SAMPLE PAPER for Class XII (Maths) Paper of XI... · 2020. 12. 3. · SAMPLE PAPER for Class XII (Maths) RESONANCE Page No # 2 1. A boy throws a ball upwards with velocity v 0 = 20

SAMPLE PAPER

for

Class XII (Maths)

RESONANCE Page No # 2

1. A boy throws a ball upwards with velocity v0 = 20 m/s as shown. The wind imparts a horizontal acceleration of4 m/s2 to the left. The angle at which the ball must be thrown so that the ball returns to the boy's hand is-(g = 10 m/s2)

0

wind

(A) tan–1 (1.2)

(B) tan–1 (0.2)

(C) tan–1 (2)

(D) tan–1 (0.4)

2. A certain force applied to mass m1 gives it an acceleration of 10 m/s2. The same force applied to mass m2gives it an acceleration of 15 m/s2. If the two masses are joined together and the same force is applied to thecombination, the acceleration will be-

(A) 6 m/s2 (B) 3 m/s2 (C) 9 m/s2 (D) 12 m/s2

3. An astronaut on a strange planet finds he can jump a maximum horizontal distance of 30 m. If his initial speedis 9 ms–1 then find (a) acceleration due to gravity at that planet (b) the maximum height to which he can jump:-

(A) 9.8 ms–2, 30 m (B) 4.9 ms–2, 30 m (C) 2.7 ms–2, 30 m (D) 2.7 ms–2, 15 m

4. A river flows with a speed more than the maximum speed with which a person can swim in still water. Heintends to cross the river by shortest possible path. Which of the following is correct ?

(A) He should start normal to the river bank

(B) He should start in such a way that, he moves normal to the bank, relative to the bank

(C) He should start in a particular (calculated) direction making an obtuse angle with the direction of watercurrent

(D) The man cannot cross the river, in that way

5. The ratio of tensions in the string connected to the block of mass m2 in figure-(a) and figure-(b) respectively is(friction is absent everywhere) :

[m1 = 50 kg, m2 = 80 kg and F = 1000 N]

m2

m1F

m2

m1

F

(a) (b)

(A) 7 : 2

(B) 2 : 7

(C) 3 : 4

(D) 4 : 36. The acceleration-time graph of a particle is shown. The respective velocity-time graph of particle is :-

a

0 t1 t2

t

(A)

v

0 t1 t2t

(B)

v

0t1 t2 t

(C)

v

0 t1 t2t

(D)

v

0 t1 t2t

PART - I (PHYSICS)SECTION - I

Straight Objective Type


7. A huge rectangular compartment falls vertically down with acceleration a. A gun fired at corner P requires to hitQ. The bullet fired will hit Q if :-

Pv

Q

(A) a < g (B) a > g (C) a = g (D) any of (A), (B) or (C)

8. A man holds an umbrella at 30° with the vertical to keep himself dry. He, then, runs at a speed of 10 ms–1 andfinds the rain drops to be hitting vertically. Speed of the rain drops with respect to the running man and withrespect to earth are :-

(A) 20 ms–1, 510 ms–1 (B) 310 ms–1, 20 ms–1

(C) 10 ms–1, 320 ms–1 (D) 20 ms–1, 10 ms–1

9. A monkey of mass 40 kg climbs on a massless rope of breaking strength 600N. The rope will break if themonkey- (g = 10 m/s2)

(A) Climbs up with a uniform speed of 5 m/s (B) Climbs up with an acceleration of 5 m/s2

(C) Climbs down with an acceleration of 4 m/s2 (D) Climbs down with a uniform speed of 5 m/s

10. At what angle with the horizontal should a ball be thrown so that the range R is related to the time of flight T asR = 5T2 ? (g = 10 ms–2)

(A) 30° (B) 45° (C) 60° (D) 90°

11. The driver of a three-wheeler moving with a speed of 36 km/h sees a child standing in the middle of the road andbrings his vehicle to rest in 4.0 seconds just in time to save the child. What is the average retarding force on thevehicle ? The mass of the three-wheeler is 400 kg and the mass of the driver is 65 kg.

(A) 1062 N (B) 1162.5 N (C) 1000 N (D) 162.5 N

12. A chain consisting of 5 links, each of mass 0.1 kg is lifted vertically with a constant acceleration of 2.5 m/s2.The force of interaction between the top link and link immediately below it will be :-

(A) 6.15 N (B) 4.92 N (C) 9.84 N (D) 2.46 N

13. A body of mass m resting on a smooth horizontal plane starts moving under a constant force F. During itsrectilinear motion, the angle between the direction of force and horizontal plane varies as = kx, where k isa constant and x is the distance travelled by the body from the initial position. What is the velocity of the body?

(A) mksinF

(B) mksinF2

(C) mkcosF

(D) mkcosF2

14. A lift is going up. The total mass of the lift and the passenger is1500 kg. The variation in the speed of the lift is as given in the graph.The tension in the rope pulling the lift at t = 11th seconds will be:-

2 10 12t(s)

3.6

spee

d (m

/ s)

(A) 17400 N

(B) 14700 N

(C) 12000 N

(D) Zero


15. A block of mass 200 kg is set into motion on a frictionless horizontal surface with the help of frictionless pulleyand a rope system as shown in figure. What horizontal force F should be applied to produce in the block anacceleration of 1 m/s2 ?

Fa=1m/s2

(A) 200 N (B) 50 N (C) 150 N (D) 100 N

16. While launching a rocket of mass of 2 × 104 kg, a force of 5 × 105 N is applied for 20s. What is the velocityattained by the rocket at the end of 20s ?

(A) 500 ms–1 (B) 1000 ms–1 (C) 250 ms–1 (D) 50 ms–1

17. Three equal weights A, B, C of mass 2 kg each are hanging on a string passing over a fixed frictionless pulleyas shown in the figure. The tension in the string connecting weights B and C is (g = 10 m/s2) :-

AB

C

(A) zero (B) 13.3 N (C) 3.3 N (D) 19.6 N

18. Force constant of a spring is 100 N/m. If a 10 kg block attached with the spring is at rest, then find extensionin the spring. (g = 10 m/s2)

(A) 0.5 m

(B) 1 m

(C) 10m

(D) 2m

19. In the figure , the blocks A , B and C of mass m each have acceleration a1 , a2 and a3 respectively. F1 and F2 areexternal forces of magnitudes 2 mg and mg respectively

(A) a1 = a2 = a3 (B) a1 > a2 > a3 (C) a1 = a2 , a2 > a3 (D) a1 > a3 > a2


20. The figure shows mass m moves with velocity u. Find the velocity of ring at that moment. Ring is restricted tomove on smooth rod.

(A) 2u

(B) u (C) 2 u (D) 2u3

SECTION - IIInteger Type Questions

21. A bird flies to and fro between two cars which move with speeds 5 ms–1 and 10 ms–1 in opposite direction asshown in figure. If the speed of the birds is 10 ms–1 and the initial distance of separation between them is 750m. The total distance covered by the bird till the cars meet is 100D. The value of D is.

d

5 ms–1 10 ms–1

22. A mass M is hung with a light inextensible string. Tension in horizontal part of string is Mg x . The value of x

is

M30o

23. In the given figure, if velocity of block C at a particular instant is –20 m/s j . The speed of rod (A) at that instant

will be 5V. The value of V is :(string is attached to wedge)

C

= 37ºB

A j

i

Ans. 3


24. Two weights W1 & W2 in equillibrium and at rest, are suspended as shown in figure. Then the ratio 2

1WW4

is :

25. In the given figure : (All the pulleys are ideal and string are inextensible massless). The speed of block B is10V. The value is.

80 m/sA

B

20 m/s

j

i

PART - II (MATHS)SECTION - I

Straight Objective Type26. If , are the roots of the equation , 2 x2 + 4 x 5 = 0 , the equation whose roots are the reciprocals

of 2 – 3 and 2 – 3 is :

(A) x2 + 10 x 11 = 0 (B) x2 + 10 x + 11 = 0

(C) 11 x2 + 10 x + 1 = 0 (D) 11 x2 10 x + 1 = 0

27. The number of values of the pair (a, b) for which a (x + 1)2 + b (– x2 – 3x – 2) + x + 1 = 0 is an identity in x is

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

28. If (1 + k) tan2x – 4 tan x – 1 + k = 0 has real roots, then which one of the following is not true?

(A) k2 < 5 (B) tan (x1 + x2) = 2 (C) for k = 2, x1 = / 4 (D) None of these

29. The solution set of the inequation , log1/2 (2x+2 –4x) – 2 is :

(A) 132, (B) 132, (C) (– , 2) (D) None of these

30. Consider the equation x2 + x – n = 0, where ‘ n ‘ is an integer lying between 1 to 100. Total number ofdifferent values of ‘ n ’ so that the equation has integral roots, is :

(A) 6 (B) 4 (C) 9 (D) None of these


31. The inequalities , y (– 1) – 4 , y (1) 0 and y (3) 5 are known to hold for y = a x2 + b x + c then theleast value of ‘ a ’ is :

(A) 41

(B) 31

(C) 41

(D) 81

32. If the equation , 3x2

– 4 x + 13 = sin xa

has a solution , then ‘ a ‘ is equal to : (n I)

(A) (2 n + 1) 2

(B) 3 (4 n + 1) 2

(C) 3 (1 + 4 n) (D) None of these

33. If , be the roots of R,0x17x4 2 such that 1 < < 2 and 2 < < 3, then the number of integral

values of is :

(A) 1 (B) 2 (C) 3 (D) 434. The graph of quadratic polynomical f(x) = ax2 + bx + c is shown below

–1 1x

(A) 2ac

(B) x 0xf (C) ac > 0 (D) 1ac

35. Let a, b, c be real. If a x2 + bx + c = 0 has two real roots and where < – 2 and > 2, then

(A) 0ac

ab24 (B) 0

ac

ab24 (C) 0

ac

ab24 (D) 0

ac

ab24

36. If the ratio of the roots of the equation 2x nx n 0 is p : q and roots are positive, then p q nq p

is

equal to(A) 1 (B) –2 (C) 0 (D) 2

37. The number of real solutions of the equation cos5 x + sin3 x = 1 in the interval [0, 2 ] is(A) 2 (B) 1 (C) 3 (D) infinite

38. If a, b , c R and the quadratic equation x2 + (a + b) x + c = 0 has no real roots, then(A) c (a + b + c) > 0 (B) c + (a + b + c) c > 0(C) c – c (a + b + c) > 0 (D) c (a + b – c) > 0

39. The minimum value of the expression (3sinx – 4cosx – 10)(3sinx + 4cosx – 10) is -

(A) 49 (B) 2

260193 (C) 84 (D) 45

40. If tan A & tan B are the roots of the quadratic equation x2 ax + b = 0, then the value ofsin2 (A + B) is:

(A) 2

2 2a

a (1 b) (B)

2

2 2a

a b(C)

2

2a

(b c)(C)

2

2 2a

b (1 a)


41. If |x2 – 2x – 8| + |x2 + x – 2| = 3 | x + 2|, then the set of values of ‘x’ will be :

(A) [1, 4] {–2} (B) [1, 4] (C) [–2, 1] [4,) (D) (–, –2] [1, 4]

42. If x4 + 2x3 + 3x2 + 2x + 4 = 0 has four roots , , , then (1 + 2) (1 + 2) (1 + 2) (1 + 2) is equal to

(A) 2 (B) 4 (C) 8 (D) 16

43. If x R, the least value of the expression 1x2x5x6x

2

2

, is

(A) – 1 (B) – 1 / 2 (C) – 1 / 3 (D) None of these

44. If ,0sin2tan3 2 then is equal to Zn

(A) 4n2

(B) 6

1n n (C) 6

1n n (D) 3n

45. The number of solutions of 2 sin2x + sin22x = 2, 2,0x is

(A) 4 (B) 5 (C) 7 (D) 6

SECTION - II

Integer Type Questions

46. If a, b and c are the roots of the equation x3 + 2x2 + 1 = 0, find :bac

acb

cba

47. If sin and cos are the roots of the quadratic equation 0ac0cbxax2 . Then find the value of

acab 22

.

48. The number of real values of x satisfying the equation log2 (3 – x) –log2

x54

3sin

7xlog21

2

49. If 7

then find the value of

2cos

cos2cos

1.

50. If (1 + tan 5o) (1 + tan 10o) (1 + tan 15o)...........(1 + tan 45o) = 2k, then the value of ‘k’ is ______ .


PART - III (CHEMISTRY)SECTION - I

Straight Objective Type

Atomic masses (in u) : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27,Si = 28, P = 31, S = 32, Cl = 35.5, Ar = 40, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65,As = 75, Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]

51. If two moles of an ideal gas at 546K occupies a volume of 44.8 litres, the pressure must be

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

52. Match List - I with List - II and select the correct answer using the codes given below the lists :

( and m are respectively the azimuthai and magnetic quantum no.)

List - I List - II

(A) Number of value of for an energy level (1) 0, 1, 2, ....... (n –1)

(B) Value of for a particular type of orbital (2) + to – through zero

(C) Number of values of m for = 2 (3) 5

(D) Value of ‘m’ for a particular type of orbitals (4) n

Code :

A B C D A B C D

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

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

53. Ionization energy of a hydrogen-like ion A is greater than that of another hydrogen like ion B. Let r, u, E and Lrepresent the radius of the orbit, speed of the electron, energy of the atom and orbital angular momentum of theelectron respectively (for the same n). In ground state

(A) rA > rB (B) uA > uB (C) EA > EB (D) LA > LB

54. Number of electron having the quantum numbers

21s ,0 ,4n in Zn+2 ion is/are

(A) 1 (B) 0 (C) 2 (D) 5

55. 512gm of S8 is convertyed to FeS2 with 10% efficiencty. The FeS2 formed is roasted to convert sulphur in FeS2to SO2 with 50% efficiency. The SO2 is then completely oxidised to SO3 which is then absorbed in water togive H2SO4. Find the number of moles of NaOH needed to neutralise completely the H2SO4 thus formed. [Atwt Fe = 56, S = 32, O = 16]

(A) 2.4 mole (B) 4.2 mole (C) 1.6 mole (D) 4 mole

56. Three volume of a gaseous hydrocarbon containing carbon, hydrogen and sulphur is burnt in an excessof oxygen to yield three volumes of CO2, three volumes of SO2 and six volumes of water vapour. The formula ofthe compound is :

(A) C6H6S (B) C4H4S (C) CH4S (D) C2H6S


57. A particle X moving with a certain velocity has a debroglie wave length of A1 , if particle Y has a mass of 25%

that of X and velocity 75% that of X, debroglies wave length of Y will be :-

(A) A3 (B)

A33.5 (C)

A88.6 (D)

A48

58. Photon having wavelength 310nm is used to break the bond of A2 molecule having bond energy 288 kg mol–1

then % of energy of photon converted to the K.E. is

[hc = 12400 ev A , 1 ev = 96 kJ/mol]

(A) 25 (B) 50 (C) 75 (D) 80

59. In the above figure mercury columns of 10 cms each are trappedbetween gas column of 10cm each. If Patm = 75 cm of Hg then thegas pressure in the topmost column will be : Hg

Hg

P = ?gas

10cm

10cm

10cm

10cm

Hg

(A) 55cm of Hg

(B) 35cm of Hg

(C) 65 cm of Hg

(D) 45 cm of Hg

60. Which of the following graph does not represents Boyles’ law correctly.

(A)

Pv

V

(B)

1/P

V

(C)

nP

nV

(D)

P

V

61. 1st excitation potential for the H-like (hypothetical) sample is 24 V.

Then incorrect statement is:

(A) Ionisation energy of the sample is 36 eV

(B) Ionisation energy of the sample is 32 eV

(C) Binding energy of 3rd excited state is 2 eV

(D) 2nd excitation potential of the sample is v9

832

62. 1M 100 ml NaCl is mixed with 3M 100 ml HCl solution and 1M 200 ml CaCl2 solution. then :

(A) The ratio of concentration of cation and anion = 3/4 M

(B) The ratio of concentration of cation and anion = 2 M

(C) [Cl–] = 3/2 M

(D) None of these


63. Following graph is constructed for the fixed amount of the gas. Which of the following option is incorrect :

V

T

1 3

2

(A) From 1 - 2 pressure will increase

(B) From 2 - 3 pressure remains constant

(C) Gas pressure at (3) is greater at state (1)

(D) From 1 - 2 pressure will decrease

64. In a sample of H-atom electrons make transition from 5th excited state to ground state, producing all possibletypes of photons, then number of lines in infrared region are :

(A) 4 (B) 5 (C) 6 (D) 3

65. Molarity of 3%

Vw

aqueous solution of urea is

(A) 0.3m (B) 0.5 m (C) 0.1m (D) 0.2m

66. Calculate mass of solute in resulting solution made by mixing 100ml 8%

Vw

aqueous solution of NaOH and

200gm 15%

Ww

aqueous solution

(A) 40gm (B) 30gm (C) 48gm (D) 38gm

67. 23222 SO8OFe2O11FeS4

42442242 SOH2MnSO2SOKOH2KMnO2SO5

Calculate volume of 0.2 M KMnO4 solution required to react completely with SO2 liberated from 6gms of FeS2in first reaction :

(A) 300ml (B) 500ml (C) 100ml (D) 200ml

68. Which of the following element's nucleus has maximum density ?

(A) 12C6 (B) 16O8 (C) 31P15 (D)All have same density

69. The graphical representation of energy of electron & atomic number is :-

(A) E

Z2

(B) E

Z2

(C) E

Z2

(D)

EZ2

70. Two particles A and B are in motion. Momentum of B is half the momentum of A. If wavelength of A is5 × 10–8 metre, then wavelength of particle B will be :

(A) 10–9 m (B) 5 × 10–8 m (C) 10–7 m (D) 5 × 10–7 m


SECTION - IIInteger Type Questions

71. For the reaction 3A + 2B 3C, the number of moles of C produced by 5 moles of A and 8 moles of B is

72. Li metal is one of the few substances that reacts directly with molecular nitrogen :

6Li(s) + N2(g) 2Li3N(s)

How many grams of the product, lithium nitride, can be prepared from 4.2g of lithium metal and 5.6 g ofmolecular nitrogen ? (Atomic weight : Li = 7, N = 14)

73. When mixture of 10 mole of SO2, 16 mole of O2 were passed over catalyst, 8 mole of SO3 were formed. Whatis the ratio of unreacted O2 moles to that of unreacted SO2 moles ?

74. The electronic velocity in the fourth Bohr’s orbit of hydrogen is v. The velocity of the electron in the first orbitwould be :

75. What would be the maximum number of emission lines for atomic hydrogen that you would expect to see withthe naked eye if the only electronic energy levels involved are those as shown in the Figure ?


ANSWER KEY

PART - I (PHYSICS)1. (D) 2. (A) 3. (D) 4. (D)

5. (C) 6. (D) 7. (A) 8. (B)

9. (B) 10. (B) 11. (B) 12. (B)

13. (B) 14. (C) 15. (D) 16. (A)

17. (B) 18. (B) 19. (D) 20. (C)

21. 5 22. 3 23. 3 24. 5

25. 4

PART - II (MATHS)26. (C) 27. (B) 28. (D) 29. (C)

30. (C) 31. (D) 32. (C) 33. (B)

34. (A) 35. (A) 36. (C) 37. (C)

38. (B) 39. (A) 40. (A) 41. (A)

42. (B) 43. (C) 44. (B) 45. (D)

46. 8 47. 2 48. 1 49. 4

50. 5

PART - III (CHEMISTRY)51. (A) 52. (B) 53. (B) 54. (B)

55. (C) 56. (C) 57. (B) 58. (A)

59. (A) 60. (D) 61. (A) 62. (A)

63. (D) 64. (C) 65. (B) 66. (D)

67. (C) 68. (D) 69. (D) 70. (C)

71. 5 72. 7 73. 6 74. 4

75. 4

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SAMPLE PAPER for Class XII (Maths) Paper of XI... · 2020. 12. 3. · SAMPLE PAPER for Class XII (Maths) RESONANCE Page No # 2 1. A boy throws a ball upwards with velocity v 0 = 20