FTRE Sample Paper Class 11 to 12 Paper 1

SAMPLE PAPER FOR PRACTICE

FIITJEE Talent Reward Exam For Class 11 going to 12

Paper 1 IQ, Physics, Chemistry, Mathematics & Biology

Time: 3 Hours Maximum Marks: 198

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

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

Section - IV 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 –V (IQ, PCBM) Page - 2

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

IQ Section – I

Part – A Single Answer Questions

Direction (Question 1 – 3) : A pyramid of letters is given below. Study the pyramid and select the correct

alternative to fill in the missing term.

1. LBQF, UXYL, GTRM,? (A) HEVO (B) DSXT (C) VEOG (D) IUXY 2. ZWOHL, BQFLM, GTRMQ, ? ESJGZ (A) OXCQG (B) HESFR (C) OCXCQ (D) XCJQG 3. PJXZM, LBQZG, ? (A) DQZYS (B) AUCBO (C) UACBO (D) DZWYS 4. (i) P + Q means ‘P is the father of Q’. (ii) P Q means ‘P is the brother of Q’. (iii) P – Q means ‘P is the wife of Q’. (iv) P + Q means ‘P is the mother of Q’, then answer the following question. If P – R + Q, which of the following statements is true? (A) P is the mother of Q (B) P is the aunt of Q (C) P is the sister of Q (D) P is the brother of Q

5. A is the father of C and D is the son of B. E is the brother of A. If C is the sister of D, how is B related to

E? (A) Daughter (B) Brother – in – law (C) Husband (D) Sister – in – law 6. Manish went 15 km from his house to the North. Then, he turned West and covered 10 km. Then, he

turned South and covered 5 km. Finally, turning to East, he covered 10 km. Then, he turned South and covered 5 km. In which direction is he from his house?

(A) East (B) West (C) North (D) South

Page - 3 Sample Paper FTRE - PAPER - I –V (IQ, PCBM)


Directions (Question 7) : Insert the missing letter from among the given alternatives.

7.

(A) U (B) W (C) V (D) X Directions (Question 8) : In this question, certain pairs of words are given out of which the words in all

pairs except one, bear a certain common relationship. Choose the pair in which the words are differently related.

8. (A) Donald : Comedy (B) Holmes : Suspense (C) Premchand : Novel (D) Robinson : Adventure 9. In a unit test, Parth’s marks in Mathematics are more than his marks in History but not more than

Geography. His marks in Science are more than that in History but not as much as in Mathematics and his marks in English are not as much as in Geography. In which of the given subjects did he score the lowest?

(A) History (B) English (C) Science (D) Data inadequate 10. A clock buzzes 1 time at 1 o’ clock, 2 times at 2 o’clock, 3 times at 3 o’clock and so on. What will be the

total number of buzzes in a day? (A) 150 (B) 156 (C) 100 (D) None of these 11. What will be the angle between the hour hand and the minute hand, if a clock shows 8 : 30 pm? (A) 90° (B) 75° (C) 60° (D) 85° Directions (Questions 12 – 14): In the following diagram, the square represents girls, the circle represents

tall persons, the triangle is for chess players and the rectangle stands for singers. On the basis of the given diagram, answer the following questions.

12. Which letter represents tall girls who are singers but do not play chess? (A) C (B) D (C) G (D) H



13. Which letter represents tall girls who do not play chess and are not singers? (A) C (B) D (C) E (D) G

14. Which letter represents tall persons who are gents and singers but do not play chess? (A) I (B) J (C) K (D) L

Directions (Questions 15 – 16) : In these questions, there are statements followed by two or three

conclusions. You have to take the given statements to be true, even if they seem to be at variance from commonly known facts and then decide, which of the given conclusions logically follow from the given statements.

15. Statements :

Some pictures are frames. Some frames are idols. All idols are curtains. Conclusions :

I. Some curtains are pictures. II. Some curtains are frames. III. Some idols are frames. (A) I and II follows (B) II and III follow (C) I and III follow (D) All follow 16. Statements :

All dolls are cute. All cute are humans. Conclusions :

I. All dolls are humans. II. No cute can be a doll. (A) Only I follows (B) Only II follows (C) Neither I nor II follows (D) Both I and II follow Directions (Question 17) : In this question, five problem figures are given. Select a figure from the answer

figures which will continue the same series as given in the problem figure. Problem Figures

17.

Answer Figures



Directions (Question 18) : This question consists of two sets of figures. Figures (1), (2), (3) and (4)

constitute the problem set while (A), (B), (C) and (D) constitute answer sets. There is a definite relationship between figure (1) and (2), establish a similar relationship between figures (3) and (4) by choosing a suitable figure from answer set.

18

.

Directions (Questions 19 – 23) : Read the following information and answer the questions.

Seven dignitaries – F, G, H, I, N, O and P are to be seated together at a diplomatic ceremony. They will be seated in a row of seven chairs, numbered from 1 to 7, from front to back. Any seating is acceptable as long as all seven dignitaries are seated, one on each chair, and the seating conforms to the following rules :

I. F must sit on the chair immediately behind O’s chair. II. G cannot sit on the chair immediately in front of N’s chair and G cannot sit on the chair immediately

behind N’s chair. III. There must be exactly two chairs between the chairs of H and P. IV. There must be at least one chair between the chairs of I and P. V. N must sit on chair 3.

19. Which of the following seating arrangement, from chair 1 through chair conforms to the rules? (A) F, I, N, P, G, O, H (B) G, P, N, I, H, O, F (C) I, G, N, P, O, F, H (D) I, H, N, P, O, F, G 20. If F sits on chair 6 and H sits on chair 7, which of the following dignitaries must sit on chair 2? (A) G (B) I (C) N (D) O 21. If the seating arrangement, from chair 1 through chair 7, is G, I, N, H, O, F, P which of the following

pairs of dignitaries can interchange seats without violating the rules? (A) F and G (B) G and H (C) G and I (D) H and P 22. If O sits on chair 1 and H sits on chair 7, then the number of chairs between F’s chair and I’s chair must

be: (A) zero (B) one (C) two (D) three 23. If H sits in chair 4 and F sits in chair 6, then the dignitaries in chairs 1 and 7, respectively, must be: (A) G and O (B) G and P (C) I and P (D) I and I Directions (Questions 24 – 27) : Answer the questions on the basis of the following information.



The plan above shows an office block of six officers A, B, C, D, E and F. Both B and C occupy offices to

the right of the corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices an opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s but on the same side.

24. If E sits in his office and faces the corridor, whose office is to his left? (A) A (B) B (C) C (D) D 25. Whose office faces A’s office? (A) B (B) C (C) D (D) E 26. Who is / are F’s neighbor(s)? (A) A only (B) A and D (C) D only (D) B and C 27. D was heard telling someone to go further down the corridor to the last office on the right. To whose

room was he trying to direct that person? (A) A (B) B (C) C (D) F

Directions (Questions 28 – 30) : Read the following information and answer the questions based on them :

A pastry chef, who is visiting a culinary school, wishes to schedule three classes on pastry making – one at 10 am, one at 2 pm and one at 6 pm. Eight student chefs – Q, R, S, T, W, X, Y and Z – who have registered to attend class will each be assigned to one of the three classes. Each class will contain either two or three student chefs. The assignment of student chefs to each class must conform to the following conditions :

I. Q must be assigned to a class to which only one other student is assigned. II. R must be assigned to the same class as Y. III. S must not be assigned to the same class as X. IV. T must be assigned to either the 10 am class or the 6 pm class. V. X must be assigned to a class that meets earlier in the day that the class to which W is assigned.



28. Which of the following is a possible assignment of students to the classes?

10 am 2 pm 6 pm

(A) Q, X R, T, Z S, W, Y

(B) Q, W R, X, Y S, T, Z

(C) R, X, Y S, W, Z Q, T

(D) R, X, Y Q, S, W T, Z

29. If S and Q are assigned to the 6 pm class, which of the following must be the group of students

assigned to the 10 am class? (A) R, T, Y (B) R, Y, Z (C) T, W, Z (D) T, X, Z 30. If Q and Z are assigned to the 10 am class, which of the following must be the group of students

assigned to the 6 pm class? (A) R, T, Y (B) R, W, Y (C) S, T, W (D) S, T, X

Physics Section – II

Part – A

Single Answer Questions

31. If the dimension of length is expressed as Gxcyhz where G, c and h are the universal gravitational constant, speed of light and planck’s constant respectively then the value of x will be

(A) 1

2 (B)

3

2 (C) 1 (D)

3

2

32. Acceleration of centre of mass of disc will be greater if (A) friction is absent between disc and surface (B) Friction is present between disc and surface (C) Acceleration of the disc is independent of friction between

disc and surface (D) None of these

F

33. A ball of mass 1 kg moving with velocity i

ˆ ˆV 3i 4j r

collides with the wall and after collision its

velocity is f

ˆ ˆV 2i 6j r

. Which of the following unit vector is perpendicular to wall?

(A) 1 ˆ ˆ3i 4 j5

(B) 1 ˆ ˆ5i 2j29

(C) 1 ˆ ˆ2i 6j40

(D) 1 ˆ ˆ5i 2j29

34. A particle moves with a velocity ˆ ˆ ˆV 5i 3j 6k r

m/s under the influence of a constant force

ˆ ˆ ˆF 10i 10j 20kN r

. The instantaneous power applied to the particle is

(A) 200 J/s (B) 40 J/s (C) 140 J/s (D) 170 J/s 35. Two waves get superposed on a string y1 = 3 sin (2πx + 20πt) where x, y1 and y2 are in meter and t in

second. Then the distance between two adjacent nodes on the string is (A) 25 cm (B) 50 cm (C) 75 cm (D) 100 cm



36. Which of the following represent a traveling wave?

(A) A

yx Vt

(B) y = A sin (ax + Vt) (C) y = Alog (x – Vt) (D) y = A(x2 – Vt2)

37. The resultant of Ar

and Br

makes angle α with Ar

and β with Br

, then choose from the following the correct option.

(A) α < β (B) α < β if A < B (C) α < β if A > B (D) α < β if A = B 38. The ratio of radii of curvature at the point of projection and highest point for maximum

horizontal range is

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

2 (D)

1

2

39. A solid sphere is rolling without slipping on rough ground as shown in figure. It collides elastically with an identical sphere B at rest. There is no friction between two spheres. Radius of each sphere is R and mass is m. Then linear velocity of first sphere after it again starts pure rolling is

(A) 2

R5 (B)

2R

7

(C) 7

R10

(D) 7

R5

A

ω

B

40. A man swims to and fro along the bank of a river with a velocity v relative to water. If the velocity of flow is u, the average speed of the man (for to and fro motion) is

(A) 0 (B) uv (C) u v

2

(D)

2 2v u

v

41. T –x graph for an accelerating rod

placed on smoothhorizontal surface

Stress = T

smooth

x

F



(A) (B) (C) (D) 42. A long capillary tube of mass π gram, radius 2 mm and negligible thickness is partially immersed in a liquid of surface tension 0.1 N/m. Take angle of contact zero and neglect buoyant force of liquid. The force required to hold the tube vertically will be (g = 10 m/s2) (A) 10.4 π mN (B) 10.8π mN (C) 0.8π mN (D) 4.8π mN

43. Find the minimum value of mass

of hanging block so that kg block slips over 4 kg block.

(A) 30 kg (B) 20 kg (C) 10 kg (D) 2 kg block will not slip over

4kg for any value of mass M

T

x O

T

O

T

x

M

4 kg

2 kg

T

x x O O



44. A small block is given a velocity V along the incline in the downward direction at the highest point on an inclined plane, then block moves with constant velocity. After reaching at lowest point, block is given same speed V up the incline. Find time taken by block to reach the lowest point again. (Assume v ≤ 2

g sinl )

(A) 2

v

l

(B)

2v

l

(C) gsin

l

(D) it will not return

45. A particle of mass m is at a distance 2R from the centre of a thin spherical shell of mass M and having radius R as shown in figure. The gravitational field at the centre of shell is

(A) zero (B) 2

GM

R

(C) 2

G(M m)

4R

(D)

2

GM

4R

46. A bob of mass m is in equilibrium with the help of two inextensible strings connected to fixed support. The bob is slightly displaced perpendicular to the plane of figure and released. The time period of oscillation of bob is

(A) 2g

l

(B) d

2g

(C) d

2g

l (D)

2 24 d2

2g

l

47. A spring mass system hanging from the ceiling of an elevator is at rest. The elevator starts accelerating upward with acceleration a. Choose from the correct alternative

(A) Amplitude of oscillation is ma

k

(B) Amplitude of oscillation is mg

k

(C) Time period of oscillation is 2

m2

k

(D) Time period of oscillation is 2m

2k

k

a

m



48. Two spheres of specific gravity 0.8 & 1.6 are of equal size and are connected through string & placed in liquid container as shown in figure, if spheres are in equilibrium with respect to container then tension in the string will (take volume of each sphere V0 = 250 CC) (A) 1N (B) 2N (C) 3N (D) none of these

49. A train having 60 wagons each weighing 25 ton is moving with a speed of 72 km/hr, if the frictional force is 10N per ton, the power developed is :

(A) 3 × 105 W (B) 3 × 106 W (C) 3 × 107 W (D) 3 × 104 W 50. A solid sphere of mass m is released from the height 4r above the ground level on a rough track (Sufficient to prevent slipping) shown in the figure. The track ends in the form of a circular arc of radius r. Find the speed of the sphere when it reaches the point Q.

(A) 10gr

7 (B)

30gr

7

(C) 50gr

7 (D) 10gr

Chemistry Section – III

Part – A


51. Which of the following contains maximum number of atoms? [At. Wt: Na = 23, Al = 27, He = 4, Mg = 24] (A) 2 gram sodium (B) 2 gram aluminium (C) 2 gram helium (D) 2 gram magnesium 52. The principal quantum number of an orbit of hydrogen atom is 3. How many maximum number of

subshells are associated with the orbit? (A) 6 (B) 3 (C) 9 (D) 4 53. Which of the following molecule experiences the lowest bond pair-bond pair repulsion? (A) BCl3 (B) BeCl2 (C) CCl4 (D) NCl3 54. Addition of which of the following ion can increase the temperature of water by maximum extent? (A) Mg2+ (B) Ca2+ (C) Be2+ (D) Na+ 55. By how many times will the most probable velocity of an ideal gas increase by increasing the

temperature two times of its initial value?

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

56. Which of the following oxides contains the central atom at its highest oxidation state? (A) CO2 (B) NO2 (C) SO2 (D) N2O3



57. The following reaction is accompanied with evolution of -68 kJ mol-1 energy.

2 2 3N (g) 3H (g) 2NH (g) .Therefore, the heat of formation of NH3(g) is:

(A) -22.66 kJ mol-1 (B) -68 kJ mol-1 (C) -34 kJ mol-1 (D) -136 kJ mol-1 58. For which of the following reversible reaction the equilibrium constant Kp> Kc?

(A) 2 2N (g) O (g) 2NO(g) ƒ (B) 2 22NO(g) O (g) 2NO (g) ƒ

(C) 2 4 2N O (g) 2NO (g)ƒ (D) 2 2 2 54NO (g) O (g) 2N O (g) ƒ

59. 22Pb(OH) (aq) Pb (aq) 2OH (aq)ƒ

Addition of which of the following substance increase the solubility of Pb(OH)2 according to above reaction

(A) NH4Cl (B) PbCl2 (C) NaCl (D) KCl 60. Which of the following substance reacts with hydrogen through formation of free radical intermediates? (A) Sulphur (B) Phosphorus (C) Chlorine (D) Sodium 61. Which of the following substance is used to distinguish between BaCl2 and MgCl2? (A) HCl (B) H2SO4 (C) NaNO3 (D) NH4Cl 62. Which of the following substance on heating forms a coloured gas along with other products? (A) Li3N (B) NaNo3 (C) LiNO3 (D) KNH2 63. Which of the following reaction does not form boron?

(A) 2B H

(B) 3Bl

(C) 3 2BCl H

(D) 3 3H BO

64. The most thermally unstable halide of carbon is: (A) CF4 (B) CCl4 (C) CBr4 (D) Cl4 65. What is the hybridization of oxygen in OF2? (A) sp (B) sp2 (C) sp3 (D) sp3d 66. The most basic compound out of the following is:

(A)

(B)

(C)

(D)

67. Which of the following compound has maximum acidic strength? (A) HO—CH2—CH2—CH2COOH (B) O2N—CH2—CH2—CH2COOH (C) Cl—CH2—CH2—CH2COOH (D) H2N—CH2—CH2—CH2COOH



68. Which of the following reaction does not produce ethylene (CH2 = CH2)?

(A) CH3CH2Cl Alcohol /KOH

(B) 2Conc. H SO

3 2 180°CCH CH OH

(C) 2H /NiHC CH (D)

Zn2 2ClCH CH Cl

69. Which of the following reagent can distinguish between CH3CH2CH=CH2 and CH3CH2C CH? (A) Br2/CCl4 (B) AgNO3/NH4OH (C) HCl2O (D) NO2Cl 70. Which of the following substance on ozonolysis reaction forms acetone?

(A)

(B)

(C)

(D)

Mathematics Section – IV

Part – A


71. If na 7 7 7 ..... having n radical signs then by methods of mathematical induction

which of the following is true

(A) na 7 n 1 (B)

na 3 n 1 (C) na 4 n 1 (D)

na 3 n 1

72. If the 6th term in the expansion of

8

2

108

3

1x log x

x

is 5600, then value of x is

(A) 2 (B) 5 (C) 10 (D) 10

73. If O is the origin and the line OP of length r makes an angle with x – axis and lies in the XZ plane,

then the coordinate of P are

(A) r cos ,0,r sin (B) r sin ,0,r cos

(C) 0,sin ,r cos (D) r cos ,r sin ,0



74. If (1+3+5+………+P) + (1+3+5+………+q) = (1+3+5+………..+r) where each set of parentheses contains

the sum of consecutive odd integers as shown, the smallest possible value of p + q + r, (where p > 6) is (A) 12 (B) 21 (C) 45 (D) 54

75.

3

3xx

4

1 cot xlim

2 cot x cot x

is

(A) 11

4 (B)

3

4 (C)

1

2 (D) none of these

76. The point 2at ,2bt lies on the hyperbola

2 2

2 2

x y1

a b for

(A) All real values of t (B) 2t 2 5 (C)

2t 2 5 (D) no real value of t

77. Given the following frequency distribution with some missing frequencies

Class 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 - 80

Frequency 180 ---- 34 180 136

50

If the total frequency is 685 and median is 42.6 then the missing frequencies are (A) 81,24 (B) 80,25 (C) 82, 23 (D) 832, 22 78. The only statement among the following that is a tautology is

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

79. The general solution of the trigonometrical equation sinx cosx 1 is

(A) x 2n ,n I (B) x 2n ,n I2

(C) n

x n 1 ,n I4 4

(D) none of these

80. Let z be a complex number such that the imaginary part of z is non zero and 2a z z 1 is real. Then

a cannot take the value

(A) -1 (B) 1

3 (C)

1

2 (D)

3

4 81. The equation of the circle passing through the point (1,0) and (0,1) and having the smallest radius is

(A)2 2x y 2x 2y 1 0 (B)

2 2x y x y 0

(C) 2 2x y 2x 2y 7 0 (D)

2 2x y x y 2 0

82. Let I be the set of integers, N the set of Non – Negative integers; pN the set of non-positive integers, E

is the set of even integers and P is set of prime numbers. Then



(A) pN N (B)

pI N N (C) pN N 1 0 (D) E P

83. If P (X) = 2ax bx c and 2Q x ax dx c, where a, b, c R, then P x Q x 0 has

(A) no real root (B) exactly two real roots (C) at least two real roots (D) none of these 84. There are three piles of identical yellow, black and green balls and each pile contains at least 20 balls.

The number of ways of selecting 20 balls if the number of black to be selected is twice the number of yellow balls is

(A) 6 (B) 7 (C) 8 (D) 9 85. Three distinct points A, B, C, are given in the two dimensional coordinate plane such that the ratio of the

distance of anyone of them from the point (1,0) to the distance from the point (-1,0) is equal to 1/3. Then the circum centre of the triangle ABC is at the point

(A) 5

,02

(B) 5

,03

(C) (0,0) (D) 5

,04

86. The eccentricity of an ellipse with its centre at the origin is ½. If one of the directrix is x = 4, then the

equation of the ellipse is

(A) 2 24x 3y 12 (B)

2 23x 4y 12 (C) 2 23x 4y 1 (D)

2 24x 3y 1

87. The focus of the parabola 24y 12x 20y 67 0 is

(A) 7 5

,2 2

(B) 3 5

,4 2

(C) 17 5

,4 2

(D) 5 3

,2 4

88. Two numbers x and y are chosen at random without replacement from the first 30 natural numbers. The

probability that 2 2x y is divisible by 3 is

(A) 3

29 (B)

3

55 (C)

5

29 (D)

47

87

89. If 0sin32 k and

2cosx 1 2k ; , are the values of x between 0 00 and360 with , then

(A) 0180 (B)

0200 (C) 04 40 (D)

05 20

90. For a regular polygon, let r R be the radii of the inscribed and circumscribed circles. There is no regular

polygon with

(A) r 2

R 3 (B)

r 3

R 2 (C)

r 1

R 2 (D)

r 1

R 2



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FTRE Sample Paper Class 11 to 12 Paper 1

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