Space for Rough Work - FUTURE EDGE · ... is descending with an acceleration of 2 m/s2. The mass of the block A is 0.5 kg. The force exerted by the block A on block B is (Take g =

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Space for Rough Work

SAMPLE PAPER CLASS_11th_S.T.D (Engineering)




Section - IPHYSICS

(Single Choice Correct Options)1. Maximum and minimum magnitudes of the resultant of two vectors of magnitude p and q are in the ratio 3 : 1. Which

of the following relation is true ?(A) p = 2 q (B) p = q(C) pq = 1 (D) None of these

2. An engine of a train moving with uniform acceleration passes an electric pole with velocity u and the last compartmentwith velocity v. The middle point of the train passes past the same pole with a velocity of

(A)u v2

(B)2 2u v

2

(C)2 2u v2

(D)2 2u v

2

3. A projectile is thrown with a velocity of 10 2 m / s at an angle of 455o with horizontal. The interval between the mo-

ment when speed is 125 m/s is

(g = 10 m/s2)(A) 1.0 s (B) 1.5 s (C) 2. 0 s (D) 0.5 s

4. Velocity versus displacement graph of a particle moving in a straight line is as shwon in figure. V

X

The acceleration of the particle(A) Is constant (B) Increases linearly with x(C) Increases parabolically with x (D) None of these

5. An elevator in which a man is standing is moving upwards with a constant speed of 10 m/s. If the man drops a coin froma height of 2.45 m, it reaches the floor of the elevator after a time (g = 9.8 m/s2)

(A) 2 s (B)1 s2 (C) 2s (D)

1s

2




6. The elevator shown in figure, is descending with an acceleration of 2 m/s2. The mass of the block A is 0.5 kg. The forceexerted by the block A on block B is

(Take g = m/s2)

(A) 2N (B) 4 N (C) 6 N (D) 8 N

7. A block of mass m is placed on a wedge of mass M and inclination assshown in figure. All surface are smooth and the wedge is free to slide onthe horizontal surface. If the system is released from rest, then thenormal reaction between the block and the wedge is

(A) mg cos

(B) less than mg cos

(C) Greater than mg cos

(D) May be less or greater than mg cos depending upon whether m is less or greater than M

8. Figure shows two blocks P and Q pushed against the wall with the force F. The wall is smooth but the surface in contactof P and Q are rough

Which of the following is true for the system of block to be at rest against the wall ?

(A) F should be more than the weight of P and Q (B) F should be equal to the weight of P and Q

(C) F should be less than the weight of P and Q (D) System cannot be in equilibrium (at rest)




9. Minimum force required to pull the lower block is (Take g = 10 m/s2)

(A) 1 N (B) 5 N (C) 7 N (D) 10 N

10. A block A of mass 2 kg rests on another block B of mass 8 kg which rests on a horizontal floor, as shown in the figure. Thecoefficient of friction between A and B is 0.2 while that between B and the floor is 0.5. When a horizontal force of 30 Nis applied on B, the force of friction between A and B is

(Take g = 10 m/s2)

(A) Zero (B) 4 N (C) 5 N (D) 6 N

11. A block of mass m is placed at rest on a horizontal rough surface with angle of friction . The block is pulled with a forceF at an angle with the horizontal. The minimum value of F required to move the block is

(A)

mg sin

cos ( ) (B)

mg coscos ( ) (C) mg tan (D) mg sin

12. System shown in figure, is released from rest. Pullley and spring are massless andthe friction is absent every where.

The speed of 5 kg block when 2 kg block leaves the contact with ground is (Forceconstant of the spring k = 40 N/m and g = 10 m/s2)

(A) 2 m / s (B) 2 2 m / s

(C) 2m / s (D) 4 2 m / s




13. A block of mass m is connected to a spring of force constant k. Initially the block is at rest and the spring has naturallength. A constant force F is applied horizontally towards right. The maximum speed of the block will be (there is nofriction between block and the surface)

(A)F

2 mk (B)Fmk (C)

2 Fmk (D)

2Fmk

14. A uniform circular disc of radius a is taken. A circular portion of radius b has been removed from it as shown in figure. Ifthe centre of hole is at a distance c from the centre of the disc, the distance x2 of the centre of mass of the remainingpart from the initial centre of mass O is given by

(A)

2

2 2b

(a b ) (B)

2

2 2cb

(a b )

(C)

2

2 2c

(a b ) (D)

2

2 2a

(a b )

15. n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius r as shown in

figure. The masses of the balls are 2 n 1m m mm, , ....2 2 2

respectively. What is the minimum velocity which should be im-

parted to the first ball of mass m such that nth ball complete the vertical circle.

(A)

n 13 5 gr4

(B)n 14

5 gr3

(C)

n 13 5 gr2

(D)

n 12 5 gr3




16. A thin disc of mass 9 M and radius R form which a disc of radius R/3 is cut is shown in figure. Then moment of inertia ofthe remaining disc about O, perpendicular to the plane of disc is.

(A) 4 MR2 (B) 9 MR2 (C) 237 MR9

(D) 240 MR9

17. A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude of angularmomentum of the disc about the origin O is

(A)

21MR

2 (B) 2MR (C)

23MR

2 (D) 2 2MR

18. A mass M is supported by a massless string wound round a uniform cylinder of mass M and radius R. On releasing themass from rest, it will fall with acceleration

(A) g (B) g/2 (C) g/3 (D) 2 g/3




19. The rod shown in figure, Rotates without slipping about A after a gentle push is given at top (B). If N is the normal

reaction by ground on the rod and f is the frictional force at point A, then

(A) N < mg and f is directed towards right (B) N = mg and f = 0

(C) N > mg and f is directed towards left (D) N < mg and f directed towards left

20. A solid ball of radius r rolls inside a hemispherical shell of radius R. It is released from rest from point A as shown in

figure. The angular velocity of centre of the ball in position B about the centre of the shell is

(A) g2

5(R r) (B) 10g

7(R r) (C) 2 g

5(R r) (D) 5 g

2(R r)




Section - IICHEMISTRY

(Single Choice Correct Options)

21. 1 litre CO and 1.75 litre CH4 at the same temperature and pressure were mixed together. What is the relation betweenthe masses of two gases in the mixture ?

(A)4co CHm > m (B)

4CH com m (C)4co CHm < m (D)

4co CHm > 2m

22. At low pressure vander Waal’s equation for 3 moles a real gas will have its simplified form

(A)PV 3

RT Pb

(B)

PV 33aRTv

(C)

PV 1RT 3Pb

(D)

PV 3aRTv

23. At constant pressure what would be the percentage decrease in the density of an ideal gas for a 10% increase in thetemperature.

(A) 10% (B) 9.1% (C) 11% (D) 12.09%

24. The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [ oa is Bohr radius] :

(A)

2

2 204

hma (B)

2

2 2016

hma (C)

2

2 2032

hma (D)

2

2 2064

hma

25. The orientation of an atomic orbital is governed by

(A) Azimuthal quantum number (B) Spin quantum number

(C) Magnetic quantum number (D) Principal quantum number

26. Maximum number of electrons in a subshell of an atom in determined by the following

(A) 4 2l (B) 2 1l (C) 4 2l (D) 22n




27. The orbital angular momentum of an electron in 2s orbital is :

(A)

1.2 2

h(B) Zero (C)

2h

(D)

2.2h

28. Equivalent weight of MnO4– in acidic, neutral and basic media are in ratio of:

(A) 3 : 5 : 15 (B) 5 : 3 : 1 (C) 5 : 1 : 13 (D) 3 : 15 : 5

29. In the reaction,

VO + Fe2O3 FeO + V2O5,

The equivalent weight of V2O5 is equal to its

(A) molecular weight (B) molecular weight / 4 (C) molecular weight /6 (D) molecular weight /8

30. The n-factor of K4[Fe(CN)6] in the given reaction would be

Zn2+ + K4[Fe(CN)6] K2Zn3[Fe(CN)6]2 + K+

(A) 2 (B) 3 (C) 4 (D) 6

31. The n-factor of FeS2 in the following reaction,

FeS2 Fee3+ + SO2, would be

(A) 5 (B) 6 (C) 10 (D) 11

32. The molarity of concentrated sulphuric acid ( = 1.834 g cm–3) containing 95% of H2SO4 by mass is.

(A) 4.44 M (B) 8.88 M (C) 13.32 M (D) 17.78 M




33. 5.6 litres of oxygen at STP is equivalent to

(A) 1 mole (B) 1/2 mole (C) 1/4 mole (D) 1/8 mole

34. The types of bonds present in CuSO4.5H2O are only

(A) Electrovalent and covalent (B) Electrovalent and co-ordinate covalent

(C) Electrovalent, covalent and co-ordinate covalent (D) Covalent and co-ordinate covalent

35. The hydrogen bond is strongest in:

(A) O – H ……… S (B) S – H ……… O (C) F – H ……… F (D) F – H ……… O

36. The correct order of hybridization of the central atom in the following species NH3, [PtCl4]2–, PCl5 and BCl3 is

(A) dsp2, dsp3, sp2 and sp3 (B) sp3, dsp2, dsp3, sp2 (C) dsp2, sp2, sp3, dsp3 (D) dsp2, sp3, sp2, dsp3

37. The states of hybridization of boron and oxygen atoms in boric acid (H3BO3) are respectively

(A) sp3 and sp2 (B) sp2 and sp3 (C) sp2 and sp2 (D) sp3 and sp3

38. Ortho-Nitrophenol is less soluble in water than p- and m-Nitrophenols because:

(A) o-Nitrophenol is more volatile steam than those of m- and p-isomers.

(B) o-Nitrophenol shows intramolecular H-bonding

(C) o-Nitrophenol shows intermolecular H-bonding

(D) Melting point of o-Nitrophenol is lower than those of m- and p-isomers.

39. Which one of the following is an amphoteric oxide ?

(A) Na2O (B) SO2 (C) B2O3 (D) ZnO

40. Mendeleev arranged the elements in the increasing order of

(A) Atomic number (B) Atomic radius (C) Atomic mass (D) Valency




Section -IIIMATHEMATICS

(Single Choice Correct Options)41. Let m = tan 3 and n = sec 6 , then which one of the following statement holds good?

(A) m & n both are positive (B) m & n both are negative

(C) m is positive and n is negative (D) m is negative and n is positive.

42. Let y =

112 13 123 .....

, then the value of y is

(A)13 3

2(B)

13 32

(C)15 3

2(D)

15 32

43. 116 people participated in a knockout tennis tournament. The players are paired up in the first round, the winners of thefirst round are paired up in the second round, and so on till the final is played between two players. If after any round,there is odd number of players, one player is given a bye, i.e. he skips that round and plays the next round with thewinners. The total number of matches played in the tournament is

(A) 115 (B) 53 (C) 232 (D) 116

44. PQRS is a square. SR is a tangent (at point S) to the circle with centre O and TR = OS. Then, the ratio of area of the circle

to the area of the square is

(A)3

(B)117

(C)3

(D)7

11




45. The two legs of a right triangle are sin + sin

32 and cos –

3

cos2 . The length of its hypotenuse is

(A) 1 (B) 2 (C) 2 (D) Some function of

46. Exact value of cos2 73º + cos2 47º sin2 43º + sin2 107º is equal to :

(A) 1/2 (B) 3/4 (C) 1 (D) None

47. If

sin2 sin3 sin4cos2 cos3 cos4 = tan k is an identity then the value of k is equal to :

(A) 2 (B) 3 (C) 4 (D) 6

48. Which of the following conditions imply that the real number x is rational?

I x1/2 is rational

II x2 and x5 are rational

III x2 and x4 are rational

(A) I and II only (B) I and III only (C) II and III only (D) I, II and III

49. If x2 + 2

1x

= 7 then the value of 33

1x

x equals (x > 0)

(A) 18 (B) 21 (C) 24 (D) 27

50. Number of positive integers x for which f (x) = x3 – 8x2 + 20x – 13, is a prime number, is

(A) 1 (B) 2 (C) 3 (D) 4

51. In the inequality below the value of the angle is expressed in radian measure. Which one of the inequalities below istrue?

(A) sin 1 < sin 2 < sin 3 (B) sin 3 < sin 2 < sin 1

(C) sin 2 < sin 1 < sin 3 (D) sin 3 < sin 1 < sin 2

52. If a, b, c are real numbers such that a2 + 2b = 7, b2 + 4c = – 7 and c2 + 6a = – 14 then the value of a2 + b2 + c2 is

(A) 14 (B) 21 (C) 28 (D) 35




53. Each side of triangle ABC is divided into 3 equal parts. The ratio of the area of hexagon UVWXYZ to the area of triangleABC is

(A) 59

(B) 23

(C)12

(D)34

54. If 3 + 14

(3 + d) + 2

14

(3 + 2d) +...... + upto o = 8, then the value of d is :

(A) 9 (B) 5 (C) 1 (D) None of these

55. Starting with a unit square, a sequence of squares is generated. Each square in the sequence has half the side length ofits predecessor and two of its sides bisected by its predecessor's sides as shown. This process is repeated indefinitely.The total area enclosed by all the squares in limiting situation, is

(A)54

sq. unitss (B)7964

sq. unitss (C) 7564

sq. unitss (D)1

12 sq. unitss

56. If the sum of the first 11 terms of an arithmetical progression equals that of the first 19 terms, then the sum of its first30 terms, is

(A) Equal to 0 (B) Equal to – 1 (C) Equal to 1 (D) Non unique




57. In an A.P. with first term 'a' and the common difference d (a, d 0), the ratio ' ' of the sum of the first n terms to sum

of n terms succeeding them does not depend on n. Then the ratio da

and the ratio ' ', respectively aree

(A)12

, 14

(B) 2, 13

(C)12

, 13

(D)12

, 2

58. If S = 12 + 32 + 52 + ....... + (99)2 then the value of the sum 22 + 42 + 62 + ....... + (100)2 is

(A) S + 2550 (B) 2S (C) 4S (D) S + 5050

59. A circle with center A and radius 7 is tangent to the sides of an angle of 60°. A larger circle with center B is tangent to thesides of the angle and to the first circle. The radius of the larger circle is

(A) 30 3 (B) 21 (C) 20 3 (D) 30

60. In a convex polygon, the degree measures of the interior angles form an arithmetic progression. If the smallest angle is159° and the largest angle is 177°, then the number of sides in the polygon, is

(A) 21 (B) 27 (C) 30 (D) 31

ANSWER KEYSection- I (PHYSICS)

1 (A) 2 (C) 3 (A) 4 (B) 5 (B)6 (B) 7 (B) 8 (D) 9 (A) 10 (A)11 (A) 12 (B) 13 (B) 14 (B) 15 (A)16 (A) 17 (C) 18 (D) 19 (A) 20 (B)

Section- II (CHEMISTRY)21 (B) 22 (B) 23 (B) 24 (C) 25 (C)26 (A) 27 (B) 28 (A) 29 (C) 30 (B)31 (D) 32 (D) 33 (C) 34 (C) 35 (C)36 (B) 37 (B) 38 (B) 39 (D) 40 (C)

Section- III (MATHEMATICS)

41 (D) 42 (D) 43 (A) 44 (A) 45 (C)46 (C) 47 (B) 48 (A) 49 (A) 50 (C)51 (D) 52 (A) 53 (B) 54 (A) 55 (A)56 (A) 57 (C) 58 (D) 59 (B) 60 (C)

STEP TO SUCCESSTALENT SEARCH EXAMINATION

SAMPLE PAPER CLASS 11th (ENGINEERING)




Space for Rough Work - FUTURE EDGE · ... is descending with an acceleration of 2 m/s2. The mass of the block A is 0.5 kg. The force exerted by the block A on block B is (Take g =

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