FTRE Sample Paper Class 10 to 11 Paper 1

SAMPLE PAPER FOR PRACTICE

FIITJEE Talent Reward Exam For Class 10 going to 11 Paper 1 I.Q, Physics, Chemistry & Mathematics Time: 3 Hours

Maximum Marks: 270

Important Instruction Question Paper Code (Q.P Code as Mentioned on Top) MUST be correctly marked in the answer OMR sheet before attempting the paper. Mentioning wrong CODE or no CODE will give wrong results. 1. This Question Paper contains 5 Sections. All questions will be Multiple Choice questions out of four choices with marking scheme in table below: Section

Subject

Question Nos.

Section - I

I.Q Physics Chemistry Mathematics

Q. No. 1 to 30 Q. No. 31 to 50 Q. No. 51 to 70 Q. No. 71 to 90

Section - II

2. 3. 4. 5.

Marking Scheme for each questions Correct Answer Wrong Answer +3 -1 +3 -1 +3 -1 +3 -1

The Question Paper contains blank spaces for your rough work. No additional sheets will be provided for rough work. Blank papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices, in any form, are not allowed. Write your Name, Registration No. and Test Centre in the space provided at the bottom of this sheet. Answers have to be marked on the OMR sheet.

Name of the Candidate

:

______________________________________________________________

Exam Centre

:

_________________ Date of Examination : ________________________

Registration Number

:

______________________________________________________________

Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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Section –I

IQ

Straight objective Type This section contains 30 multiple choice questions numbered 1 to 30. Each question has 4 choices (A) (B), (C) and (D), out of which only one is correct. 1.

In the following number sequence how many 4’s are there that are immediately preceded by 6 and immediately followed by 5? 34265436459864538746821764586459745 (A) Two (B) Three (C) Four (D) none of these

2.

Given below is a sequence in which some letters are missing. From the choices, select the choice that gives the letters that can fill the blanks in the given series. (A) bbdcbac (B) bbcdabc (C) bcbbabc (D) bcdbabc

3.

If FISH is written as EHRG in a certain code, then how will JUNGLE be written in that code? (A) ITMFKD (B) ITNFKD (C) KVOHMF (D) TIMFKD

4.

If ‘air’ is called ‘green’, ‘green’ is called ‘blue’, blue is called ‘sky’ ‘sky is called ‘yellow’, ‘yellow’ is called ‘water’ and ‘water’ is called ‘pink’, then what is the colour of clear sky? (A) green (B) sky (C) pink (D) water Directions (Q.No. 5 to 7). In each of the following questions, a number series is given with one term missing. Choose the correct alternative that will continue the same pattern and replace the question mark in the given series.

5.

6.

7.

2, 12, 36, 80, 150 ? (A) 194

(B) 210

(C) 252

(D) 258

34, 18, 10, 6, 4, ? (A) 3

(B) 2

(C) 1

(D) 0

(C) 3624

(D) 6763

3624, 4363, 3644, 4563, 3664, ? (A) 4763 (B) 3763

8.

How many pairs of letters are there in the word ‘BUCKET’ which have as many letters between them in the word as in the alphabet? (A) One (B) Two (C) Three (D) Four

9.

In the certain code, RABBIT is RBDEMY, then HBRSISY is the code of (A) HAPPENS (B) HATTERS (C) HAPPINESS

(D) HAMBUGS

10. Pointing to a photograph Ramesh said, “She is the sister of my father’s mothers’s only child’s son” How is the person in the photograph related to Ramesh? (A) sister (B) Aunt (C)Mother (D)Cousin 11. Starting from his house Ram travelled 10m towards West, then turns towards the right and travels, 40m. He then travels 25m East followed by 50m towards the south to reach his college. What is the approximate distance between his house and the college? (A) 10m (B) 50m (C) 20m (D) 18m Regional Head Quarters FIITJEE TOWERS, No.3, First Lane, (Next to ApexPlaza), Nungambakkam High Road, Nungambakkam, Chennai – 600 034.

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

12. How is my sister’s husband’s father’s wife’s only daughter-in-law’s father related to me? (A) Brother (B) Uncle (C) Father (D) Cannot be deterimined 13.

Find the total number of triangles in the following figure

(A) 25 (C) 21

B

A

E

D

(B) 18 (D) 20

C

F

H

G

J

I

14. Looking into a mirror, the clock shows 9:30 as the time. The actual time is (A) 3 : 30 (B) 2 : 30 (C) 4 : 30

(D) 6 : 30

15. One night, three naughtly boys stole a basket full of apples from the garden, hid the loot and went to sleep. Before retiring they did some quick counting and found that the fruits were less than a hundred in number. During the night one boy awoke, counted the apples and found that he could divide the apples into three equal parts if he first took one for himself. He then took one apple, ate it up and took 1/3 of the rest, hid them separately and went back to sleep. Shortly thereafter, another boy awoke, counted the apples and he again found that if he took one for himself the loot could be divided into three equal parts. He ate up one apple, bagged 1/3 of the remainder, hid them separately and went back to sleep. The third boy also awoke after sometime, did the same and went back to sleep. In the morning, when all woke up and counted apples, they found that the remaining apples again totalled 1 more than what could be divided into three equal parts. How many apples did the boys steal? (A) 67 (B) 79 (C) 85 (D) none of these 16.

Study the pattern of the arrangement of numbers and find out how would you get the number in the middle using the four numbers around it. Hence find out, what number would come in place of “?” (A) 3 (B) 5 (C) 6 (D) 4

3

3

2

12

2

5

4

72

3 6

5

5

17. Which year will have the same calendar as that of 2001? (A) 2005 (B) 2006 (C) 2007

(D) 2009

18. If 9 * 3 = 729 and 5 * 4 = 625, then 8 * 2 = (A) 64 (B) 85

(D) 68

(C) 16

?

2

1

19. Among B, F, J, K and W each having a different weight. F is heavier than only J. B is heavier than F and W but not as heavy as K. Who among them is the third heaviest? (A) W (B) F (C) K (D) B 20. Unscramble the letters in the words given in this question and find the odd one out (A) UPJM (B) WKLA (C) PEELS (D) UNR

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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Directions (Q.No. 21 to 24) Six dice with their upper faces erased are as shown:

The sum of the numbers of dots on the opposite faces is 7.

21. If the dice I, II and III have even number of dots, on their bottom faces, then what would be the total number of dots on the top faces? (A) 7 (B) 12 (C) 14 (D) 21 22. If the dice I, II and III have even number of dots on their bottom faces and the dice IV, V and VI have odd number of dots on their top faces, then what would be the difference in the total number of top face dots between these two sets? (A) 0 (B) 1 (C) 2 (D) 3 23. If odd numbered dice have odd number of dots on their bottom faces, what would be the total number of dots on the top faces of these dice? (A) 4 (B) 6 (C) 10 (D) 12 24. If even numbered dice have even number of dots on their top faces, what would be the total number of dots on the top of these dice? (A) 18 (B) 14 (C) 12 (D) 10 Directions (Q.No.25 to 27) Answer the questions on the basis of the information given below. In the given diagram, the rectangle represents females, the triangle represents uneducated, the circle represents rural and the square represents teachers. Study the diagram carefully and answer the following questions

7 9 10

2 8

12

4 11

6

13 14

5

25. Who among the following is an uneducated female, who is not a rural resident? (A) 4 (B) 5 (C) 9

(D) 11

26. Who among the following is a male, who is rural resident and also a teacher? (A) 6 (B) 7 (C) 12

(D) 10

27. Who among the following is an uneducated female, who belongs to rural area? (A) 4 (B) 2 (C) 11

(D) 5

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

Directions (Q.No. 28 to 30) Answer the questions on the basis of the information given below: Four persons teach different subjects to students of different classes. B does not teach Mathematics and Science. C does not teach students of Standard I and IV. C does not teach Science. Students of Standard below IV are too young to learn computers. A teaches students of Standard III. B does not teach students of Standard II and IV. D and A donot teach English. Each person teaches a single subject. 28. Who teaches students of Standard II? (A) A (B) B

(C) C

(D) D

29. Who teaches English? (A) A

(C) C

(D) D

(B) B

30. C teaches which of the following subjects and to which standard? (A) Mathematics, III (B) English, I (C) Mathematics, II (D) Science, II

Section – II

PCM

Physics Physics contains 20 multiple choice questions numbered 31 to 50. Each question has 4 choices (A), (B), (C) and (D) out of which only one is correct.

31. Calculate the current shown by the ammeter A in the given circuit. (A) 3.6 A (B) 4.6 A (C) 5 A (D) 6 A

32. A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance R, to a 100 V mains as shown in the figure. What should be the value of R such that the heater may operate with a power of 62.5 W? (A) 2 Ω (B) 3 Ω (C) 5 Ω (D) 6 Ω 33. Magnetic field intensity B at the centre of the circular loop is (A) 0 (C)

 0 l 4 R

(B) (D)

0  2    l 4R 0I2     

O I

θ

R I

4R

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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34. Match list I with list –II for a concave mirror of focal length 20 cm, and select the correct answer using the code given below the list. List – I contains object distance and List II contains Nature of its image. COLUMN – I

COLUMN – II

P

10 cm

1

Magnified, inverted and real

Q

30 cm

2

Equal size, inverted and real

R

40 cm

3

Smaller, inverted and real

S

50 cm

4

Magnified, erect and virtual

Codes : (A) (B) (C) (D)

P 1 2 4 4

Q 2 4 1 2

R 4 1 2 3

S 3 3 3 1

35. A uniform electric field and a uniform magnetic field are present in the same direction. An electron is projected in this region with a velocity in the same direction. Therefore, (A) the velocity of electron will decrease in magnitude. (B) the velocity of electron will increase in magnitude. (C) the electron will turn to its right. (D) the electron will turn to its left. 36. When an electron and a proton enter at right angles to a uniform magnetic field. (Given that

mp me

= 1840)

Choose the INCORRECT statement. (A) rp = 1840 re when velocity is same (B) rp = re when momentum is same (C) rp = 43 re when kinetic energy is same (D) rp = 920 re when velocity is same A

37. Three infinite straight wires A, B and C carry currents as shown in figure. The resultant force on wire B per metre length is (A) 4μ0/πd towards A (B) 2μ0/πd towards C (C) 4μ0/πd towards C (D) zero

1A

B

C

2A

3A

d

d

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

38. A point source of light B is placed at a distance L in front of the centre of a mirror of width d hung vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror at a distance 2L from it as shown. Find the greatest distance over which he can see the image of the light source in the mirror. (A) 2d (B) 3d (C) 4d (D) none

39. Analyze following figures and find ‘r’. (A) 30° (C) 60°

0

0

30

glass

(B) 45° (D) 90°

air

40. A light beam is traveling from Region I to Region IV (Refer Figure). The refractive index in 4

air

0

60

3  4  1 (B) sin1   8 1  1  (C) sin   4 1  1  (D) sin   3 (A) sin1 

n0

Region II



n0 2

0

0

r

glass

air

60

Region I

n n n Regions I, II, III and IV are n0, 0 , 0 and 0 , 2 6 8 respectively. The angle of incidence θ for which the beam just misses entering Region IV is

45

water

0

45

Region IV

Region III

n0 8

n0 6

0.2m

0.6m

41. The near point of a hyper metropic eye is 1 m. The near point of the normal eye is 25 cm. The power of the lens required to correct this defect is P dioptre. Determine P. (A) 4.0 (B) 3.0 (C) 2.0 (D) 0.5

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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42. The diagram shows four systems of charged particles. Each system contains two charged particles at point A and point B as shown in the figure. A third point charge q 0 is kept at point P in each system. The direction of electrostatic force experienced by the charge q0 will be

System 1; AP = BP = r and AB is a straight line

(A) (B) (C) (D)

System 1 ↑ ↓ ↑ ↑

System 2; AP = BP = r and AB is a straight line

System 3; AP = BP = r and AB is a circular arc of radius r and centre at P

System 2 → ← → →

System 3 ← → → ←

43. The instrument for measuring a potential difference is (A) voltmeter (B) voltammeter (C) ammeter

System 4; AP = BP = r and AB is a circular arc of radius r and centre at P

System 4 ↓ ↑ ↓ ↑ (D) none of these

44. Of the following, the copper conductor that has the least resistance is (A) thin, long and hot (B) thick, short and cool (C) thick, long and hot (D) thin, short and cool 45. An certain resistor dissipates 0.5 W when connected to a 3 V potential difference. When connected to a 1 V potential different, this resistor will dissipate : (A) 0.5 W (B) 0.167 W (C) 1.5 W (D) 0.056 W 46. Constant current is sent through a helical coil. The coil: (A) tends to get shorter (B) tends to get longer (C) tends to rotate about its axis (D) produces zero magnetic field at its center 47. A current is flowing in a circular loop of wire in clockwise direction. The magnetic field at the centre of the wire is (A) directed perpendicularly downward to the plane of loop. (B) zero (C) directly proportional to the radius of the loop (D) directed perpendicularly upward to the plane of loop

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

48. There are four mediums, separated by three parallel interfaces as shown in the figure. An incident ray strikes on the point A of first medium with angle of incidence 60° and emerges from point C as shown in the figure. Find the value of

1  2 , 1  2

(A) 2.0 (C) 3.0

(B) 2.5 (D) 4.0

49. Two infinite long wires are carrying current 2I and I respectively as shown in the figure. Find the ratio of magnitude of magnetic field at Q to P (A) 1

P I Q

1 2 2 (C) 3

2I

(B)

a

a

(D) 2 2a

2a

50. Find the current through the battery when switch S is closed (given R = 10 Ω) (A) 2A (C) 1/2 A

(B) 1A (D) 1/4 A

Chemistry Chemistry contains 20 multiple choice questions numbered 51 to 70. Each question has 4 choices (A), (B), (C) and (D) out of which only one is correct. 51. The correctly balanced coefficients for the following reaction will be

FeS2  O2  Fe2O3  SO2 (A) 2,1,1,4

(B) 2,3,2,4

52. Conversion of sugar into CO2 is an example of (A) Oxidation only (B) Reduction only

(C) 4,4,2,2

(D) 4,11,2,8

(C) Redox change

(D)Physical change

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Sample Paper FTRE - PAPER - I – X (IQ, PCM) 53. Which of the following is the smallest in size (A) N3(B) O2-

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(C) F-

(D) Na+

54. The number of electrons that take part in forming the bond in N 2 is (A) 2 (B) 6 (C) 10

(D) 3

55. The pH of baking soda solution is (A) > 7 (B) < 7

(C) 7

(D) 0

56. Which of the following is an acid salt? (A) Na2S (B) Na2SO3

(C) NaHSO3

(D) Na2SO4

57. The first ionization potential of Na, Mg, Al and Si are in the order of (A) Na < Mg > Al < Si (B) Na > Mg > Al > Si (C) Na < Mg < Al > Si (D) Na > Mg > Al < Si 58. In the reaction, 3Cl2 + 6NaOH   NaClO3 + 5NaCl + 3H2O, which element loses as well as gains electrons? (A) Na (B) O (C) Cl (D) None 59. Which of the following is a member of alkyne family? (A) C7H14 (B) C10H22 (C) C9H16

(D) C16H12

60. The pH of a solution is 5.0. Its hydrogen ion concentration is decreased 100 times, the solution then will be (A) More acidic (B) Basic (C) Neutral (D) Of the same acidity 61. Identify the pair of elements (At no.) representing s-block elements? (A) 7,15 (B) 9,17 (C) 2,10 62. Identify the salt formed from strong acid and weak base (A) Na2SO4 (B) (NH4)2SO4 (C) CH3COONH4 63. IUPAC name of chain isomer of butane is (A) 2-methyl butane (B) 2-methyl butane–2 (C) 2-methyl propane 64. The molecule that deviates from octet rule is (A) NaCl (B) BF3

(C) MgO

65. Which set has the strongest tendency to form anions? (A) Ga, In, Te (B) Na, Mg, As (C) N, O, F

(D) 11,12

(D) K2CO3 (D) 2,2-dimethyl propene

(D) NCl3

(D) V, Cr, Mn

66. Silicon has 4 electrons in the outer most orbit. In forming the bond: (A) It gains electrons (B) It looses electrons (C) It shares electrons (D) Either (A) or (B) 67. The number of chain isomers possible for a molecule having molecular formula C 5H12: (A) 2 (B) 3 (C) 4 (D) 5 68. The compound with highest boiling point is Regional Head Quarters FIITJEE TOWERS, No.3, First Lane, (Next to ApexPlaza), Nungambakkam High Road, Nungambakkam, Chennai – 600 034.

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

(A) n – hexane (C) 2,2 – dimethyl propane

(B) n – pentane (D) 2-methyl butane

69. The metal used as a catalyst for the hydrogenation of unsaturated hydrocarbon is (A) Ni (B) Cr (C) V (D) Zn 70. The pH of a solution formed by mixing 40 mL of 0.10 M HCl with 10 mL of 0.45 M of NaOH is (A) 10 (B) 12 (C) 8 (D) 6

Mathematics Straight Objective Type Mathematics contains 20 multiple choice questions numbered 71 to 90. Each question has 4 choices (A), (B), (C) and (D) out of which only one is correct. 71. The value of cosec  65  θ   sec  25  θ   tan 55  θ   cot 35  θ  is (A) 0

(B) 1

(C) -1

(D) 2

1 p2  1 is , then 2 p p 1 (A) cos θ (B) sin θ (C) cosecθ (D) secθ r 73. A round balloon of radius subtends an angle α at the eye of the observer while the angle of elevation 2 of its centre is 2β, then the height of the centre of balloon is 72. If sec θ  tan θ 

(A) r sin β cos ec (C)

α 2

β cos ecα 2 r α (D) cos ec sin β 2 2 (B) r sin

r α cos ec sin2β 2 2

2 74. If D is a point on the side BC of ΔABC such that ADC  BAC, then CA is

(A) CB  CD

(B) AB  CD

(C) AD  CD

(D) BD  DC

75. ABC is a right triangle right angled at C. Let BC = a, CA =b, AB = c and let p be the perpendicular length from C on AB, then (A)

1 1 1  2  2 2 p a b

(B)

1 1 1  2  2 2 2p a b

(C)

1 1 1  2  2 2 p a b

(D) None of these

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76. A circle is inscribed in a triangle ABC having sides 8 cm, 10 cm and 12 cm as shown in the figure. Then AD, BE and CF are

C F

E

10 cm

8 cm



A

B

D 12 cm

(A) 7, 5, 3

(B) 10, 5, 7

(C) 5, 3, 7

(D) 3, 5, 7

77. If α and β are the zeros of the quadratic polynomial f  x   kx2  4x  4 such that α2  β2  24, then

2 3 2 (C) k  1 or k   3

2 3 2 (D) k  1 or k  3

(A) k  2 or k 

(B) k  2 or k  

78. If the H.C.F. of 210 and 55 is expressible in the form 210  5  55y, then y is (A) 19 (B) 20 (C) -19 79. If Sn  nP 

(D) -20

1 n  n  1 Q where Sn denotes the sum of the first n terms of an A.P., then the common 2

difference is (A) P + Q

(B) 2P + 3Q

(C) 2Q

(D) Q

99

80. The coefficient of x in (x + 1) (x + 3) (x + 5) … (x + 199) is (A) 1 + 2 + 3 + … + 99 (B) 1 + 3 + 5 + … + 199 (C) 1 . 3 . 5 . …. . 199 81. If α, β are the zeros of the polynomial f  x   ax2  bx  c, then (A)

b2  2ac a2

(B)

82. The value of x in the equation (A) x = -5, 5/2

b2  2ac c2

(C)

(D) None of these

1 1 is equal to  α2 β2

b2  2ac a2

(D)

b2  2ac c2

x 1 x  3 1   3 , x  2, 4 is x2 x4 3

(B) 5, -5/2

(C) -5, -5/2

83. The 8th term from the end of the A.P. 7, 10, 13, …, 184 is (A) 161 (B) 162 (C) 163

(D) 5, 5/2

(D) 164

84. In a triangle ABC, O is a point inside of it. Bisectors of AOB, BOC and COA meet in sides AB, BC and CA at points D, E and F respectively. Which of the following is correct? (A)

AD BE CF   1 DB EC FA

(B)

DB BE CF   1 AD EC FA

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(C)

Sample Paper FTRE - PAPER - I – X (IQ, PCM)

AD EC CF   1 DB BE FA

(D)

AD BE FA   1 DB EC CF

85. If in a right angled triangle ABC, B  90, AC = 10 cm and radius of incircle is 1 cm, then the perimeter of the triangle is (A) 20 cm (B) 22 cm (C) 24 cm (D) 26 cm

86. In the given figure, PAB and PCD are two secants and PA = 5 cm, AB = x cn, PC = 7 cm and CD = 3cm. The value of x is

5



P 7

(A) 8 cm

B

x

A

(B) 12 cm

C

3

(C) 9 cm

D

(D) 16 cm A

87. In the given figure, PA, PB and QR are the tangents on the circle at point A, B and S respectively, Q and R are the points at PA and PB respectively. If PA = 12 cm, then the perimeter of ΔPQR is

Q 

S

P

R

(A) 20 cm

(B) 25 cm

(C) 22 cm

B

(D) 24 cm

2 88. If 2cos α  1  0 and α lies in 3rd quadrant, then the value of sin α tan α is

(A)

2

(B) -1

(C)

1

(D)

2

1 2

y

89. If the diagram shows the graph of

polynomial f  x   ax2  bx  c, then

x

 b D   21, 4a   

(A) a < 0, b < 0 and c < 0 (B) a > 0, b < 0 and c > 0 (C) a < 0, b > 0 and c > 0 (D) a < 0, b > 0 and c < 0

x’

x

f(x)  ax2  bx  c

90. If n is a natural number, then 9  4 (A) 5 (B) 13 2n

2n

is always divisible by (C) both 5 and 13

y’

(D) None of these

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Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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Regional Head Quarters FIITJEE TOWERS, No.3, First Lane, (Next to ApexPlaza), Nungambakkam High Road, Nungambakkam, Chennai – 600 034.