NTSE stage-1 Mock Test 1

NTSE(STAGE-I) CLASS-X PRACTICE TEST PAPER-1

Time : 1½ Hr.

Max. Marks : 100

GENERAL INSTRUCTIONS 1. The booklet given in the examination hall is the Question Paper.

2. A student has to write his/her answers in the OMR sheet by darkening the appropriate bubble with the help of HB Pencil as the correct answer(s) of the question attempted.

3. Paper carries 100 questions. 20 question from Mathematics (1–20), 20 question from Science(21-50), 20 question from Social Science (51–70) & 30 question from Mental Ability (71–100) each of 1 (one) mark. 4. Blank papers, clip boards, log tables, slide rule, calculators, mobile or any other electronic gadgets in any form is not allowed.

5. There is no negative marking. Do not spend too much time on a particular question. 6. Before answering the paper, fill up the required details in the blank space provided in the answer sheet. 7. In case of any dispute, the answer sheet available with the institute shall be final.

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PRACTICE TEST PAPER-1(NTSE) 1.

Find the value of sin2 50 + sin2 100 + sin2 150 +.......................+ sin2 850 + sin2 900 . (A) 9

2.

1 2

(B) 5

1 2

(C) 9

3 2

(D) 5

1 4

A Rhombus of side of 10 cm has two angles of 60º each. Find its area. (A) 35 3 cm2

(B) 40 3 cm2

(C) 45 3 cm2

(D) 50 3 cm2

3.

The shadow of a tower is 30 metres when the sun’s altitude is 30º. When the sun’s altitude is 60º, then the length of shadow will be (A) 60 m (B) 15 m (C) 10 m (D) 5m

4.

A triangle with side lengths in the ratio 3 : 4 : 5 is inscribed in a circle of radius 3. The area of the triangle, is equal to (A) 8.64

5.

(B) 12

(C) 6

(D) 10.28

If a sphere of radius 10 cm is melted and converted into 8 balls. Find the surface area of each ball in cm. (A) 75 

(B) 60 

(C) 50 

(D) 100 

n

6.

 ( x  x ) is equal to : i

i 1

n

(A) x 



 (B) n x   

xi

i 1

7.

n



 x 

(C) x  nx

i

i 1

(D) 0



Find the median of the following frequency distribution : Class

0-10

10-20

20-30

30-40

40-50

Frequency

2

12

22

8

6

(A) 25

(B) 30

(C) 28

(D) 15

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #1

8.

In the given figure, AB, CD and EF are perpendiculars to BF. If the lengths of different segments are as indicated in the figure, then p : q is equal to : (A) a : b (B) b : a (C) (a + b) : a (D) (a + b) : b

9.

In the given figure, if A = CED, then the value of x is : (A) 4

C 8

(B) 6

10

D X

(C) 7

7

E 2

(D) 5

A

B

9

10.

In a triangle ABC, if angle B = 90º and D is the point in BC such that BD = 2 DC, then (A) AC2 = AD2 + 3 CD2 (B) AC2 = AD2 + 5 CD2 (C) AC2 = AD2 + 7 CD2 (D) AC2 = AB2 + 5 BD2

11.

n coplanar straight meet at a point. The angles between consecutive lines are xº, 2xº, ...., nxº. The value of n in order that the minimum angle be 24º, is : (A) 3 (B) 4 (C) 5 (D) 6

12.

ABCD is a cyclic quadrilateral. The tangents drawn at the points A and C of the circle intersect at P. If ABC = 1200, the value of APC will be : (A) 900 (B) 800 (C) 700 (D) 600

13.

If the roots of the equation x2 – 8x + a2 – 6a = 0 are real and distinct, then find all possible values of a . (A) –2 < a < 8

(B) 2 < a < 8

(C) –2  a  8

(D) 2  a  8

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #2

14.

If 2a = b, the pair of equations ax + by = 2a2 – 3b2, x + 2y = 2a – 6b possess : (A) no solution (B) only one solution (C) only two solutions (D) an infinite number of solutions

15.

The value of 'm' so that x4 + 6x3 + 13x2 + mx+ 4 is completely divisible by x2 + 3x + 2 is : (A) 13 (B) 12 (C) 6 (D) 0

16.

If the system of equations 3x + 4y = 12 and (a + b) x + 2 (a – b) y = 5a – 1 has infinitely many solutions then a & b satisfy the equation (A) a – 5b = 0 (B) 5a – b = 0 (C) a + 5b = 0 (D) 5a + b = 0

17.

Solution of

x–a x–b x–c    3 is bc c a ab (A) a + b – c (B) a – b + c

(C) –a + b + c

(D) a + b + c

18.

If ,  are the zeroes of x 2 – 6x + k = 0. What is the value of k if 3  + 2 = 20. (A) –16 (B) 8 (C) – 2 (D) – 8

19.

In the figure C is a right angle, DE  AB, A E = 6, EB = 7 and BC = 5. The area of the quadrilateral EBCD is C D

A

(A) 27.5 20.

7

(C) 22.5

B

(D) 20

Let XYZ be right a Z. Let Ax denotes the area of the circle with diameter YZ. Let Ay denote the area of the circle with diameter XZ and let Az denotes the area of the circle diameter XY. Which of the following relations is true ? (A) Az = Ax + Ay

21.

(B) 25

E

6

5

2 2 (B) Az = A x  A y

2 2 2 (C) A z  A x  A y

2 2 2 (D) A z  A x  A y

Absolute refractive index of a substance is (A) speed of light in air / speed of light in the medium. (B) speed of light in water / speed of light in the medium. (C) speed of light in the medium / speed of light in air. (D) speed of light in medium/speed of light in water. Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #3

22.

A lactometer is based on (A) Universal law of Gravitation. (C) Centripetal force.

(B) Achimedes’ principle. (D) Newton’s second law of motion

23.

A 150 m long train is moving with a uniform velocity of 45 km/hr. The time taken by the train to cross a bridge of length 850 m is (A) 56 s (B) 68 s (C) 80 s (D) 92 s

24.

The amount of sound energy passing each second through a unit area is called (A) Loudness or Intensity of sound (B) Amplitude of sound (C) Pitch of the sound (D) Frequency of sound

25.

The critical angle for a medium is the angle of incidence in the medium for which the angle of refraction in air is (A) 180º (B) 90º (C) 0º (D) 360º

26.

If the current in a wire is flowing in the vertically downward direction and a magnetic field is applied from west to east, then the direction of force on the wire is towards (A) North (B) South (C) East (D) West

27.

Resistance n, each of r ohms when connected in parallel to give an equivalent resistance of R ohms. If these resistances were connected in series, the combination would have a resistance in ohms, equal to : (A) n2R (B) R/n2 (C) R/n. (D) nR

28.

The biogas plant consists of an underground tank, which is made of bricks is called (A) slurry (B) overflow tank (C) digester (D) inlet chamber.

29.

A machine gun of mass M fires n bullets per second. The mass and speed of each bullet is m and v respectively. The force exerted on the machine gun is (A) zero. (B) mvn. (C) Mvn. (D) Mvn/m.

30.

The work done to change the velocity of the car from initial velocity ‘u’ to a velocity ‘v’ is equal to (A) change in potential energy. (B) change in kinetic energy. (C) difference of the masses of two bodies. (D) change in the shapes of the two bodies.

31.

Which of the following is not matter ? (A) larva of volcanic erruption

(B) pain

(C) wood

(D None of these

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #4

32.

Which one of the following statements is incorrect ? (A) All elements are homogeneous. (B) Compounds always contain two or more different elements. (C) A mixture is not always heterogeneous. (D) Air is a heterogeneous mixture.

33.

Hydrogen and oxygen combine in the ratio of 1 : 8 by mass to form water. What mass of oxygen gas would be required to react completely with 3 g of hydrogen gas ? (A) 24 g (B) 27 g (C) 21 g (D) 3 g

34.

The empirical formula of a compound is CH2O and its vapour density is 30, then the molecular formula of the compound will be (A) CH2O (B) C2H4O2 (C) C4H8O4 (D) C3H6O3

35.

116 g of Fe3O4 has 1.5 moles of Fe. Calculate the molecular weight of Fe3O4 without using atomic weights of Fe and O. (A) 232

36.

37.

(B) 174

(C) 348

Rutherford performed his alpha scattering experiment using (A) silver (B) gold (C) mercury

(D) 116

(D) diamond

Electrons revolve in some definite circular orbits around the nucleus without emission of energy. This statement was given by (A) Rutherford

(B) Bohr

(C) Thomson

(D) Somerfield

38.

When copper sulphate reacts with hydrogen sulphide gas the colour of precipitate formed will be (A) white (B) green (C) orange (D) black

39.

A reaction in which two aqueous solutions react to form an insoluble substance is (A) freezing (B) condensation (C) precipitate formation (D) None of these

40.

The metal which is least reactive, is (A) Ag (B) Au

41.

(C) Cu

(D) Pt

Which of the following equation sums up photosynthetic reaction most accurately : (A) CO + H2O  CH2O + O2

(B) 6CO2 + 6H2O  C6H12O6 + 6O2

(C) 6CO2 + 12H2O  C6H12O6 + 6O2 + H2O

Light  l C6H12O6 + 6O2 + 6H2O (D) 6CO2 + 12H2O Chlorophyl

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #5

42.

43.

In amoeba absorption of the digested nutrients occurs in – (A) cytoplasm (B) plasma membrane (C) contractile vacuole

(D) pseudopodia

Which one does not produce any digestive enzyme ? (A) Pancreas (B) Liver (C) Stomach

(D) Buccal cavity

44.

Systolic pressure of heart is higher than diastolic pressure because (A) Blood is forcefully pumped into arteries by the heart during systole and not during diastole (B) Arteries offer resistance to the flowing of blood during systole only (C) Arteries contract during systole only (D) Volume of blood in heart is greater during systole than during diastole.

45.

Which of the following has least urea ? (A) Renal artery (B) Renal vein

(C) Aorta

(D) Afferent arteriole

46.

Phototropic movements of roots and stems are due to : (A) Action of gravity (B) Effect of light (C) Epinasty and Hyponasty (D) None of these

47.

The metabolic rate is controlled by: (A) Pancreas (B) Liver

48.

(D) Pituitary

(C) Cerebellum

(D) Pons

The largest part of brain is (A) Cerebrum

49.

(C) Thyroid

(B) Medulla oblongata

Somatic chromosome number is 40. What shall be the chromosome number in the cells of seminiferous tubules ? (A) 40

(B) 20

(C) 10

(D) 23

50.

Mendel’s law do not explain principle which is : (A) Segregation of genes (B) Dominance (C) Linkage (D) Independent assortment

51.

Calcium carbonate, Magnesium carbonate, Potash and Lime are rich in : (A) alluvial soils (B) red soils (C) black soils (D) all of the above

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #6

52.

53.

Trees with hardwood and dense canopy are generally found in (A) Deciduous forests (B) Evergreen forests (C) Tidal forests Which of the following is correct ? (A) every fifth person in the world is a Chinese (C) both (A) and (B)

(D) Alpine forests

(B) every sixth person in the world is a Indian (D) none of the above

54.

What was the primary objective of green revolution in India ? (A) To increase forest (B) Modernization of agriculture (C) To increase cash crop cultivation (D) To introduce method of paddy cultivation

55.

Where does the coldest zone of climate lie ? (A) 30° – 45° N and S (B) 45° – 65° N and S

(C) 65° – 90° N and S

(D) 0° – 10° N and S

Which one is an important rabi crop ? (A) Paddy (B) Water melon

(C) Wheat

(D) Maize

56.

57.

Doldrums are belts of low atmospheric pressure obtained in the regions from the equator to a distance of(A) 5 degree latitude towards the north only (B) 5 degree latitude towards the south only (C) 5 degree latitude towards north and south (D) 15 degree latitude towards north and south

58.

The part of the Himalayas lying between Satluj and Kali rivers is known as (A) Kumaon Himalayas. (B) Assam Himalayas. (C) Punjab Himalayas. (D) Kashmir Himalayas.

59.

Bamboo drip irrigation is prevelant in which of the following state ? (A) Rajasthan (B) Meghalaya (C) Karnataka

60.

61.

The largest producing sector in 1973 was : (A) Primary Sector (C) Service Sector

(D) Madhya Pradesh

(B) Secondary Sector (D) None of the above

State focused more on human resource development is (A) West Bengal. (B) Tamil Nadu. (C) Kerala.

(D) Gujarat.

62.

The proportion of people living under poverty in different countries is called (A) international poverty line. (B) gross domestic product. (C) intra-world poverty line. (D) income of a country.

63.

The Panchayati Raj institutions in India are established as per Constitutional directions of the (A) Preamble (B) Directive Principles (C) Federalism (D) Fundamental Rights Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #7

64.

Rajya Sabha can delay the money bill for – (A) One mouth

65.

(B) Two month

(C) Six month

(D) 14 days

The State Legislative Assembly participates in the election of I. President II. Vice-President III. Members of Legislative Council of the State IV. Rajya Sabha (A) I, II and III

66.

(C) I and III

(D) I, II, III and IV

The right to seek advisory opinion of the Supreme Court on any question of law or fact belongs to (A) the President

67.

(B) I, III and IV

(B) High Courts

(C) the Governor

(D) all these

Where can impeachment proceedings against the President be initiated? (A) In Lok Sabha (B) At a joint sitting of the two Houses specially called for the purpose (C) In either House of Parliament (D) In the Supreme Court

68.

An important aspect of Hitler’s ideology related to political concert of living space was known as : (A) Lehnestorm

69.

(C) Lebrantin

(D) Lebensracim

A new form of organization developed in the 1905 Revolution was called – (A) Trade Union

70.

(B) Lebenstien

(B) Triple Alliance

(C) Soviets

(D) Mensheviks

The Non-Cooperation Movement in Awadh was led by (A) Baba Ramchandra.

(B) Bal Gangadhar Tilak.

(C) C.R.Das.

(D) Lala Lajpat Rai.

Direction (71 to 73) : Find the missing terms – 71.

2, 3, 6, 15, 45, ? (A) 135

(B) 135.5

(C) 157

(D) 157.5

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #8

72.

G, AD, BA, BH, CE, DB, ? (A) DI

73.

(B) DH

4

7

3

2

416

749

309

?

(A) 304 74.

(B) 104

(C) EI

(D) EH

(C) 204

(D) 404

If in any code language NATIONAL is written as MZGRLMZO than how is JAIPUR written in that language (A) QRZKFI

75.

76.

(B) QZRKFI

SUPER = 97, SUPREME = 79, LABOUR = ? (A) 79 (B) 96

(C) QZRFKI

(D) QZRIFK

(C) 89

(D) 49

If any two letters in the word PRISON have as many letters between them in the word as there are in the English alphabet, they form an alpha-pair. How many such alpha-pairs are there in the word PRISON ? (A) 4

77.

(B) 1

(C) 2

(D) 3

If the following scrambled letters are rearranged to form the name of a city, the city so formed is famous for its : AABHILRW (A) Locks

78.

(B) Steel Plant

(C) Temples

(D) Textile

Three persons A, B and C are Standing in a queue. There are five persons between A and B and eight persons between B and C. If there be three persons ahead of C and 21 persons behind A, what could be the minimum number of persons in the queue. (A) 41

79.

(B) 40

(C) 28

(D) 27

If + is x,– is +, x is  and  is –, then what is the value of given equation 21 ÷ 8 + 2 – 12 × 3 = ? (A) 14

(B) 9

(C) 13.5

(D) 11

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #9

Direction : (80 to 81) The following symbols have been used.

80.

x

Stands for equal to

<

Stands for not equal to

–

Stands for greater than

+

Stands for not greater than

>

Stands for less than

=

Stands for not less than

If p + q = r, then it is not possible that (A) p > q < r

81.

(B) p < q + r

(C) p × q > r

(D) p + q × r

(C) p > q + r

(D) p > q > r

If p = q = r, then it is possible that (A) p < q > r

(B) p × q × r

Direction : (82 to 84) Read the following information carefully and answer the questions given below it. (i) Seven books are placed one above the other in a particular way . (ii) The history book is placed directly above the civics book. (iii) The geography book is fourth from the bottom and the English book is fifth from the top. (iv) There are two books in between the civics and economics books. 82.

To find the number of books between the civics and the science books, which other extra piece of information is required, from the following ? (A) There are two books between the geography and the science books. (B) There are two books between the mathematics and the geography books . (C) There is one book between the English and the science books. (D) The civics book is placed before two books above the economics book.

83.

To know which three books are kept above the English book, which of the following additional pieces of information, if any, is required? (A) The economics book is between the English and the science books. (B) There are two books between the English and the history books. (C) The geography book is above the English book. (D) No other information is required.

84.

Which book is placed in the middle of the arrangement ? (A) History (B) Civics (C) Geography

(D) English

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #10

85.

Pointing to a man in a photograph, Anita said "His brother's father is the only son of my grandfather". How is the Anita related to the man in the photograph ? (A) Mother

86.

(B) Aunt

(C) Sister

(D) Daughter

‘A + B’ means ‘A is the son of B’, ‘A – B’ means ‘A is the wife of B’. ‘A × B’ means ‘A is the brother of B’, ‘A ÷ B’ means ‘A is the mother of B’, ‘A = B’ means ‘A is the sister of B’. Which of the following represents P is the maternal-uncle of Q ? (A) R × P ÷ Q

(B) P × R ÷ Q

(C) P + R ÷ Q

(D) P + R × Q

Direction : (87 to 90) Answer the questions based on the following information. All the roads of a city are either perpendicular or parallel to one another. The roads are all straight. Roads A, B, C, D and E are parallel to one another . Roads G, H, I, J, K, L and M are parallel to one another. I.

A is 1 km east of road B.

II.

B is 1/2 km west of C.

III. D is 1 km west of E. IV. G is 1/2 km south of H V. I is 1 km north of J. VI. K is 1/2 km north of L. VIII. K is 1 km south of M. 87.

88.

Which among the following is necessarily true? (A) E and B intersect

(B) D is 2 km west of B

(C) D is at least 2 km west of A

(D) M is 1.5 km north of L.

If E is between B and C, then which of the following is false? (A) D is 2 km west of A. (B) C is less than 1.5 km from D (C) Distance from E to B added to distance from E to C is 1/2 km. (D) E is less than 1 km from A.

89.

If E is between B and C, then distance between A and D is (A) 1/2 km

90.

(B) 1 km

(C) 1.5 km

(D) 1.5 to 2 km

Which of the following possibilities would make two roads coincide ? (A) L is 1/2 km north of I (B) C is 1 km west of D (C) I is 1/2 km north of K (D) E and B are 1/2 km apart. Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #11

91.

If it was Saturday on 17th November, 1962 what will be the day on 22nd November, 1964 ? (A) Monday (B) Tuesday (C) Wednesday (D) Sunday

92.

My watch was 8 minutes behind at 8 pm on Sunday but within a week at 8 pm on Wednesday it was 7 minutes ahead of time. During this period at which time this watch has shown the correct time : (A) Tuesday 10 : 24 am (B) Wednesday 9 : 16 pm (C) It cannot show the correct time during this period (D) None of the above

93. (i) (ii) (iii) Which number is opposite to number 2 ? (A) 4 (B) 6

(C) 5

(D) 3

(i) (ii) (iii) Which letter will come on the blank surface ? (A) C (B) A

(C) D

(D) E

94.

Direction : (95 to 96) Some equal cubes are arranged in the form of a solid block as shown in the adjacent figure. All the visible surfaces of the block (except the bottom) are then painted.

95.

96.

How many cubes do not have any of the faces painted ? (A) 27 (B) 8 (C) 10

(D) 12

How many cubes have one face painted ? (A) 9 (B) 24

(D) 20

(C) 30

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #12

97.

How many triangles are there in the figure ?

(A) 10

(B) 14

(C) 22

(D) 24

Directions (98): In the following question, there is a diagram marked (X), with one or more dots placed in it. The diagram is followed by four other figures, marked (A), (B), (C) and (D) only one of which is such as to make possible the placement of the alternative in each case.

98. (X)

(A)

(B)

(C)

(D)

Direction : (99) In the following question, there is a relationship between the two figures on the left of the sign (: :). The same relationship exists between the figures to the right of the sign (: :), of which one is missing. Find the missing one from the alternatives.

:

99.

(A)

::

:? (B)

(C)

(D)

Directions : (100) In the following question, there are figures of which three are similar in a certain way, and one is different. Find the one that is different from the rest.

100.

(A)

(B)

(C)

(D)

Space for rough work

NTSE_ STAGE-I _PRACTICE TEST PAPER-1_PAGE #13

ANSWERKEY NTSE(STAGE-I) CLASS-X PRACTICE TEST PAPER-1 Que s.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

Ans.

A

D

C

A

D

D

A

A

B

B

C

D

A

D

B

17

18

19

20

21

22

23

24

25

26

27

28

29

30

D

A

C

A

A

B

C

A

B

B

A

C

B

B

32

33

34

35

36

37

38

39

40

41

42

43

44

45

D

A

B

A

B

B

D

C

D

D

A

B

A

B

47

48

49

50

51

52

53

54

55

56

57

58

59

60

C

A

A

C

C

B

C

B

C

C

C

A

B

A

62

63

64

65

66

67

68

69

70

71

72

73

74

75

A

B

D

B

A

C

D

C

A

D

A

C

B

B

77

78

79

80

81

82

83

84

85

86

87

88

89

90

D

C

B

C

B

C

D

C

C

B

D

A

D

C

92

93

94

95

96

97

98

99

100

A

C

C

D

C

D

A

C

C

Que s. 16 Ans.

A

Que s. 31 Ans.

B

Que s. 46 Ans.

B

Que s. 61 Ans.

C

Que s. 76 Ans.

A

Que s. 91 Ans.

D