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. Marking Scheme for each questions

Correct Answer Wrong Answer

Section - I I.Q Q. No. 1 to 30 +3 -1

Section - II

Physics Q. No. 31 to 50 +3 -1

Chemistry Q. No. 51 to 70 +3 -1

Mathematics Q. No. 71 to 90 +3 -1

2. The Question Paper contains blank spaces for your rough work. No additional sheets will be provided for

rough work.

3. Blank papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic devices,

in any form, are not allowed.

4. Write your Name, Registration No. and Test Centre in the space provided at the bottom of this sheet.

5. 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) Page - 2

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

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?

3 4 2 6 5 4 3 6 4 5 9 8 6 4 5 3 8 7 4 6 8 2 1 7 6 4 5 8 6 4 5 9 7 4 5 (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. 2, 12, 36, 80, 150 ? (A) 194 (B) 210 (C) 252 (D) 258 6. 34, 18, 10, 6, 4, ? (A) 3 (B) 2 (C) 1 (D) 0 7. 3624, 4363, 3644, 4563, 3664, ? (A) 4763 (B) 3763 (C) 3624 (D) 6763 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

Page - 3 Sample Paper FTRE - PAPER - I – X (IQ, PCM)

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

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 (B) 18 (C) 21 (D) 20

I

E F

B C A

D G

J H

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

12

2

3

2 5 4 72 6

5

3 3

2

1

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 (C) 16 (D) 68 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



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

9

7

10

6 13

14

8

11

4

2

5

12

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



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 (B) B (C) C (D) D 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 (B) 0 2 l

4 R

(C) 0l

4 R

(D)

2

0I

4 R

O

θ I

R

I



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 :

P Q R S (A) 1 2 4 3 (B) 2 4 1 3 (C) 4 1 2 3 (D) 4 2 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 p

e

m

m = 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 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

d

A B C

1A 2A 3A

d



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° (B) 45° (C) 60° (D) 90°

45

0

water

air 60

0

r glass

air 45

0

300

glass

air 60

0

40. A light beam is traveling from Region I to Region

IV (Refer Figure). The refractive index in 4

Regions I, II, III and IV are n0, 0 0n n

,2 6

and 0n

8,

respectively. The angle of incidence θ for which the beam just misses entering Region IV is

(A) 1 3

sin4

(B) 1 1

sin8

(C) 1 1

sin4

(D) 1 1

sin3

Region I Region II Region III Region IV

0n

0n

2

0n

6

0n

8

0 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



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 q0 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

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

System 1 System 2 System 3 System 4 (A) ↑ → ← ↓ (B) ↓ ← → ↑ (C) ↑ → → ↓ (D) ↑ → ← ↑

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



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 (B) 2.5 (C) 3.0 (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

(B) 1

2

(C) 2

3

(D) 2

2a 2a

Q I

P

2 I

a a

50. Find the current through the battery when switch S is closed

(given R = 10 Ω) (A) 2A (B) 1A (C) 1/2 A (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

2 2 2 3 2FeS O Fe O SO

(A) 2,1,1,4 (B) 2,3,2,4 (C) 4,4,2,2 (D) 4,11,2,8 52. Conversion of sugar into CO2 is an example of (A) Oxidation only (B) Reduction only (C) Redox change (D)Physical change



53. Which of the following is the smallest in size (A) N3- (B) O2- (C) F- (D) Na+

54. The number of electrons that take part in forming the bond in N2 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 (D) 11,12 62. Identify the salt formed from strong acid and weak base (A) Na2SO4 (B) (NH4)2SO4 (C) CH3COONH4 (D) K2CO3 63. IUPAC name of chain isomer of butane is (A) 2-methyl butane (B) 2-methyl butane–2 (C) 2-methyl propane (D) 2,2-dimethyl propene

64. The molecule that deviates from octet rule is (A) NaCl (B) BF3 (C) MgO (D) NCl3 65. Which set has the strongest tendency to form anions? (A) Ga, In, Te (B) Na, Mg, As (C) N, O, F (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 C5H12: (A) 2 (B) 3 (C) 4 (D) 5 68. The compound with highest boiling point is



(A) n – hexane (B) n – pentane (C) 2,2 – dimethyl propane (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 θ θ θ θcosec 65 sec 25 tan 55 cot 35 is

(A) 0 (B) 1 (C) -1 (D) 2

72. If θ θ1

sec tan ,p

then

2

2

p 1

p 1

is

(A) θcos (B) θsin (C) θcosec (D) θsec

73. A round balloon of radius r

2subtends an angle α at the eye of the observer while the angle of elevation

of its centre is β2 , then the height of the centre of balloon is

(A) α

βr sin cosec2

(B) β

αr sin cosec2

(C) α

βr

cosec sin22 2

(D) α

βr

cosec sin2 2

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

1 1 1

p a b (B)

2 2 2

1 1 1

2p a b (C)

2 2 2

1 1 1

p a b (D) None of these



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

B

8 cm 10 cm

12 cm

A

C

F E

D

(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 2f x kx 4x 4 such that α β2 2 24, then

(A) 2

k 2 or k3

(B) 2

k 2 or k3

(C) 2

k 1or k3

(D) 2

k 1or k3

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 (D) -20

79. If n

1S nP n n 1 Q

2 where nS denotes the sum of the first n terms of an A.P., then the common

difference is (A) P + Q (B) 2P + 3Q (C) 2Q (D) Q

80. The coefficient of 99x 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 (D) None of these

81. If α β, are the zeros of the polynomial 2f x ax bx c, then α β2 2

1 1 is equal to

(A)

2

2

b 2ac

a

(B)

2

2

b 2ac

c

(C)

2

2

b 2ac

a

(D)

2

2

b 2ac

c

82. The value of x in the equation x 1 x 3 1

3 , x 2, 4x 2 x 4 3

is

(A) x = -5, 5/2 (B) 5, -5/2 (C) -5, -5/2 (D) 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) 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

1DB EC FA

(B) DB BE CF

1AD EC FA



(C) AD EC CF

1DB BE FA

(D) AD BE FA

1DB 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 A

x B

3 D

C 7

P

(A) 8 cm (B) 12 cm (C) 9 cm (D) 16 cm

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

S

Q

B R

P

A

(A) 20 cm (B) 25 cm (C) 22 cm (D) 24 cm

88. If α22cos 1 0 and α lies in 3rd quadrant, then the value of α αsin tan is

(A) 2 (B) -1 (C) 1

2 (D)

1

2

89. If the diagram shows the graph of

polynomial 2f x ax bx c, then

(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

2f(x) ax bx c

x

x’

y

b D,

21 4a

y’

90. If n is a natural number, then 2n 2n9 4 is always divisible by

(A) 5 (B) 13 (C) both 5 and 13 (D) None of these

x



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FTRE Sample Paper Class 10 to 11 Paper 1