statements that follow : What is the total cost of one pen, and one pencil and 1 note book ? Statements : I. The total cost of 5 pen, 6 pencils and 7 note books is Rs. 178 II. The total cost of 6 pens, 4 pencils and 2 note books, is Rs. 124 Which one of the following is correct ? (1) Statement I alone is sufficient to answer the quaetion (2) Statement II alone is sufficient to answer the question (3) Statement I and II together are sufficient to answer the question (4) Both statements are not sufficient to answer the question

43.

Which one of the following differs the rest ? (1) MGDLFC (2) JQVIPU (3) ZUBXTA (4) DYSCXR

44.

Which one of the following fits inside the bracket? 714 ( ) 65 if 953 (RVXYS)28 (1) UWZSR (2) UWZRS (3) TZWVU (4) TZWUV

45.

If ‘X’ was born on December 6, 1983 and ‘Y’ on February 4, 1984, then when will ‘Y’ be half in age as compared ot ‘X’ ? (1) April 4, 1984 (2) April 5, 1984 (3) April 6, 1984 (4) April 8, 1984

46.

47.

Five persons P, Q, R, S and T are sitting in a row. Q in between P and T. To find who among them is in the middle, which of the following information given in the following statements is/are sufficient? Statements : I. P is left of Q and right S. II. R is at the right end. Select the correct answer using the code given below. (1) I only (2) II only (3) Either I or II (4) Both I and II

48.

Certain blank spaces are left in the following series. Which is the group of letters given below, if put in the blank spaces in sequence, will complete the series ? _ ab _ a _ ba _ ab _ _ ab _ (1) bbaabbb (2) babaaaa (3) abaaaba (4) aaaaaaa

49.

If the letters of the word ‘BLUE’ are arranged according to dictionary, what is the position of the word ‘UBLE’ ? (1) 19 (2) 20 (3) 21 (4) 22

50.

All except one does not belong to the same group. Which one is that ?

(1)

(2)

(3)

(4)

Famine : Hunger : : War : ___________ (1) Enmity (2) Insecurity (3) Destruction (4) Infantry

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Roll No.

NTSE 14_SAT

National Talent Search Examination, 2014 (For student Studying in Class-10)

Scholastic Aptitude Test Time : 90 minutes

Max. Marks : 100

Instructions to Candidates Read These instructions very carefully before attempting questions 1.

Please write your Roll No. as given on your Admission Card very clearly (only one digit in one box) Please see that no box is left unfilled even zeroes appearing in the Roll No. are correctly transferred to the appropriate boxes on the booklet and the Answer Sheet.

Example : For N.T.S.E.

2.

There are 100 questions in this paper Each question is to be answered.

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NTSE STAGE_II (SAT) PAPER-2014 1.

Which one of the following statements is NOT true about evolution ? (1) Evolution leads to generation of diverse forms of life. (2) Time dating and fossil studies help in understanding of evolution. (3) Evolution is not always progressive series of changes that occur in organism. (4) Human beings have not evolved from chimpanzees.

2.

Which one of the following is known as energy currency of cell ? (1) Adenosine diphosphate (2) Adenosine triphosphate (3) Pyruvate (4) Glucose

3.

An analysis of soil sample revealed 0.1 mg of a pesticide and 1 mg of the same pesticide was found in grains. However in the adipose tissue of birds the concentration was 2 mg. The reason for this is the phenomenon known as (1) Bio-absorption (2) Bio-translocation (3) Bio-magnification (4) Bio-multiplication

4.

Diseases that spread by vectors such as mosquitoes are (1) Encephalitis and Malaria (2) Syphilis and AIDS (3) Tuberculosis and sleeping sickness (4) Kala-azar and SARS

5.

Which one of the following is correct route for passage of sperms ? (1) Testes — scrotum — vasdeferens — urethra — penis (2) Scrotum — testes — urethra — vasdeferends — penis (3) Tetes — vasdeferens — urethra — seminal vesicles (4) Testes — vasdeferens — urethra — penis

6.

Suggest which among the following is NOT a function attributed to endoplasmic reticulum (1) Detoxification of poisons and drugs (2) Digestion / egestioin of foreign materials outside the cell (3) Manufacture of fat and lipid molecules (4) Biogenesis of membranes

7.

In nitrogen cycle, atmospheric nitrogen is fixed by bacteria and converted into ammonia. Ammonia is further converted into other forms of nitrogen . At the end of the cycle it returns to the atmosphere by the process of : (1) Ammonification (2) Nitrification (3) Denitrification (4) Assimilation

8.

Cell organelles that are involved in the waste diposal system of the cell are : (1) Golgi apparatus. (2) Lysosomes (3) Chromosomes (4) Ribosomes

9.

Sequence of events which occure in a reflex action are (1) Receptor — motor neuron — CNS — sensory neurong — effector muscle (2) Effector muscle — CNS — sensory nerve — sensory organ (3) CNS — sensory neuron — motor neuron — effector muscle (4) Receptor organ — sensory neuron — CNS — motor neuron — effector muslce

10.

Movement of food in digestive tract is due to (1) Concentration gradient (2) Secretions (3) Peristalsis (4) Villi A pea plant with round green (RRyy) pea seed is crossed another pea plant with wrinkled yellow (rrYY) seeds What would be the nature of seed in the first generation (F1 generation) ? (1) Round green (2) Wrinkled green (3) Wrinkled yellow (4) Round yellow

11.

12.

Some organisms are sensitive to different levels of air pollution and are used as pollution indicators. Suggest which among the following fits into the category (1) Fungi (2) Fresh water algae (3) Bacteria (4) Lichens

13.

A group of laboratory mice having tails are bred together and their progeny studied. The progeny and again bred them for four successive generations. What do you think would be the nature of the new progeny ? (1) All mice born will have tails. (2) All mice born will have no tails. (3) The ratio of tail less to tailed mice will be 1 : 3 (4) The ratio of tail less to tailed mice will be 1 : 4

14.

Which of the following statements is NOT correct? (1) Tendons are tissues with great strength and flexibility (2) Bones are connected to each other by tendons (3) Cartilage smoothens bone surface at joints (4) Tendons connect muslces to bones

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15.

Which of the following are the correct examples of matter ? (1) Glass bottle, water and noise (2) Air, wood and vacuum (3) Silver foil, hot air and chalk (4) Sand, oxygen and light flash

16.

Two identical beakers labeled as (X) and (Y) contain 100 cm3 of water each at 20ºC . To the water in the beaker (X) 100 g of water at 0ºC was added and stirred to mix thoroughly.To the beaker (Y) 100g of ice at 0ºC was added and stirred till it melten into water. The water in the beaker (Y) will be (1) hotter than water in beaker X (2) Colder than water in beaker X (3) heavier than water in beaker X (4) lighter than water in beaker X

17.

18.

19.

20.

At 283 K a saturated solution of solid X can be prepared by dissolving 210g of it in 100 g of water.The maximum amount of X which can be dissolved in 100 g of water at 313 K is 620 g. An attempt is made to dissove 50.0 g of X in 100g of water at 313 K. A. All the 50.0 g of X will dissove at 313 K. B. At 313 K 29.0 g of X will remain undissoved C. Solubility of X decreases with increases of temperature D. On cooling the solution of X from 313 K to 283 K more than 210 g of X will crystallize out. Which of the above statements are correct ? (1) A and B (2) A and D (3) B and C (4) A,C and D Two elements A and B contain 13 and 8 protons respectively. If the number of neutrons in them happen to be 14 and 8 respectively ; the formula unit mass for the compound between And B unit would be : (1) 43 (2) 75 (3) 102 (4) 112 The reaction of burning of carbon in oxygen is represented by the equation: C(s) + O2(g) ¾®CO2(g) + Heat + Light When 9.0 g of solid carbon is burnt in 16.0 g of oxygen gas, 220g of carbon dioxide is produced.The mass of carbon dioxide gas formed on burning of 30g of carbon in 320 g of oxygen would be (Note : atomic mass of C = 120 u, O = 16.0u) (1) 6.60 g (2) 7.33 g (3) 8.25 g (4) 1100g An atom of an element (X) has its K, L and M shells filled with some electrons. It reacts with sodium metal to form a compound NaX. The number of electrons in the M shell of the atom (X) will be (1) Eight (2) Seven (3) Two (4) One

21.

Oxygen gas reacts with hydrogen to produce water. The reaction is represented by the equation : O2 (g) + H2(g) ¾® H2O (g) The above reaction is an exampleof (a) Oxidation of hydrogen (b) Reduction of oxygen (c) Reduction of hydrogen (d) Redox reaction (1) (a), (b) and (c) (2) (b), (c) and (d) (3) (a), (c) and (d) (4) (a), (b) and (d)

22.

Match the items of Column I with the items of the Column II Column I

Column II

a) NH4OH + CH3COOH ® (i) Thermal CH3COONH4 + H2O decomposition (ii) Thermite reaction (iii) Photochemical reaction

b) 2AgBr ®2Ag + Br2 c) ZnCO3 ® ZnO + CO3 d) 2AI + Fe2O3 ® 2Fe + Al2O3

(1) d-ii, c-iv, b-i, a-iii (3) b-ii, d-i, a-iii, c-iv

(iv) Neutralization reaction

(2) c-i, a-ii, c-iii, d-iv (4) a-iv, b-iii, c-i, d-ii

23.

Which of the following represents the correct order of the acidic strength for equimolar aqueous solutions of HCl, H2SO4, NH4OH and NaOH (1) HCl < NH4OH < NaOH < H2SO4 (2) NH4OH < NaOH < H2SO4 < HCl (3) HCl < H2SO4 < NH4OH < NaOH (4) NaOH < NH4OH < HCl < H2SO4

24.

Metals like sodium, potassium calcium and magnesium are extracted by electrolysis of their chlorides in molten state. These metals are not extracted by reduction of their oxides with carbon because a) reduction with carbon is very expensive b) carbon readily makes alloys with these metals. c) carbon has less affinity for oxygen d) carbon is a weaker reducing agent than these metals. (1) (a) and (b) (2) (b) and (c) (3) (c) and (d) (4) (d) and (a)

25.

A hydrocarbon has a molecular formula as C6H12 . It does not react with hydrogen to give C6H14 nor does it react with chlorine to give C6H12Cl2 . The hydrocarbon C6H12is a) A saturated hydrocarbon b) An unsaturated hydrocarbon c) An open chain hydrocarbon d) A cyclo-alkane (1) (a) and (b) (2) (c) and (d) (3) (d) and (b) (4) (a) and (d)

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26.

27.

An organic compound is a clear liquid having a molecular formula C4H8O. It has an open chain structure. Without any carbon-carbon double bond. The compound can be a) an alcohol b) an ester c) an aldehyde d) a ketone (1) (a) and (b) (2) (c) and (d) (3) (b) and (d) (4) (d) and (a) An element with atomic number 17 is placed in the group 17 of the long form periodic table. Element with atomic number 9 is placed above and with atomic number 35 is placed below it. Element with atomic number 16 is placed left and with atomic number 18 is placed right to it. Which of the following statements are correct . a) Valency of the element with atomic number 18 is zero. b) Elements with same valency will have atomic number 16,17 and 18. c) Valency of elements with atomic number 9,17 and 35 is one. d) Element with atomic number 17 is more electronegative that element with atomic numbers 16 and 35 (1) (a), (b) and (c) (2) (a), (c) and (d) (3) (b), (c) and (d) (4) (a) , (b) and (d)

28.

A car is moving with a constant speed of 70 km/ h. Which of the following statements is correct ? (1) The acceleration of the car is definitely zero. (2) The car has an acceleration only if it is moving along a curved path (3) The car may have an acceleration even if it is moving along a straight path (4) The car may not have an acceleration even if it is moving along a curved path

29.

A box of mass 20 kg is pushed along a rough floor with a velocity 2 m/s and then let go. The box moves 5 m on the floor before coming to rest. What must be the frictional force acting on the box ? (1) 4 N (2) 2 N (3) 20 N (4) 8 N

30.

Two objects, one 4 times as massive as the other, are approching each other under their mutual graitational attraction. When the sepration between the objects is 100 km, the acceleration of the lighter object is 1 m/s2 When the separation between them is 25 km, the acceleration of the heavier object is (1) 1m/s2 (2) 2m/s2 2 (3) 8m/s (4) 4m/s2

31.

A spring balance measures the weight of an object in air to be 0.1 N. It shows a reading of 0.08 N when the object is completely immersed in water. If the value of acceleration due to gravity is 10m/s2 the volume of the object is (1) 20 cm3 (2) 80 cm3 3 (3) 200 cm (4) 2 cm3

32.

A force of 10 N is applied on an object of mass 1 kg for 2 s, which was initially at rest. What is the work done on the object by the force? (1) 200 J (2) 20 J (3) 16 J (4) 180J

33.

Stethoscope of doctors for finding quality, strength and frequency of human heart beat is based on the principle of (1) SONAR (2) Reverberation (3) Multiple reflection (4) Echo

34.

A ray of light is incident in medium 1 on a surface that separates medium 1 from medium 2 Let v1 and v2 represent the velocity of light in medium 1 and medium 2 respectively. Also let n12 and n21 represent the refractive index of medium 1 with respect to medium 2 and refractive index of medium 2 with respect to medium 1, respectively. If i and r denote the angle of incidence and angle of refraction, thenv1 v2 sin i sin i (1) = n21 = v (2) = n21 = v sin r sin r 2 1 (3)

v1 sin i = n12 = v sin r 2

(4)

v2 sin i = n12 = v sin r 1

35.

A convex lens has a focal length of 0.5 m. It has to be combined with a second lens, so that the combination has a power of 15 diopter. Which of the following could be the second lens? (1) A concave lens of focal length 2 m. (2) Another convex lens of focal length 0.5 m. (3) A concave lens of focal length 0.5 m. (4) A convex lens of focal length 2 m.

36.

Which of the following statement is correct ? (1) A person with myopia can see nearby objects clearly (2) A person with hypermetropia can see nearby objects clearly (3) A person with myopia can see distant objects clearly (4) A person with hypermetropia can not see distant objects clearly

37.

Consider two conducting plates A and B between which the potential difference is 5 volt, plate A being at a higher potential. A proton and an electron are released at plates A and B respectively. The 2 particales then move towards the opposite plates- the proton to plate B and the electron to plate A. Which one will have a larger velocity when they reach their respective destination plates ? (1) Both will have the same velocity. (2) The electron will have the larger velocity. (3) The proton will have the larger velocity. (4) None will be able to reach the destination point.

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38.

Which one of the statement best describes the nature of the field lines due to a bar magnet? (1) Field lines start from the north pole and end on the south pole. Any number of field lines can pass through a point. (2) Field lines start from the north pole and end on the south pole. Only one field line passes through a point. (3) Field lines are continuous lines passing inside and outside the magnet. Only one field line passes through a point. (4) Field lines are continuous lines passing inside and outside the magnet. Any number of field lines can pass through a point.

39.

Which of the following statements is correct? (1) AC generator generates a higher voltage (2) DC generator generates a higher voltage (3) AC generator has a permanent magnet whereas a DC generator has an electromagnet (4) There is a split-ring commutator in a DC generator but not in an AC generator

40.

A star produces its energy through the process of (1) Nuclear fusion (2) Chemical reaction (3) Nuclear fission (4) Gravitational atraction between different parts of the star.

41.

If f is an acute angle such that tanf = 2/3 then evaluate æ 1 + tan f ö çç ÷÷ . è sin f + cos f ø (1) –

(3) 42.

(2) –

(1) 4 5

(2) 4 6

(3) 4 7

(4) 4 11

In DABC, XY is paralled to A C and divides the triangle into the two parts of equal area. Then the

(1)

2 +1 2

(2)

2- 2 2

(3)

2+ 2 2

(4)

2 -1 2

47.

P is point in the interor of an equilateral triangle with side a units. If P1, P2 and P3 are the distance of P form the three sides of the triangle, the P1 + P2 + P3 2a (1) equals units 3 a 3 (2) equals units 2 (3) is more than a unit (4) Cannot be determined unless the location of P is specified

48.

In how many ways can given square be cut into two congruent trapeziums? (1) Exactly 4 (2) Exactly 8 (3) Exactly 12 (4) More than 12

49.

In how many ways can you position 6 into ordered summands? [For exp, 3 can be partitioned into 3 ways as 1 + 2, 2 + 1, 1 + 1 + 1] (1) 27 (2) 29 (3) 31 (4) 33

50.

The number of integers n ( b

58. Out of the options, 14 cannot be made as it required 2, Rs. 5 coins & 4, Rs. 1 coin i.e. 5, 5, 1, 1, 1, 1.

Let a < b

then

then

|a – b| + |b – a|

|a – b| + |b – a|

=a–b+a–b

=b–a+b–a

= 2a – 2b

59. Ascending order 1, 3, 4, 6, 7, 8, 8, 9, 12, 15 Median =

= 2b – 2a

i.e. +ve

60. Average speed = 6 km/hr.

i.e. +ve

So answer is always +ve if a ¹ b 6= 56.

4 4 pR3 = p (r 3 +r 3 +r 3 +..........r 3) 1 2 3 n 3 3

... (i)

2

S1 = 4pR S2 = 4p(r12 + r22 + r32 + ...........+ rn2 ) From (i) , we get R3 = r13 + r23 + r33 +...... + rn3 If all smaller sphere are of equal radius i.e. r then,

7+8 = 7.5. 2

2´4´ x 4+x

24 + 6x = 8x 2x = 24 x = 12 km/hr.

4 3 4 pR = p ´ nr 3 3 3

R3 = nr3 S1 R2 (nr 3 )2 / 3 n2 / 3 ´ r 2 = 2 S2 = n ´ r 2 = nr nr 2

nS1 = n2/3 S2 Þ n1/3S1 = S2

\ S2 > S1.

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NTSE STAGE-II (2014) CLASS-X [MAT]

HINTS & SOLUTIONS ANSWER KEY Que s. Ans.

1 1

2 3

3 1

4 4

5 4

6 1

7 1

8 3

9 1

10 4

11 3

12 1

13 2

14 4

15 3

Que s.

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Ans.

1

2

2

2

3

2

4

3

1

2

1

1

4

3

4

Que s. Ans.

31 3

32 2

33 1

34 2

35 4

36 2

37 4

38 1

39 4

40 4

41 3

42 3

43 3

44 4

45 1

Que s.

46

47

48

49

50

Ans.

3

4

4

2

4

1.

+51, +102, +153, +204,..... Ans 520

2.

NAJ31, BEF28, RAM31, RPA30, YAM31 JANUARY 31 DAYS FEBRUARY 28 DAYS MARCH 31 DAYS APRIL 30 DAYS....

7.

8.

14.

15.

(8+3)×(9–3) = 44 (4+2)×(12–3) = 54 (10+6)×(13–8) = 80 (7×5×12)÷10 = 42 (5×6×8)÷10 = 24 (9×6×15)÷10 = 81 11+1 = 2 22+2 = 6 33+3 = 30 44+4 = 260 55+5 = 3130

17.

FAST (62+12+192+202) = 798 LAST (122+12+192+202) = 906 BUSY (22+212+192+252) = 1431

30. Than MANIPUR = 14M13V11J9 31.

By Difference’s difference

32.

(22+32+42) – (12+52) = 3 (72+82+92) – (62+102) = 58

41.

(72+22)–(32+52) = 19 (82+52)–(72+42) = 24 (62+42)–(32+52) = 18

44.

953 (RVXYS) 28 All letter’s position from back side R - 9, V - 5, X - 3, Y - 2, S - 8 So, 714 (TZWUV) 65.

2×1+4=6 6×2+6=18 18×4+8=80 80×8+10=650

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[86]

NTSE STAGE-II (2014) CLASS-X [SAT]

HINTS & SOLUTIONS ANSWER KEY Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans. Que. Ans.

15. 16.

17.

18.

1 4 16 2 31 4 46 2 61 3 76 3 91 1

2 2 17 2 32 1 47 2 62 1 77 2 92 2

7 3 22 4 37 2 52 3 67 4 82 2 97 3

8 2 23 4 38 3 53 1 68 2 83 3 98 1

Noise, vaccume and light flash not example of matter. X Y 100 ML ® water 100 ml ® water 20ºC 0ºC ® 100 g ¬ water 100 g ice ¬ 0ºC ¯ more cooling y is colder than x At 313 k it from saturated solution. therefore all 50 gm. will be dissolve. when temperature down to 283 K (62 – 21 = 41 gm.) will be crystall cut. A = Al B z = 13 z=8 valency = 3 valency = 2 = Al2O3

20.

formula mass

19.

3 3 18 3 33 3 48 4 63 4 78 4 93 2

4 1 19 4 34 1 49 3 64 1 79 1 94 4

5 4 20 2 35 1 50 3 65 4 80 3 95 3

6 2 21 4 36 1 51 2 66 2 81 1 96 3

21.

and

22.

= 27 × 2 + 16 × 3 = 102

Q

® LR 12 gm C give CO2 = 44 gm

\

3 gm C give CO2 =

44 3 × 12 1

13 1 28 2 43 4 58 1 73 3 88 1

14 2 29 4 44 3 59 3 74 2 89 3

15 3 30 4 45 3 60 1 75 4 90 4

Q M shell is the valency therefore valency = 7

O2 + H2 ® H2O (g) O.S. of O2 become ¾®zero to – 2 Qit will be reduced Oxidation state of H2 becomes zero to + 1 it will be oxidised Q therefore reaction will be redox NH4 OH + CH3COOH ® CH3COONH4 + H2O base acid salt

Order of acidic strength H2SO4 > HCl > NH4OH Strongest acid

24. =1

12 4 27 2 42 4 57 3 72 2 87 2

ZnCO3 D ZNO + CO2 (thermla decompostion) 2Al + Fe2O3 ®Al2O3 + 2Fe (Thermite reaction)

32 mole of O2 = 32

1 4

X ® K, L, M shell 2,8,7 X = Cl

11 4 26 2 41 1 56 4 71 1 86 3

2AgCl hn 2Ag + Br2 (Photo chemical decomposition)

23.

=

10 3 25 4 40 1 55 3 70 2 85 4 100 4

(neutralisation reaction)

C(g) + O2 ¾® CO2 (g) 3 mole of = 12

9 4 24 3 39 4 54 3 69 3 84 3 99 3

strong acid

> NaOH

Weak base

strong bas

Na, K, Ca, Mg (i) Qthese matals can lose e– easily as compared to C therefore these are better reducing agent as compare to C. (ii) due to strong electropositive behaviour of these metals having strong tendency to react with oxygen.

= 11 gm

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[87]

25.

Molecular formula ® C6H12

32.

Given :F = 10 N, m = 1 kg, t = 2s, u = 0 W =? s = 0 + 1/2 (10/1) (2)2 = 20 m W = 10×20 = 200 J

33.

Stethoscope is based on multiple reflection of sound.

cyclohexane 26.

27.

M.F. C4H8O

29.

30.

v1 sin i = v = n21 sin r 2

35.

f1 = 0.5 m, P1 =

36. 37.

(d) atomic no. 17 is Cl atomic no. 16 is S atomic no. 35 is Br Q Cl is more electronegative Body moving with constant speed can have acceleration only if it moves along a curved path. m = 20 Kg, u = 2 m/s, v = 0, S = 5 m v2 = u2 – 2 aS 0 = 4 - 2a x 5 a = 0.4 m/s2 F = ma = 20 x 0.4 = 8 N F=

G(m)( 4m)

38.

(100 ´ 10 3 )2 for smaller mass G(m)( 4m) m(1) =

39.

(1010 )

1010 4 for bigger mass

1 =2D 0.5

P1 + P2 = 1.5 2 + P2 = 1.5 P2 = –0.5 D 1 \ f2 = =–2m - 0.5

(a) Atomic no 18 it will be Ar ® inert gas valency = zero (c) 9, 17, 35, all are belong same group that is 17 and have same valency.

28.

34.

40.

Myopia, means person can see nearby objects.

W = DKE 5(q) = 1/2 mv2 10 q v2 = m mp > me \ ve > vp Magnetic field line are continuous lines passing inside and outside the magnet, only one field line passes through a point DC generator has split ring (commutator), whereas AC generator does not. Energy of star is due to Nuclear Fusion.

Gm =

G(m)( 4m) (4 m) (a) =

31.

(25 ´ 10 3 )2

Gm 1010 104 a= = = 625 ´ 1010 2500 4 ´ 625 ´ 10 6 2 a = 4 m/s Buoyant force B = 0.02 rl g v¢ = 0.02 100 × 10 ×V¢ = 0.02 V¢ = 0.02 × 10–4 m3 = 2 cm3

41.

æ 2 ç 1+ ç 3 ç 2 3 + çç 13 è 13

ö ÷ ÷ ÷ ÷÷ ø

æ 3 ç 1ç 2 ç 13 13 çç + 2 è 3

ö ÷ ÷ ÷ ÷÷ ø

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[88]

æ ç ç = ç çç è

ö ÷ ÷ ÷ ÷÷ 13 ø 5 3 5

æ -1 ç ç 2 ç çç 5 13 è 6

3 (3x) 2 DE = AE – AD

ö ÷ ÷ ÷ ÷÷ ø

AE =

6 æ - 1ö 1 13 ÷ ´ ´ ç =– 5 è 2 ø 5 13 3

=

=

3x –x 2

=

x 2

AD = 1 42.

6- 5 Þ

6 +

3 –

5- 2

5 –

–

5–

6+ 2 2–

6 +

=

27 2 x 2 x + 4 4

=

28 x 2 = 4

2

Þ0

43.

AE 2 + DE 2

4

p(x) = 3x2 – 5x + 2 = 3(x2 – 2

5 2 x+ ) 3 3

2

5 2 æ5ö æ5ö 2 = 3[ x - x + ç ÷ - ç ÷ + ] 3 3 è6ø è 6ø

46.

æ BX ö ç ÷ è AB ø

2

BX = AB

2

éæ 5ö 25 2 ù = 3 êç x - 6 ÷ - 36 + 3 ú êëè ø úû

1–

2 éæ 5ö - 25 + 24 ù ê ú x + ç ÷ =3 6ø 36 êëè úû

=

7x=4

7

1 2

1 2

1 BX =1– 2 AB

AB - BX = AB

2 éæ 5ö 1ù ê ú x ç ÷ =3 6ø 36 ú êëè û

7x 2 =

2 -1 2

AX 2- 2 = AB 2

2

5ö 1 æ = 3çx - ÷ 6ø 12 è so minimum value is – 44.

45.

1 12

Let |x| = y y2 + y – 6 = 0 (y + 3) (y – 2) = 0 y = – 3 or y = 2 |x| = – 3 which is not possible |x| = 2 \x= ± 2 The product of the roots is –4 3x =12 , x = 4

47.

area equilateral D =

1 3 2 a = a (P1 + P2 + 2 4

P3) 2 3 2 a ´ = P1 + P2 + P3 a 4

3a = P1 + P2 + P3 2

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[89]

48. 52. infinite tripazium can be made 49.

50.

1+1+1+1+ 1+1 2 +1 + 1 + 1 + 1 3+1+1+1 4+1+1 5 +1 2 +3+1 2 +4 3 +3 2 +2+2 2 +2 +1+1

1 way 5 way 4 way 3 way 2 way 6 way 2 way 1 way 1 way

Let radius = r area of sector APO =

120 1 ´ ppr2 = pr2 360 3

area of sector PBO =

6 way

=

n2 – 3n +3 = m2 ....(1) n2 – 3n + 3 – m2 = 0

1 2 pr 6

Now area of DAOP =

this eq. have integer roots. if a = 1, b,c Î I D is perfect sq. \ 9 – 4.1 . (3–m2 ) = k2 4m 2 – k2 = 3 (2m + k) (2m – k) = 3 × 1 2m + k = 3 2m – k = 1 on solving we get m = 1 Put m = 1 in equ.(1) n2 – 3n + 3 =1 (n – 2) × (n – 1) = 0 n = 2,1 so two values of n are possible 51.

N1 = 15x N2 = 15 y LCM ´ HCF = N1 ´ N2 225 ´ 15 = 15x 15y xy = 15 3.5 = 15 1.15 = 15 So, N1 = 3 ´ 15 = 45 N2 = 5 ´ 15 = 75 15 = 225 (45, 75) , (15, 225) two such pair exist

=

60 ´ pr2 360

1 ´ 2

r 3r ´ 2 2

3r 2 4

3 2 r 4 area of major shaded area : Area of minor shaded area Now area of DBOP =

æ1 2 3 2 ö÷ æç 1 2 3 2 ö÷ ç = ç 3 pr - 4 r ÷ : ç 6 pr - 4 r ÷ è ø è ø =

4p - 3 3 2p - 3 3

x and y are coprime 54.

or N1 = 1 ´ 15 = 15 N2 = 15 ´

x2 + y2 = 250 a2 + b2 + c2 = 250 \ x = 13 y=9 a=5 b = 12 c=9

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[90]

A1 + A2 + A3 = 21 + 20 + 57.

(1)

= 41 + = 59.

(2)

420 29

420 29

1189 + 420 1609 = 29 29

Let 4th term = x + 3d = a 7th term = x + 6d = b 10th term = x + 9d = c on solving (1) & (2) we get x = 2a – b

..(1) ..(2)

a - (2a - b) 3 10th term = x + 9d = C &d=

æ a - (2a - b ) ö ÷ =C 2a – b + 9 ç 3 è ø = 2a – b + 3a – 6a + 3b = C – a + 2b = C 2b = a + c sum of roots of equation ax2 – 2bx + c = 0

(3)

sum of roots =

2b a+c = a a

(4) 60.

58.

a2 area of square PQRS 1 2 area of square PABCD = 2 = 2 a

20 + 21 + 29 s= = 35 2 D=

35 ´ 15 ´ 14 ´ 6

=

5´7´3´5´7´2´2´3 =5´7´3´2 = 210 210 =

1 A 20 2 1

A1 = 21

210 = A2 =

1 A 29 2 2

420 29

1 A ´ 21 2 3 A3 = 20 210 =

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[91]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2015) CLASS-X [MAT]

HINTS & SOLUTIONS ANSWER KEY Ques. Ans. Ques. Ans. Ques. Ans. Ques. Ans.

1 3

2 2

3 4

4 3

5 2

6 2

7 4

8 4

9 1

10 3

11 4

12 3

13 3

14 3

15 1

16 1 31 2 46 2

17 3 32 2 47 4

18 3 33 2 48 3

19 1 34 3 49 2

20 2 35 3 50 1

21 3 36 2

22 2 37 4

23 1 38 2

24 3 39 3

25 4 40 4

26 2 41 4

27 2 42 3

28 4 43 3

29 3 44 2

30 2 45 3

19. 1.

17.

112 – 92 121 – 81 = 40

option (3) is correct. Logic:Some women are teachers, so circle representing women and teacher are intersected and some women are docors, so circle representing women and doctors are also intersected. But there is no intersection between two profession so circle representing docotr and teacher are not intersected.

252 – 212 625 – 441 = 184

20.

two series first series 3,24,63,?,195 pattern 22–1,52–1,82–1,112–1,142–1 so first ?=120 second series: 6,30,72,?,210 pattern 22+2,52+5,82+8,112+11,142+14 so second ?=132

22.

[62 – (4 × 4)] –1 = 19 =S [42 – (7 × 1)] –1 = 8 = H [82 – (5 ×10)] –1 = 13 = N

24.

2.5 1 Avg. Speed = 1 + + 0.5 = 2 4

2.5 2.5 = 1.625 1 + 0.5 + .125 26.

18.

152 – 72 225 – 49 = 176

A x

B y

C 100 – x – y

500 = 2x x = 250

B = y = 250

100 - x - y = 250 2 1000 – x – y = 500 x + y = 500 y = 250 Ans. (2)

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[92]

27.

5e + 7s + 9p = 100 × a 2e + 6s + 10p = 80 × b

35. Man × days =1600 = 400 + 350 Man = 40 40 35

5a – 25 = 7a 65 = 9a – 105 2a = 4b

45 to 47 N E T I S P R U M

7:x 90 =

1 ö æ ç 7 ´ 30 + x ÷ – 6x 2 ø è

90 = 210 +

6x –

x – 6x 2

x = 120 2

11x = 120 2 x=

9 240 9 ´ 60 = 21 = 21 min + 11 11 11 = 21 min +

D=

100 20 = = 6.66. 15 3

Total day = 10 + 10 + 10 + 10 + 10 + 6.66 = 56.66

120 = 15 e+s+p= 8 28.

+ 250 + 200 + 100 25 20 15

100 = M × D 100 = 15 × D

10e + 14s + 18p = 200 2e + 6s + 10p = 80 8e + 8s + 8p = 120

a = 25 = 2

+ 300 30

540 sec. 11

=$ =# =@ =% =& =? =* =+ ==

45.

MINT = % $ @ Ans. (3)

46.

RINSE * % $ &# Ans. (2)

47.

INTEREST % $ @ # * # & @

= 21 min 49 sce

æ

90 = 6x – ç 7 ´ 30 +

è

90 = 6x – 210 –

300 =

x=

1 ö x÷ 2 ø

x 2

11x 2

6 600 6 ´ 60 sec = 54 = 54 min + 11 11 11 =54 min +

360 sec. 11

= 54 min 32 sec.

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[93]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2015) CLASS-X [SAT]

HINTS & SOLUTIONS ANSWER KEY Que s.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Ans

3

1

2

4

2

2

1

4

3

1

3

1

4

2

4

Que s.

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

Ans

4

4

1

3

2

4

2

2

2

3

1

3

2

3

4

Que s.

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Ans

3

4

2

3

2

2

2

2

2

3

2

1

1

4

2

Que s.

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

Ans

3

4

4

4

2

3

3

1

3

4

4

3

2

1

2

Que s.

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

Ans

1

4

4

1

1

4

1

1

2

3

3

4

4

3

2

Que s.

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

Ans Que s. Ans

4 91 3

2 92 3

2 93 4

1 94 1, 3

3 95 4

1 96 4

4 97 3

3 98 3

1 99 2

2 100 2

1

4

2

1

2

15.

16.

Solubility of S = 28.6% at 50° C Amount of solute in 50 ml of saturated solution = 14.3g at 50° C at 40°C amount of S separates out = 2.4g in 50 ml remaining solute = 11.9gin 50 ml solubility of S at 40° C =

Given, amount of C = 6g amount of oxygen = 32g C + O2 ® CO2 12g 32g 44g Q 12g of C gives the amount of CO2 = 44g

44 g 12

Q 6g of C gives the amount gm of CO2 =

44 × 6 = 22g CO2 12

18.

Law of conservation of mass is only valid for chemical reactions and not for nuclear reactions.

19.

a-particle is doubly positive helium ion 24 He+ + No. of proton = Z = 2 No. of neutrons = A – Z = 4 –2 = 2 No. of electron = zero

11.9 × 100 = 23.8% 50

m/v 17.

Q 1g of C gives the amount gm of CO2 =

On compressing the gas, no. of collision of molecules at per unit area of the wall of the cylinder increases. Average Kinetic energy of the molecules remains constant as the temperature is constant.

20.

m 1 =69 for isotope 69Z m 2 = 71 for isotope71Z x1 = abundance of 69Z= 60% X2 =abundance of 71Z= 40% Relative atomis mass =

=

m1x 1 + m2 x 2 100

69 ´ 60 + 40 ´ 71 = 69.8 100

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[94]

27.

In periodic table Electropositive nature increases from top to bottom in a group Electronegative nature decreases from top to bottom is a group Atomic size decreases from left to right in a period

28.

Let them meet at time t. At that time velocity of man must be greater or equal to as that of bus. u ³ at t £ u /a

21.

22.

1 2 at + d = ut 2 23.

d = ut –

D Cu2S+ O2 ¾¾® Cu2O + SO2 X Y copper glance

d £ u (u/a) –

2Cu2O + Cu2S ¾¾® 6Cu + SO2 Y 24.

25.

(i) Nitrate ores are rarely available as all nitrates are soluble in water. (ii) Bond dissociation energy of N2 is very high as the 3 covalent bonds are present between two nitrogen atoms. Both the statement are correct but the reason is not correct explanation of assertion.

d £ 29.

1 u2 a 2 a2

u2 2a

v = u + at 0 = u – gt t = u/g = n(total time of ascent)

Snth = u + = u-

4 Structural isomers are possible for C4H9Br H3C–CH2–CH2–CH2–Br CH3–CH2–

1 2 at 2

1 a(2n - 1) 2

1 æ 2u ö gç - 1÷÷ 2 çè g ø

= g/2

–CH3 30.

g=

4 prRg 3

g A rA R A = g = r ´R B B B =3×2=6

26. Total no. of electrons of C atoms = 3 × 6 = 18 electrons Total no. of electrons of O atoms = 1 × 8 = 8 electrons Total no. of electrons of H atoms = 6 × 1 = 6 electrons Total no. of electrons in one molecule = 32 electrons No. of electrons involved in bonding = 2 × total no. of bonds = 2 × 10 = 20 electrons

31.

In all case displacement is perpendicular to force. W1 = W2 = W3 = 0

33.

fdisc =

35.

Req =

360 rev =6 60 sec fsound = 60 × fdisc = 360 Hz R R R 4R + + = 2 3 2 3

V 3V I= R = eq 4R

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[95]

36.

Bulbs are connected in parallel so V is same Heat produced by first bulb H1 = 12 × 10 = 120 J Similarily, H2 = 2× 10 = 20J H3 = 6 × 10 = 60J

37.

Magnetic field is produced by moving charge

44.

2x + y = 10 (x + y) + x = 10 x + y is max when x = 0 \ (x +y)max = 10 2x + y = 10 2(x + y) – y = 10 \ x + y is min y = 0 10 =5 2 \ (x + y)max + (x + y)min = 10 + 5 = 15 (x + y)min =

41.

42.

As the LCM of 12x and 5y is 720 so, 720 should be divisible by 5y or 144 is divisible by y. so, y should be the factor of 144 so, according the option to i.e. 144 is correct

45.

x = 5n + 2 y = 5m + 4 x + y = 5(m + n) + 6

a=

144 64

(a – d) 1. (a + d) =

=

x=

5 x=1 2

y+

1 = 1 (Not possible) y

1 5 = y 2 on solving we get 15 64

15 64

9 5 – 16 16

4 1 = 16 4

1 2 (a + d) – (a – d) =a+d–a=d

1 2 so only one integral solution possible. y = 2,

æ 9 ö - d2 ÷ = 15 ´ 4 = 5 ç 16 è ø 64 3 16 d2 =

= x2 – 2

y+

144 6 3 = = 64 8 4

(a2 – d2) 1. =

y2

7x – 2 (x2 – 2) = 9 7x – 2x2 + 4 = 9 2x2 – 7x + 5 = 0 2x (x – 1)– 5 (x – 1) (2x – 5) (x – 1) = 0

2z - 5 =–1 3 a=a–d b= a g=a+d 3a =

1

y2 +

x+y Remainder =1 5 \z=1

43.

1 =x y

y+

46.

.A, B, A + B are in AP \ 2B = A + A + B 2B = 2A + B B = 2A \ Area of bigger circle = A + B = 3A 3A = pR2

pR 2 3

A=

pr2 =

d= ±

pR2 3

r2 =

42 3

æ 1ö = 2ç ÷ è2ø

r2 =

16 3

=1

r=

4 16 4 3 = = 3 3 3

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[96]

47.

c=a+b–8 Þa+b–c=8 a=b+c–8 Þb+c–a=8 b=a+b–8 (a + b + c) = 2 (a + b + c) – 24 a + b + c = 24 a+b–c=8 2c = 16 c=8 c=a=b=8

1- cos x 1 = sin x 3 3(1 – cosx) = sinx 9(1 + cos2x – 2cosx) = 1 – cos2x 9 + 9cos2x – 18 cosx = 7 – cos\2x 8 + 10cos2x – 18 cosx = 0 5cos2x – 9 cosx + 4 = 0 5cos2\x – 5cosx – 4cosx + 4 = 0 5cosx (cosx – 1) – 4(cosx – 1) = 0 cosx = 1 cosx = 4/5 sinx =

=

54 ´ 22 – 108 7

Þ

1188 - 756 432 = 7 7

= 61

51.

135p 1 ´ 122 – ´ 3x ´ x 360 2

5 7

% Change =

6pr 2 4pr 2

´ 100 = 150 %

52.

3 5

\ cos2x – sin2x = 49.

Then area =

3 2 8 = 16 3 4

area = 48.

x=6 2

16 9 7 – = 25 25 25

DABC ~ DADE

D=

abc 4R

12 - 2r 12 = r 5

R=

abc 4D

r=

30 11 Vol. of cylinder = pr2h = pr2(2r) = 2pr3 = 127.39

æqö 2.7.7.14 sinç ÷ è2ø = 4.49 sinq æqö 7 sinç ÷ è2ø 7 æqö = æqö æ q ö = 2 secç 2 ÷ 2 sinç ÷ cosç ÷ è ø è 2ø è2ø pR2 = =

æqö 22 49 ´ sec2 ç 2 ÷ è ø 7 4

54.

æqö 77 sec2 ç 2 ÷ è ø 2

x 1 = y x -1 x2 – x = y cos72 =

50.

2 x = 12

x2 + y2 - x2 2 xy

x2 – x = 2x cos72° x – 1 = 2 cos72° x = 1 +2 cos72°

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[97]

æ 5 - 1ö ç ÷ =1+2 ç 2 ÷ è ø 5 -1 = 2 \ BD = x – 1

5 +1 2

5 +1 –1= 2

5 -1 2

=1+

=

58.

3 + a 5a + 1 , ) 2 2 these coordinats of M satisfy only 2. option. M(

59. 55.

Three digit = 3 ´ 3 ´ 2 = 18 Div. by 5 = 2 ´ 2 ´ 1 + 3 ´ 2 = 10 10 5 = 18 9 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 +9 + 10 + 11 + 12 + 13 + a + b = 13 ´ 15 91 + a + b = 195 a + b = 195 – 91 = 104 Now according to option 51 + 53 = 104 \ 2nd larger value is 51 Req. Probability =

60. ÐBAC – ÐOBC = 90 + q – q = 90

57.

areaDPBC 6 x 3 = = areaDABC 10 x 5

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[98]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2016) CLASS-X [MAT]

HINTS & SOLUTIONS ANSWER KEY 1 3 16 3 31 3 46 3 Q.1

2 3 17 2 32 4 47 3

3 2 18 1 33 2 48 3

D

3

+3

4 3 19 4 34 3 49 2

Y

3

G

5 2 20 2 35 1 50 3

2

–4

9

+3

U

3

J

3

–4

27

Q

4

+3

3

M

–4

81

+3

3

P

M

5

–4

243

I

6 1 21 2 36 3

7 4 22 4 37 4

8 3 23 2 38 4

9 2 24 3 39 3

–13

91

Q.3

14 3 29 1 44 1

15 1 30 2 45 4

Case I :

Designer

Teachers

–13

78

Professors

Designer Male

Case II :

–13

Teachers

65 –13

Clearly in both case Conclusion III is follow and either I follows or II follows.

52 Q.10

B® C® A® E® D® |–®

Q.13

From 1st and 3rd diagram :

C

B

13 3 28 3 43 4

M ale

Q.7

H

E

12 4 27 1 42 3

Professors

0.8 (.8) = .512 0.04 (.04) 3 = .000064

F

11 2 26 3 41 2

104

3

Q.2

10 1 25 2 40 1

1 (Science) 2 (Hindi) 3 (Mathematics) 4 (Sanskrit) 5 (English) (Hindi or Sanskrit)

B

A D

G

G

Y

R

Bl G

Q.14 Q.6

Þ

O

– 33 + 11 – 9 + (28 ¸ 4) × 5 = – 33 + 11 – 9 + 7 × 5 = – 33 + 11 – 9 + 35 = – 42 + 46 = 4

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[99]

Q.15

REASON ® PGYUMP 18 5 1 19

15

14 ––––® 16

7

25

21

13

6 4 7 2 = 15 Þ (6 × 4) – (7 + 2) = 15

16

–2

9 3

+2

4 5 = 18 Þ (9 × 3) – (4 + 5) Þ 27 – 9 = 18

–2 +2

8 3

–2

4 6 = ? Þ (8 × 3) – (4 + 6)

+2

Þ D

I

R

E

C

T

4

9

18

5

3

20

-2

+2

-2

+2

-2

+2

2

11

16

7

1

22

ß B

ß K

ß P

ß G

ß A

ß V

Q.16 Given C’s age = 12 yrs

10 = 14 Q.21

Q.23

3 × 12 = 18 yrs. 2 We know, A is 12 years older than B Þ A’s age = 18 + 12 = 30 yrs Þ Mother’s age = 2(30) = 60 yrs. Þ Husband’s age = 60 + 5 = 65 yrs Þ Ram’s age who is 15 yrs younger than him = (65 – 15) yrs = 50 yrs Alphabetical order : Anu (A), Joy(J), Pritam (P), Zeba (Z)

Cleary, all fathers are men and some of them can be teacher’s also, Therefore, it will be like this :

M F

Þ B’s age =

Q.17

Þ 24 –

T

Reena > Rita > Zoha and Reena = Reeta + 2 = Zoha + 5 ... (i) Also Reena + Zoha = 3(Rita – 5) by equation (i) (Rita + 2 ) + (Rita – 3) = 3(Rita – 5) 2Rita – 1 = 3Rita – 15 Þ Rita = 14 years 12 inch

Q.24

c

C b

Working days are : M T W Th F For 3 weeks : A J P Z A J P Z A J P Z A J P

2 inch

Pieces which have only two types of coatings are at edges, so no. of pieces = 2[(4 – 2) + (6 – 2)] = 2[2 + 4] = 12

Only Zeba work for 3 days. Q.18

Clearly, its Pritam who workded on 1st Wednesday then its Zeba and after her Anu.

Q.19

Printed Price = Rs 1000/After discount of 60% , price will be :

60 ö æ ÷ = Rs 400/Rs ç1000 - 1000 ´ 100 ø è Now, after this their is discount of 40% also : \ the price will be: 40 ö æ ÷ = Rs 240/Rs ç 400 - 400 ´ 100 ø è Q.20

Q.25

Pieces which have only one type of coating are at top surface of cake, so no. of pieces = [(6 – 2) × (4 – 2)] = 4 × 2 = 8

Q.26

As there are only 8 pieces of cake having chocolate cream and total pieces are 24 \ Remaining pieces = 24 – 8 = 16

Q.27

In morning Su is in the East so Monika’s face will be in North,

4 5 2 3 = 13 Þ (4 × 5) – (2 + 5) = 20 – 7 = 13 Þ Multiplying above two and subtracting sum of 2 number lying in lower row.

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[100]

Q.28

Clearly – Both the statements are sufficien. So answer is 3

Q.29

We have four horses in one race divide 16 horses in for groups

Q.30

Q.39

Logic 12 + 52 + 72 = 75 92 + 72 + 82 = 194 82 + 32 + 42 = 64 + 9 +16 = 64 + 25 = 89

Q.40

Using Net

Q.41

First bell will ring at exact 8 O’clock, in next 8 seconds 7 bells will ring.

b,c,e, g, k, ? , q , s 2 , 3 , 5 , 7 , 11 , 13 , 17 , 19 All consecutive prime numbers so alphabet correspond to 13 is m.

Q.32

6 4

5

3

2 1

\ time taken for 1 ring = Points opposite to 2 is 6. Q.33

Q.34

8 × 10 = 11.43 sec. 7 (Q 1 bell will ring at exact 11 O’clock)

2, 10, 30, 68, _____, 222 2' = 13 + 1 10 = 23 + 2 30 = 33 + 3 64 = 43 + 4 130 = 53 + 5 222 = 63 + 6

8 sec. 7

\ time taken for 10 ring =

Q.42

1. ADEF 2. AGHD 3. ABCD

T–S×B–M B is wife of M T is wife of S S is son of B From these not true statement is S is the daughter of B

4. ABDH 5. ACDH 6. AFDG 7. AGDE 8. ACDF

Q.35

(1) Either I or II ; and III follows S

9. ABED

A

10. AFBD

B

11. ACDE

F

Sol. 43-45 According to given information

9, 23, 51, 106, 219, 643 Q.36

14 28 55

113 424

9 + 14 = 23 23 + (2 × 14 =28) = 51

43.

(4) Umesh

44.

(1) Prem

45.

(4) Information inssufficient

51 + (2 × 28 = 56) = 107 Q.38

Age order Ronald > Veena

Amilia Parul > Ronal > Veena Shree > From this Parul is elder to Veena

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[101]

46.

Given codes

Q. 48

1218199 Þ 121

81

99

(11)2

(9)2

11×9

1006480 Þ 100

64

80

(10) 2

(8)2

10×8

81

49

63

814963 Þ

643648 Þ

(9)2 (7) 2

9×7

64

48

36

(8)2 (6)2

8×6

49

35

492535 Þ

25

Q.49

æ è

500 = 5 × ç10n +

7×5

Cubical box each side length = 1 meter Means side of cube a = 1 meter Rod is fixed in the each side so length or Rod =

Q.47

(3) (6 – 5)3 + (1)2 (12 – 10)3 + (2)2 (18 – 15)3 + (3)2 (24 – 20)3 + (4)2

5(n - 1)n ö ÷ 2 ø

200 = 20n + 5n (n – 1) 200 = n(15 + 5n) 40 × 5 = n(15 + 5n) \ n=5 Days = 5 × 5 = 25 Q.50

(7)2 (5)2

(3) S T A R Y ¯ ¯ ¯ ¯ ¯ g q d b e So tray Þ q b d e or b q d e Work = Man × days \ 20 × 25 = 10 × 5 + (10 + 5) × 5 + (10 + 5 × 2) × 5 + …….. 20 × 25 = 5[10 + (10 +5) + (10 + 5) × 2 + ….. (10 + 5 + n)]

3a=

3×1=

3 metre

Þ (1)3 + (1)2 = 1 Þ (2)3 + (2)2 = 8 + 4 =12 Þ (3)3 + (2)2 = 27 + 9 =36 Þ (4)3 + (4)2 = 64 + 16 =80

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[102]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2016) CLASS-X [SAT]

HINTS & SOLUTIONS ANSWER KEY 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

3

2

1

3

4

4

2

3

3

1

4

2

2

4

2

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

4

2

2

3

2

1

2

4

3

4

4

3

2

3

4

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

1

3

3

1

2

1

2

3

3

1

1

4

1

4

4

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

2

2

1

3

1

3

4

4

2

4

2

3

4

4

4

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

1

3

4

1

1

3

2

4

4

3

4

1

3

2

1

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

2

3

3

3

4

4

4

1

3

2

3

4

2

4

2

91

92

93

94

95

96

97

98

99

100

4

3

1

1

2

3

3

2

2,3

3

Q.15

One molecule of H2O, contain 8 number of neutrons of oxygen atom only. So total no. of neutrons in 5 mole of H 2O molecules will be = 5 × 8 × 6.022 × 1023 = 2.409 × 1025

Q.16

Being more reactive Fe can displace copper from its salt solution. Fe + CuSO4 (aq.) ® FeSO4 + Cu¯

Q.17

In colloidal (B, D) and suspension (A) path of light is visible. Where as in solution (C) particles do not settle down in suspension (A) solute particles are visible to naked eye.

Q.18

Al is malleable but being more reactive it forms layer of oxide on its surface on exposing to air. So it cannot be used for a- particle scattering experiment.

Q.19

2 Mg + O2 ® 2MgO

Q.20

2Al2O3 ¾Electricit ¾ ¾¾y ® 4Al + 3O2 D CaCO3 ¾¾® CaO + CO2 D 2NaHCO3 ¾¾® Na2CO3 + H2O + CO2 D 2HgO ¾¾® 2Hg + O2

Q.21

Amphoteric oxide can react with both acid and base to from salt and water. Ex. : Al2O3 & ZnO

Q.22

X = Na Y = Cl

Q.25

No. of moles of O atoms =

9.033 ´ 10 23 = 1.5 6.022 ´ 10 23

mole Mass of O-atom = 1.5 × 16 = 24 g Moles of H-atom = 1.5 × 2 = 3 moles. Q.26

General formula of carboxylic acid is CnH2nO2

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[103]

Q.28

I=

q t

h 2

Q = nte I × 1 = (n + 4.8 × 1018) × 1.6 × 10–19 N = 2.2 × 1018

s=r sv’g = 2r × v’g s × A × h × g = 2r × A × x × g

Q.29

x=

h 2

C

Q.39

(–x) A

`

R = mv 2 Q.30 Q.31

Q.32

Q.33

VA – 20 + 10 = vB (from KVL) VA – VB = 10 Magnetic force act perpendicular to velocity of charged particle magnetic field. So there is no component in direction of motion. Electric field can change only the velocity of charged particle. So velocity & momentum (mv) will be changed.

Q.40

Because kinetic energy is equal So x1= x2

Q.41

Desired No = LCM (13 & 21) k –10 Where k is a natural no. = 273 k –10 Given 500 < 273 k – 10 < 600 510 < 273 k < 610

æ dm + A ö æ 60 + 60 ö sin ç sin ç ÷ ÷ 2 è ø è 2 ø sin 60 = = = m= A 60 sin 30 sin sin 2 2

510 610 0 Þ 1 + k > 0 Þ k > -1 ....(1) 1+ k From 1st equation x = 2 + y Substituting in 2nd equation kx + y = 3 Þ k(2 + y) + y = 3

A

\

h Q.47

60º

3 - 2k y= 1+ k We know, y > 0 Þ

B

3 - 2k >0 1+ k

3ö æ Þ kÎ ç - 1, ÷ 2ø è

….(2)

x2 – 6x – 2 = 0 a2 – 6a– 2 =0 a2 – 2 = 6a Similarly b2 – 2 = 6b

tan 30º =

1 h = …(1) 3 20 + x

DABD

tan 60º =

h = BD

h=

6 a 9 - b9 6 =3 9 9 = 2 a -b 2 Q.46

Þ

n n +1 2 n n 2 2 + n - 1 3 = 3n + 1 S2 = 2 2 n n 2 3 + n - 1 5 = 5n + 1 S3 = 2 2 M n 2r - 1 n + 1 Sr = 2 S1 =

S1 + S2 + …. + Sr =

n n + 3n + 5n + ..... + (2r - 1)n + 2

3

3x

….. (2)

from (2) in (1)

....(1) .... (2)

a10 - 2a 8 a10 - b10 - 2 a 8 - b8 2a 9 = 2 a9 - b9 a 8 a 2 - 2 - b8 b 2 - 2 = 2 a 9 - b9 From eq.(1), (2)& (3)

D 20 C

In DABC

3ö æ From (1) & (2) kÎ ç - 1, ÷ 2ø è Q.45

x

30º

3x 1 = 20 + x 3 3x = 20 + x Þ 2x =20 Q.48

x = 10 metre. cosec x – sin x = a

Þ ….(3)

1 - sin 2 x cos 2 x =a Þ =a sin x sin x

..

(1) Similarly secx – cos x = b

Þ

1 - cos 2 x =b cos x

Þ

sin 2 x =b cos x

From (1)

& from (2)

cos 4 x = a2 sin 2 x sin 4 x = b2 cos 2 x

… (2) ….(3)

…. (4)

Now, multiplying eq. (2) with eq. (3) & eq. (1) with eq.(4), we get a2b = cos3x (cos3x)2/3 = cos2x = (a2b)2/3 …. (5) Þ 2 3 & b a = sin x Þ (sin3x)2/3 = sin2x = (b2 a)2/3 …. (6) Now, adding (5) & (6), we get (a2b)2/3 + (b2a)2/3 = 1

n 1 + 1 + ..... + 1 r times 2 Þ

S1 + S2 + …. + Sr =

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[105]

Q.49

35m

A

2pr2 = 4p Þ r2 = 2

B

3 h2

25m 12m

60º

D

12m C 23m Q.52

22 12 ´ 12 792 2 pr 2 ´ Then area = = = m 7 4 7 4 22 23 ´ 23 ´ When r = 23m, then area = 7 4 54819 2 = m 14 \ Increase in area =

5

V = 1m3 1 = a2 ×l

l = 90 cm

100 c, 3 90 Density = = 90 kg/m3 = .09 g/cm3 1 a=

3

æ 100 ö ÷ ´ 0.09 Weight of the cube = ç è 3 ø

A

Þ

100 ´ 100 ´ 100 9 × 27 100

Þ

10000 10 1 gm = kg Þ 3 kg 3 3 3

53m

Q.50

B

h2 =

side of square = a

54819 792 – = 302.5 m2 14 7

35m

32 - 2 2 = 5

1 2 p1 8 v1 1 = 3 = v2 1 2 10 p2 5 3

r2

Where r = 12 m

h2 =

C

66m

154 S= = 77 m 2

q

\ are of DABC = 77 ´ 11 ´ 24 ´ 42 = 924 m So area of circle = 1848 m 2

2

P

T q O

R

q

Q.53 q

2

2 ´ r 2 = 1848 7

S

R = 14 3 m

DPOT ~ DROS By AAA similarity Ð P = ÐR Since Alternate interior angles are equal therefore PT || RS

2p

Q.51 Q.54

4p Let radius of circle be 3 units 2pr1 = 2p Þ r1 = 1 3 h1

h1 = h1 =

32 - 12 = 8 8

Draw BL perpendicular to AC and join L to D. Since ÐBCL = 30º, we get ÐCBL = 60º. Since BLC is a right triangle with ÐBCL = 30º, we have BL = BC /2 = BD. Thus in ÐBCD, we observes that BL = BD and ÐDBL = 60º. This implies that BLD is an equilateral triangle and hence LB = LD. Using ÐLDB = 60º and ÐADB = 45º, we get ÐADL = 15º. But ÐDAL = 15º. Thus LD = LA. We hence have LD = LA = LB. This implies that L is the circumcentre of the

r1

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[106]

– 14y – 6y = 49 – 9 – 20y = 40 y=–2 (x – 6)2 + (y + 6)2 = (x – 3)2 + (y – 3)2 (x – 6)2 + 16 = (x – 3)2 + 25 x2 + 36 – 12x + 16 = x2 + 9 – 6x + 25 6x = 18 x=3 Center = (3, –2)

1 1 ÐBLD = ´ 60º = 30 º 2 2

D. Thus, ÐBAD =

Since ÐADC = 135º. Which is equal to ÐBAD + ÐABC. Therefore ÐABC = 105º.

Q.55

Length of PS =

R1 + r

2

- R1 - r

R2 + r 2 - R2 - r

R1 + R 2

Q.58

2

A (2, 3)

2

2 R 1R 2 PQ = PS + QS By (1), (2), (3) & (4)

- R1 - R 2

2

=

….(4)

k= Q.59

B (–1, –2)

41 7

Let x is mean Then smallest no. = x – 10 largest no. = x + 15

So series x –10, 5, x + 15 [Q median = 5]

A

B

C

5 18 +2× =k 7 7

….(3)

2 R 1r + 2 R 2 r = 2 R 1 R 2 1 1 1 + = R1 R2 r 4

4

æ - 3 + 8 6 + 12 ö æ 5 18 ö Coordinate of C = ç 7 , 7 ÷ = ç 7 , 7 ÷ è ø è ø Point C lies on line x + 2y = k

So

Q.56

3

=

….(2)

2 R 2r Length of PQ =

=

….(1)

2 R 1r Length of QS =

2

x + 2y = k

6 5

Q

x - 10 + 5 + x + 15 =x 3 2x + 10 = 3x Þ x = 10 Given

C R

Þ

Therefore numbers are 0, 5 and 25

Þ

1 (Perimeter DABC) 2 1 1 AQ = (4 + 6 + 5) = × 15 2 2 AQ =

AQ = 7.5 cm

Q.60

0 + 25 + 625 650 2 0 2 + 5 2 + 25 2 = = = 216 3 3 3 3 P(getting atleast 5) = 1 – P(getting less than 5) 4 cases = 1 + 1 + 1 1+1+2 1+2+1 2+1+1 P(getting less than 5) =

(6, –6)

(3, –7) (x, y)

4 1 = 216 54

P (getting atleast 5) = 1 –

1 53 = 54 54

Q.57 (3, 3)

Points (6, –6), (3, –7) & (3, 3) (x – 3)2 + (y – 3)2 = (x – 3)2 + (y + 7)2 y2 + 9 – 6y = y2 + 49 + 14y

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[107]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2017) CLASS-X [MAT]

HINTS & SOLUTIONS ANSWER KEY 1

1.

2

3

4

5

6

7

8

9

10

11

12

13

14

15

3

2

2

1

4

3

1

1

2

3

2

2

3

3

2

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

3

3

3

2

3

4

3

2

1

3

4

3

3

3

1

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

4

3

3

Bonus

3

1

3

2

3

4

2

1

1

2

4

46

47

48

49

50

1

4

4

4

1

On looking (i) & (ii) Good sing represent pie sie therefore pason

4.

represent mie. On looking (ii) & (iii) Good lyrics represents rie sie.

122 – 082

\ love represent tie good can be either rie or sie and accordingly (3) option follow that is rie

= 144 – 64

= 256 – 49

= 80

= 207

mie tie 2.

162 – (07)2

Option 1

ab_ab_aaa_bbaaa_bbbb ® ab/aabb/aaabbb/aaaabbbb \ (2) option abba 252 – 212 = 625 – 441

3.

= 184 24 + 25 = 40 + 41 =

=7 =9

36 + 45 = 50 + 71 =

7 + 9 = 16

9 + 11 = 20

= 11 1

5. C can be 1 or 5 or 6. But C cannot be equal to 1 because we get 5 digits in Answer. C is 5 or 6 By looking into the solution

70 + 99 = 100 + 125 =

= 13 = 15

(4) A = 2

B=3

C= 5

D=7

13 + 15 = 25

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[108]

12.

Case – I

6.

Case – II

8+1=3+6 9=9

7.

and

Case – III

Conclusion A. Some boats are pens {follow in all} 8.

Option (1) is correct.

B. Some birds are paper {Not followed by 1}

Because it complete one rotation to reach its

C. None of the pens are birds {Not followed by 3}

starting point.

\ Only A follows.

13. 9.

On comparison W becomes SE.

10.

14.

(1) ABCIA

(2) CDHIC

(3) DEGHD

(4) BDHIB

(5) CEGIC

(6) DEFHD

(7) ABDHA

(8) BEGIB

(9) CEFIC

(10) ABEGA

(11) BEFIB

(12) ABEFA

255, 3610, 4915, M , 8125 52(5), 62(10), 72(15), 82(20), 92(25) \ M = 6420 Ans.

Cube with number face painted = (n – 2)3 Þ (6 – 2)3 Þ (4)3 = 64 (Option 3). 15. 11.

\ M = U 16 Option 2 16.

Sum of Column = 14 7 + 2 + 1 + 4 = 14 3 + 8 + 1 + 2 = 14

\ GH 24 is the odd among all. Option 2.

6 + 5 + 2 + 1 = 14 2 + 4 + 4 + M = 14 Þ M = 4 Option 3

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[109]

17. (3) The expression is 56 (6 + 8) × 4 – 1 = 15.

27.

Radius of cylinder = 12 cm Height = 175 cm

18. (3) 100 – 81 27 + 3 × 6 = 115.

Height of new cylinder = 63 cm Let the radius of New cylinder r

19. (2) 68 satisfies all the given conditions.

So, volume of both cylinder should be equal (12)2 175 = r2 (63)

20. (3) (1, 9), (2, 8), (3, 7), (4, 6), (5, 5), (6, 4), (7, 3),

on solving r = 20 cm.

(8, 2), (9, 1).

Option (3). 28. Option (3)

21.

Number of regions formed by lines follows the

29 and 30

pattern Hence 11 is the answer.

22. Number of students who do not play any game If square is divided in 4 region equally then any

is h.

region with 2 points will be having a property such

a + b + c + d + e + f + g + h = 150.

that distance between them is less than

b + g = 20

2 .

This means, we need minimum of 5 points such

e = 20

that atleast one of the region has two points and

f = 35

thus there will always be a pair of points such

d = 25

that distance between them is less than

a=h

2.

a= 23.

Given

h = a = 10.

Sum of digits of x is 15.

10 + 20 + c + 25 + 20 + 10 + 35 = 150.

So, x is divisible by 3 but not by 9.

So, c = 30.

and unit’s digit is 6. so x is even number.

29.

30. Average age of A, B and C is 43 years. So,

A BC = 43. 3

Number of students who play only kabadi is 30. Option (3).

Option (2) x is divisible by 6 but not by 9. 24.

e = 10 2

Number of students play only hockey is 10. Option (1).

31.

Number in the blank box = 72 + 92 + 82 = 49 + 81 + 64 = 194.

A + B + C = 129 Statement-I Age of C is 65 years.

32.

Number of circles 15.

I is sufficient as 129 - 65 = 64 sum of (B + C).

33.

M = 5x

Option (1) is answer.

W = 3x Let y part is removed and replaced by water. M = 5x –

25 -26.

W = 3x –

5 y 8

3 y+y 8

M=W 25. Option (3)

5x –

5 3 y  3x – y + y 8 8

26. Option (4)

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[110]

x=

5 8 y y = y.. 8 5

40.

The minimum number of distinct colours needed to

A

T

13

1

20

so 13th prime is 41.

8 x 1 Required answer = 5 = . 5 8x

34.

M

1st prime is 2. 20th prime is 71. 41.

colour all the circles in the figure = 3

The digit in square is half of the sum of the number written in circle on either side of square.

35. 1 (8 + 3) = 6. 2

 x = 42.

= () H = 23 = 8

(1)4 = 1 + A. 43.

36.

C4 = (C2 . C3) C 1 = (10 – 7) 49 = 3 × 7 = 21.

37. 44. ar ABC is max.

The time gap between adjacent clock is 20, 40,

when AB = BC

R

, 80, 100

So the time in (V) clock.

AB2 + BC2 = AC2

is 12 : 20 + 60 min. = 1 : 20.

2AB2 = 72 AB = 6 = BC

45.

4, 6, 8, 10, 12

ar ABC = 1 1 ar ABC = × AB × BC = × 6 × 6 = 18 cm2. 2 2

No of cross increased by 2 So in the square there should be 4 cross.

46.

a, b, d, h, p 1 2 4 8 16

38. 47. By seen from west to east. E is a head of B

39.

and B is a head of A and A is ahead of C and D We can’t say () All king are beautiful nor . All Queen are King.

is ahead of C. By this conclusion any of the IV option are possible.

So neither nor follows.

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[111]

48.

4 option is correct because if A is at the first place then. A __ __ __ Then C & D are always together. Which contradict the given condition that C & D can not be on adjacent seat.

49.

50.

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[112]

NATIONAL TALENT SEARCH EXAMINATION NTSE STAGE-II (2017) CLASS-X [SAT]

HINTS & SOLUTIONS ANSWER KEY 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

4

3

3

1

1

1

2

2

4

4

3

4

4

3

2

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

3

1

4

1

1

4

2

1

2

4

2

3

1

3

2

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

2

2

3

3

1

4

4

4

3

3

4

3

1

2

4

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

1

1

1

1

1

3

2

4

4

1

1

4

3

2

2

61

62

63

64

65

66

67

68

69

70

71

72

73

74

75

3

3

2

2

4

1

1

3

1

3

3

3

2

1

2

76

77

78

79

80

81

82

83

84

85

86

87

88

89

90

1

4

3

2

4

4

4

4

3

2

4

1

3

3

3

91

92

93

94

95

96

97

98

99

100

1

2

4

3

3

1

3

1

3

2

1.

Slowest growth will be observed in abscisic acid and auscin as Abscisic Acid is a plant growth inhibior hormone.

2.

They are cylindrical in appearance and has one nucleus per cell.

3.

C-Cerebellum and D-Mid brain controlls most of the involumtary actions

4.

Arthropoda phylum- All the given features are the characteristic features of the phylum arthropoda.

5.

Nostoc and Bacteria both are prokaryotic on the other hand in statement II- Penicillium in fungi but spirogyra is an algae.

6.

I and II- The other two features i.e. tap root system and two cotyledons are the characteristic features of dicots and the plant with parallel vanation is a monocat plant.

8.

II and IV The groups of organs are performing similar functions but have different origin.

9.

Trichoderma - It is used as fungicides

10.

Tt(F1) × tt (P) - A test cross is that in the plant with unknown genotype is creysed with the recessive plant. so Tt is the F1 generation and tt homogggous recessive.

11.

Elphantiasis is caused by Wuchereria worm (Nematoda) and Acne is caused by bacteria staphylococcus

12.

Pancreatic juice contains trypsin and lipase along with anylase

14.

Each bacteria doubles in 20 minutes so, after 20 minutes total bacteria = 2 × 10 Similarly, after 40 minutes total bacteria are 2 × 2 × 10 Therefore, in 120 minutes, total bacteria = 26 × 10

15.

Metal oxide ® M2O3 ® M+3 O–2 Metal Nitride ® M+3 N–3 ® MN

16.

Brass ® is Homogenous mixture (Cu + Zn)

17.

glucose (C6H12O6 ) ® 1.80gm mass =180

1.80 = .01 mol 180 1 ® 6 mol .01 mol ® .01 × 6 mol =

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[113]

oxygen molecules ® .01 × 6 × NA = .01 × 6 × 6.23× 1023 = .06 × 6.023 × 1023 = 6 × 6.023 × 1021 = 36.132 × 1021 = 0.36 × 1023 36 water (H2O) 36 gm, mol = 18 = 2 mol = 2 mol × NA = 2 × 6.022 × 1023 = 12.044 × 1023 Total ‘O’ atoms = 12.044 × 1023 + 0.36 × 1023 = 12.404 × 1023 18.

35

Cl

37

1

& :

3

25

:

75

19.

Hence, C & E are not chemically same so answer is (4) 26.

Cl

Zn(s) + 2 Ag NO3 (aq) ® Zn (NO3)2 (aq) + 2 Ag(s) Hence, Zn is more reachive then Ag SoI + displace the Ag, from aqous solution.

25 ´ 35 75 ´ 37 + = 100 100 =

25.

27.

Temperature ® –5ºC– 0ºC ® T ­ at 0ºC ® Phase change

875 + 2775 3650 = = 36.5 µ 100 100

(T = constant) at 0ºC to 100ºC ® Temperature is increased

Turmeric solution will turn red by an aqueuous solution of (i) Potassium acetate (CH3COOK), because potassium acetate is basic salt

28.

From t = 0 ® 1 v ® increasing slop

20.

From t = 1 ® 2 v ® constant

D

2Cu2S + 3O2 ¾¾® 2Cu2O + 2SO2 D Cu2S + 2Cu2O ¾¾® 6Cu(s) + SO2(g)

21.

slop

dv = negative = –1 dt

Ester and Carboxylic acid R–COOR , – COOH 29.

23.

dv =a=0 dt

From t = 2 ® 3 v ® decreasing

Both graphite and diamond are allotrops of carbon all their chemical properties are same. although they show different physical properties.

slop 22.

dv = a = constant dt

RQ2

1 1 1 = = f v u

Þ

1 -10 1 + = –2 f 4 2

is covalent compound

Þf= 24.

-1 Þ concave lens 2

power (p) =

30.

X is CH3COOH, C2H4O2

1 = 2.0 D f

suppose ball will reach the ground after t1 second and leight is h1 , then h1 = 0 ×t1 + h1 = 5 t12

1 × 10 × t12 2 ........(i)

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[114]

Now, ball rebounds with velocity 5 m/s and reaches to height h2 and time taken is t2 second then v = u – gt 0 = 5 – 10 × t2 t2 = 1/2 second

we know that – H = ut + ½ gt2 H=0×t+

1 × ge t2 2 similarly for planet – H =

1 h2 = 5t2 – × 10 t 22 2

and

h2 = Given

H=

5 m 4

Þ t1 = 1 second

Þ

\ h1 = 5 × 1 = 5 m

31.

32.

5 = 3.75 m 4

Fore = rate of change in momentum F = rAv2 = rA

2 ×t

Þ t’ =

2 × 50 = 70.7

36.

R=r×

p 2 2| d v 4

15 3 = m/s2 10 2 F.B.D for block A

Þ t’ =

frequency remains unchanged. & V = fl we know that velocity of sound in air is less as compare to in water. So accourding to relation from equation wavelength is also less in air as compare in water.

15 = (8 + 2)a

Þ

1 1 ge g t2 = · (t’)2 2 e 2 2

35.

F = ma

Þ

......(ii)

1 1 ge t2 = gp (t’)2 2 2

t1 + t2 = 1.5 second

So, net displacemet = h1 – h2 = 5 –

......(i)

1 g (t’)2 2 p from equ. (i) & (ii) –

1 1 1 – × 10 × 2 2 4

h2 = 5 ×

1 × ge t2 2

a=

sl ÞR = p A D2

l

...(1)

4

volume remains unchanged vi = vf A1l1 = A2l2

\ 15 – FAB = 8 × a 15 – FAB = 8 ×

2

p 2 p æDö Dl= ç ÷ l 4 4 è5ø 2

3 2

Þ

FAB = 3N 33.

l2 = 25 l rl 2

r ´ 25l D2 ´ 4 25

\ R2 = A = p 2

W aparent = W actual – FB where FB = force of buyonce

æ ç rl R2 = 625 ç çç p ´ D2 è4

300 = 800 – FB FB = 500

34.

ge =

gp =

gp =

from equ. (i).

GM e R 2e 37.

GM p Rp2 G ´ 2M e (2Re )2

ö ÷ ÷ ÷÷ ø

Þ gp =

ge 2

R2 = 625R according to momentum conservation– pi = pf mu + 0 = (m + M)v æ m ö V= ç ÷u èm + Mø

......(i)

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[115]

initial kinetic energy – 1 mu2 2 Final kinetic energy – Ki =

\

d=0×t+

Þ

t=

....(ii)

1 (m + M)v2 2 from equ. (i) – Kf =

1 æ qE ö 2 ç ÷t 2 èmø

2md qE

1 So, t µ

q

2

Kf =

m 1 u2 (m + M) (m + M)2 2

Kf =

2 2 1 mu 2 (m + M)

t

.....(iii)

=

t

Þ t2 = 40.

m ù é 1 mu2 ê1 ú ë m + Mû 2

2

If current flowing in same direction then wires attract each other and if current is flowing in opposite direction then wires repel each other. force µ0 I1I 2 = length 2pd

1 æ mM ö 2 DK = ç ÷u 2 èm +Mø 38.

Þ

From fig. – OP =

(17)2 + (12)2 =

12 433

µoil = 39.

12 433

= 1 × sin 90º

433 = 1.734 12

If electri field is E then force of charge q – F = qE ....(i) according to newton’s law of motion – F = ma ....(ii) From eq.(i) and (ii) – qE = ma

æ qE ö a= ç ÷ èmø Now, S = ut +

1 2 at 2

1 d

RS is far so d ­ and F ¯ 41.

Possible remainders = Þ 13 = 1 ® r1 = 1 23 = 8 ® r2 = 8 Þ 33 = 27 ® r3 = 0 43 = 64 ® r4 = 1 Possible sum = 1 + 8 = 9

42.

p(x) = q(x)(x – 1) + 3(given) p(x) = q(x) (x – 3) + 5(given) Also, p(x) = (x – 1)(x – 3) + r(x) for x = 1, p(1) = r(3) for x = 3, p(3) = r(3) Suppose r(x) = Ax + B r(1) = A + B = 3 r(3) = 3A + B = 5 \ A = 1 and B = 2 r(x) = Ax + B r(–2) = – 2A+ B r(–2) = –2(1) + 2 r(–2) = – 2 + 2

given – angle of refraction (r) = 90º according to snell’s law – µoil sin i = µair sin r µoil ×

F µ

PQ is near so d ¯ and F ­

433

if angle of incidence is i then from fig. – sin i =

q2 q1

2q q

Þ t = 2

So, loss in kinetic energy – DK = Ki – Kf 2 2 1 1 mu = mu2 – 2 2 (m + M)

t1 t2 =

\

r(–2) = 0

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[116]

43.

44.

Condition for infinite many solutions.

Given,

b 3 = g 4

Let the side of square be x units. Then, Diameter of a circle = x untis

ab 6 = ag c

b 6 3 6 = Þ = g c 4 c

\c=8 So, radius of O circle =

x2 – 6x + c = 0 Þ x2 – 6x + 8 = 0 x2 + – 4x – 2x + 8 = 0 x(x – 4) – 2(x – 4) = 0 (x – 4)(x – 2) = 0 x = 4 or 2 Now, x2 – bx + 6 = 0 x2 – bx + 6 = 0 42 – b(4) + 6 = 0 or 16 + 6 – 4b = 0 or 22 = 4b 11 =b 2 For b = 5 satisfies,

45.

46.

3 p-3 p = = p p 12 p=±6 [from (1) and (2)] p=+6 [from (2) and (3)] p=6 Let a, b be the roots of x2 – bx + 6 = 0 and a, g be the roots of x2 – 6x+ c = 0 a + b = b, a + g = 6 x2 – bx + 6 = 0 2 ab = 6, ag = c x – 6x + c = 0

x 2

x x \ OD = 2 4 Let the side of equilateral D be y units Then, Þ AD2 + DC2 = AC2

Þ OA = OB = OC =

2

Þ 22 – b(2) + 6 = 0 4 + 6 = 2b 10 = 2b

Þ Þ

5=b

2

æ 3x ö æyö ç 4 ÷ + ç 2 ÷ = y2 è ø è ø 9x2 3y 2 = 16 4 4 x2 = y2 3

a+b=5 a.b = 6 (possible values a = 2, b = 3)

Þ

x2 =

so the common root will be 2.

Þ

ar.(Square) =

Þ

ar.(Square) = k.ar.(Triangle)

Þ

k=

a=2 1 S5 = (S10 – S5) 4 4S5 = S10 – S5 5S5 = S10

47.

é5 ù 5 ê 2 ´ 2 + (5 - 1)d ú = 10 2 ´ 2 + (10 - 1)d 2 2 ë û 5 10 4 + 9d (4 + 4d) = 2 2

Þ

5×

Þ Þ

20 + 20d = 8 + 18d d=–6 S30 =

4 4 . 3 3

æ 3 2ö y ÷ çç ÷ è 4 ø 16 3 3

ar.(Triangle)

16 3 3

Here, PT = 8 units and BT = 4 units Then, TB × TA = TP2 Þ 4 × TA = (8)2 Þ TA = 16 \ BA = 12

30 [2 × 2 + (30 – 1)(– 6)] 2

=

30 30 ´ -170 [4 + 29 × (–6)] = 2 2

=

-5100 = – 2550 2

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[117]

Also, in DBTP, TP2 = TB2 + BP2

Þ 82 = 42 + BP2 Þ BP2 = 64 + 16 = 48 Þ BP = 4 3 Also in DABP AB2 + BP2 = AP2

Þ (12)2 + 4 3

x2 = 2 + 2

= 2(x)2 x2 =

Þ r = 4 3 units 48.

2

2 36 -38 3 24 -27 4 18 -22 6 12 -18 9

b

b

-3 -24 27 -4 -18 22 -6 -12 18 -9

17

So Total possible values of b will be 12. 49.

2

2

-17

-1 -72 73 -2 -36 38

-8

5 cm (AC = Diameter) 2

Area of square = 5 cm2

Possible roots for a, b Î – ive a

5 cm. 2

æ 5ö ÷÷ a + a = çç 2 è 2ø 5 2a2 = 4 × 2 a2 = 5 cm2

a b b 1 72 -73

8

5 Þx= 2

AC = 2

x2 + bx + 72 = 0 (given) Possible roots for a, b Î + ive

2 4

Area of square = 2 cm2

50.

Let a1x2 + b1x + c1 = 0 and a2x2 + b2x + c2 = 0 bet the two quadratic equation since 1 is a common root. Then, Þ a1 + b1 + c1 = a2 + b2 + c2 = 0 Þ b1 = –(a1 + c1) and b2 = –(a2 + c2) Also, the discriminants of two qudratic equation are equal Then, Þ b12 –4a1c1 = b22 – 4a2c2 Þ (a1 + c1)2 – 4a1c1 = (a2 + c2)2 – 4a2c2 Þ (a1 – c1)2 = (a2 – c2)2 Þ (a1 – c1)2 = ± (a2 – c2)2 Þ a1 – a2 = c1 – c2 or a1 + a2 = c1 + c2 Now, the roots of equation, x = –

b1 ± D1 2

= a1

and c1 Side of square = OP =

2

x =

2 cm

2 cm, OQ = x cm 2 2

2

æ 2ö ÷÷ + çç è 2 ø

2

and the roots of equation 2, x =

-b2 ± D2

= 2 a1 and c2

If a1 = a2 = 1 be the common roots Then, other roots are c1 and c2 Þ c1 – c2 = a1 – a2 = 0 or c1 + c2 = a1 + a2 c1 + c2 = 2 Þ c1 = c 2 Hence, roots are either equal or their sum is 2.

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51.

53.

D1N1 = D2N2 4 16 x × 32 = x × N2 25 5 N2 = 40

Let sides of the solid brick be x, 2x and 3x Volume = Number of bricks = 6x3 Let x = 1, 6 × 1 = 6 x = 2, 6 × 8 = 48 x = 3, 6 × 27 = 222 x = 4, 6 × 64 = 384 x = 5, 6 × 125 = 750 At x = 5, no. of cubes are going above 400.

54.

Pattern to be followed.

Now, N2D2 = N3D3 40 ×

16x 16x = × N3 25 125

N3 = 50 Medians are 18, 14, 10 52.

Let the third point be C(x, y) Mean =

Then,

18 + 14 + 10 42 = = 14 3 3

Þ CA = CB = AB Þ CA2 = CB2 = AB2

55.

Clearly 2272 – 875 = 1397, is exactly divisible by N. Now, 1397 = 11 × 127 \ The required 3 – digit number is 127, the sum of whose digit is 10.

56.

Given

Þ (x – 1)2 + (y – 2)2 = (x – 2)2 + (y + 1)2 = (1 – 2)2 + (2 + 1)2

Þ x2 + 1 – 2x + y2 + 4 – 4y = x2 + 4 – 4x + y2 + 1 + 2y

Þ 2x – 6y = 0 Þ x = 3y

... (1)

sin q = cos q =

3 5 4 5

Now, sin(90 – q) =

y 1

Þ y = cosq Þy=

cos(90 – q) =

\ (x – 1)2 + (y – 2)2 = 10 Þ (3y – 1)2 + (y – 2)2 = 10

(Q x = 3y)

Þ 2y – 2y – 1 = 0 On solving we get, 3

\ x = 3 1± 3 Hence C(x, y) lies in either 1st quarant or 3rd quadrant. So, C cannot lie in the second quadrant

x 1

Þ x = sinq x =

2

Þy=1±

4 5

57.

3 5

Here, P(x) = x2 + 5Kx + K2 + 5 and P(–2) = 0 P(–3) ¹ 0 \ 4 – 10K + K2 + 5 = 0 Þ K2 – 10K + 9 = 0 Þ (K – 9) (K – 1) = 0 Þ K = 1, 9 ... (i) Also P(– 3) ¹ 0 Þ 9 – 15K + K2 + 5 ¹ 0 Þ K2 – 15K + 14 ¹ 0 Þ (K – 14)(K – 1) ¹ 0 ... (ii) Þ K ¹ 14, 1 From (i) and (ii) K=9

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58.

cos4q+ sin2q = m, Þ cos4q + 1 – cos2q = m let cos2q = x 2

Then,

1ö æ 3 Þ m = x –x + 1 = ç x - ÷ + 2ø 4 è

60.

2

2

1ö æ 1 Now, 0 £ ç x - ÷ £ 2 4 è ø 2

Þ

Þ

59.

1ö 3 æ 3 1 3 £ çx - ÷ + £ + 2ø 4 è 4 4 4 3 £m£1 4

Let number of apples, bannas and coconuts b ex, y and z respectively. 2x + 3y + z = 26 3x + 2y + 2z = 35

... (i)

45 20 = AD BD

(tangent in both triangles)

AD 9 = BD 4

... (ii)

(i) × 3, (ii) × 2 6x + 6y + 3z = 78 6x + 4y + 4z = 78 12x + 13y + 7z = 148

tan(90 – q) = cotq

Cost of 12 apples, 13 bananas and 7 coconut is Rs. 148

20 AC = (let AC = BC = x) BC 45 x2 = 900 Let AD = 9y, BD = 4y \ 9y + 4y = 30 y=

30 13

9 ´ 30 270 = 13 13 æ 10 ö Þ AD = 20 ç 13 ÷ m è ø

\ AD =

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