Silver Line Prestige School PCB/XII/code-M

Page - 1

PHYSICS, CHEMISTRY & MATHEMATICS

Do not open this Test Booklet until you are asked to do so. Read carefully the Instructions of this Test Booklet.

Important Instructions :

1. Immediately fill in the particular on this page of the Test Booklet with Blue/Ball Point Pen.

Use of pencil is strictly prohibited.

2. The answer sheet is kept inside this Test Booklet. When you are directed to open the Test

Booklet, take out the Answer Sheet and fill in the particulars carefully.

3. The test is of 3 hours duration

4. The Test Booklet consists of 90 questions. The maximum marks are 360.

5. There are three parts in the question paper A, B, C consisting of Physics, Chemistry and

Mathematics having 30 questions in each part of equal weightage. Each question is allotted

4 (four) marks for each correct response.

6. Candidate will be awarded marks as stated above in instructions No. 5 for correct response of

each question, ¼ (one fourth) marks will be deducted for indication incorrect response of each

question. No deduction form the total score will be made if no response is indicated for an

item in the answer sheet.

7. Questions form 1 to 30 Section –A Physics are only one correct choice type(+4/-1), Questions

from 31 to 60 Section –B Chemistry are only one correct choice type (+4/-1). Questions from

61 to 90 Section –C Mathematics are also only one correct choice type (+4/–1). Response

filling up more than one response will be treated as wrong answer and mark for wrong

response will be deducted accordingly as per instruction 6 above.

8. Use Blue/Black Ball point Pen only for writing particulars/marking response on answer

sheet. Use of pencil is strictly prohibited.

9. No candidate is allowed to carry any textual material, printed or written, bits of papers, pager,

mobile phone, any electronic device, etc., except the Admit Card inside the examination

hall/room.

10. Rough work is to be done on the space provided for this purpose in the Test Booklet only.

This space is given at the bottom of each pages.

11. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on

duty in the Room/Hall. However, the candidates are allowed to take away this Test Booklet

with them.

12. The CODE for this booklet is M. Make sure that the CODE printed on the Answer Sheet is the

same as that on this booklet. In case of discrepancy, the candidate should immediately report

the matter to the Invigilator for replacement of both the Test Booklet and the Answer Sheet.

13. Do not fold or make any stray marks on the Answer Sheet.

Name of the Candidate (In capital letters : ____________________________________________

Roll Number : in figures

: in words ____________________________________________________________

Name of Examination Centre : ______________________________________________________

Candidate’s Signature : ________________ Invigilator’s Signature ___________________

Test Booklet

Code

M

Silver Line Prestige School PCB/XII/code-M

Page - 2

PART – A PHYSICS

1. A length L of wire carries a steady current I. It is bent first to form a circular plane coil of one turn. The same length is now bent more sharply to give a double loop of smaller radius. The magnetic field at the centre caused by the same current is

(a) A quarter of its first value (b) Unaltered (c) Four times of its first values (d) A half of its first value 2. An infinitely long straight conductor is

bent into the shape as shown in the figure. It carries a current of i ampere and the radius of the circular loop is r metre. Then the magnetic induction at its centre will be

(a) )1(2

4

0 +ππ

µ

r

i

(b) )1(2

4

0 −ππ

µ

r

i

(c) Zero (d) Infinite 3. A helium nucleus makes a full rotation

in a circle of radius 0.8 metre in two seconds. The value of the magnetic field B at the centre of the circle will be

(a) 0

1910

µ

−

(b) 10–19 µ0

(c) 2 × 10–10 µ0 (d) 0

19102

µ

−×

4. In the figure shown there are two

semicircles of radii r1 and r2 in which a current i is flowing. The magnetic induction at the centre O will be

(a) )( 210 rrr

i+

µ

(b) )(4

210 rri

−µ

(c)

+

21

210

4 rr

rriµ

(d)

−

21

120

4 rr

rriµ

5. Circle loop of a wire and a long

straight wire carry currents Ic and Ie, respectively as shown in figure. Assuming that these are placed in the same plane. The magnetic fields will be zero at the centre of the loop when the separation H is

(a) πc

e

I

RI

(b) πe

c

I

RI

(c) RI

I

e

cπ

(d) RI

I

c

eπ

6. Two particles X and Y having equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describe circular path of radius R1 and R2 respectively. The ratio of mass of X to that of Y is

(a) 2/1

2

1

R

R (b) 1

2

R

R

(c) 2

2

1

R

R (d) 2

1

R

R

7. A deutron of kinetic energy 50 keV is describing a circular orbit of radius 0.5 metre in a plane perpendicular to magnetic field B. The kinetic energy of the proton that describes a circular orbit of radius 0.5 metre in the same plane with the same B is

(a) 25 keV (b) 50 keV (c) 200 keV (d) 100 keV

8. An electron enters a magnetic field whose direction is perpendicular to the velocity of the electron. Then

(a) The speed to the electron will increase (b) The speed of the electron will decrease (c) The speed of the electron will remain the same (d) The velocity of the electron will remain the same

Space for rough work

Silver Line Prestige School PCB/XII/code-M

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9. When a proton is released from rest in a room, it starts with an initial acceleration a0 towards west. When it is projected towards north with a speed v0 it moves with an initial acceleration 3a0 towards west. The electric and magnetic fields in the room are

(a) downev

maeast

e

ma

0

00 3,

(b) upev

mawest

e

ma

0

00 2,

(c) downev

mawest

e

ma

0

00 2,

(d) upev

maeast

e

ma

0

00 3,

10. The figure shown three situations

when an electron moves with velocity V travels through a uniform magnetic field B. In each case, what is the direction of magnetic force on the electron

(a) +ve z–axis, –ve x-axis, +ve y–axis (b) –ve z–axis, –ve x-axis and zero (c) +ve z-axis, +ve y-axis and zero (d) –ve z-axis, +ve x-axis and zero 11. In a large building, there are 15 bulbs

of 40W, 5 bulbs of 100W, 5 fans of 80W and 1 heater of 1 kW. The voltage of the electric mains is 220 V. The minimum capacity of the main fuse of the building will be

(a) 8 A (b) 10 A (c) 12 A (d) 14 A 12. A wire when connected to 220V mains

supply has power dissipation P1. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is P2. Then P2 : P1 is

(a) 1 (b) 4 (c) 2 (d) 3

13. Find the power of the circuit

(a) 1.5 W (b) 2 W (c) 1 W (d) None of these 14. The total power dissipated in Watts

in the circuit shown here is (a) 16 (b) 40 (c) 54 (d) 4 15. Consider a thin square sheet of side

L and thickness t, made of a material

of resistivity ρ. The resistance between two opposite faces, shown by the shaded areas in the figure is

(a) Directly proportional to L

(b) Directly proportional to t (c) Independent of L (d) Independent of t 16. Two conductors have the same

resistance at 0°C but their temperature coefficients of resistance

are α1 and α2. The respective temperature coefficients of their series and parallel combinations are nearly

(a) 2

,2

2121 αααα ++ (b) 21

21 ,2

αααα

++

(c) 2

, 2121

αααα

++ (d)

21

2121 ,

αα

αααα

++

17. A battery of internal resistance 4Ω is connected to the network of resistances as shown. In order to give the maximum power to the network,

the value of R (in Ω) should be (a) 4/9 (b) 8/9 (c) 2 (d) 18

Space for rough work

Silver Line Prestige School PCB/XII/code-M

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18. The effective resistance between points P and Q of the electrical circuit shown in the figure is

(a) 2Rr/(R+r) (b) 8R (R+r)/(3R+r) (c) 2r + 4R (d) 5R/2 + 2r 19. Shown in the figure below is a meter-

bridge set up with null deflection in the galvanometer

The value of the unknown resistor R is

(a) 220 Ω (b) 110 Ω

(c) 55 Ω (d) 13.75 Ω 20. In the circuit shown in the figure, if the

potential at point A is taken to be zero, the potential at point B is

(a) –2V (b) +1V (c) –1V (d) +2V 21. Equivalent resistance between the

points A and B is (in Ω)

(a) 5

1 (b)

4

11

(c) 3

12 (d)

2

13

22. In uniformly charged sphere of total

charge Q and radius R, the electric field E is plotted as function of distance from the centre. The graph which would correspond to the above will be

23. The figure gives the electric potential

V as a function of distance through five regions on x-axis. Which of the following is true for the electric field E in these regions

(a) E1 > E2 > E3 > E4 > E5 (b) E1 = E3 = E5 and E2 < E4 (c) E2 = E4 = E5 and E1 < E3 (d) E1 < E2 < E3 < E4 < E5 24. A ball of mass 1 g and charge 10–8 C

moves from a point A. Where potential is 600 V to the point B where potential is zero. Velocity of the ball at the point B is 20 cm/s. The velocity of the ball at the point A will be

(a) 22.8 cm/s (b) 228 cm/s (c) 16.8 m/s (d) 168 m/s 25. In the figure below, what is the

potential difference between the points A and B and between B and C respectively steady state

(a) VAB = VBC = 100 V (b) VAB = 75 V, VBC = 25 V (c) VAB = 25 V, VBC = 75 V (d) VAB = VBC = 50 V

Space for rough work

Silver Line Prestige School PCB/XII/code-M

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26. Two point charges +q and –q are held fixed at (–d, 0) and (d, 0) respectively of a (X, Y) coordinate system. Then

(a) E at all points on the Y – axis is along î

(b) The electric field E at all points on the X – axis has the same direction (c) Dipole moment is 2qd directed along î (d) Work has to be done in bringing a test charge from infinity to the origin

27. An elementary particle of mass m and charge +e is projected with velocity v at a much more massive particle of charge Ze, where Z > 0. What is the closest possible approach of the incident particle

(a) 2

0

2

2 mv

Ze

πε (b)

2

04 mv

Ze

πε

(c) 2

0

2

8 mv

Ze

πε (d)

2

08 mv

Ze

πε

28. Electric potential is given by V = 6x – 8xy2 – 8y + 6yz – 4z2 Then electric force acting on 2C point charge placed on origin will be (a) 2 N (b) 6 N (c) 8 N (d) 20 N

29. Two identical charged spheres are suspended by strings of equal lengths.

The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 g cm–3, the angle remains the same. If density of the material of the sphere is 1.6 g cm–3, the dielectric constant of the liquid is

(a) 1 (b) 4 (c) 3 (d) 2

30. Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If Q1 coulomb and Q2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the centre of one ring to that of other is

(a) Zero (b) R

QQq

0

21

4.2

)12()(

πε

−−

(c) R

QQq

0

21

4

)(2

πε

+ (d)

R

QQq

0

21

4.2

)12()(

πε

++

PART – B CHEMISTRY

31. Which of the following does not react by SN1 mechanism

Cl Cl (a) (b) Cl Cl (c) (d) 32. CH3 – CH – CH2 – CH2 – CH3 CH2 CH2 CH3 Total number of mono chlorination products possible excluding stereoisomer of this compound – (a) 5 (b) 4 (c) 6 (d) 7 33. The most stable carbocation among

the following is – CH3

(a) (b)

OCH3 OCH3 (c) (d) 34. CH2OH

42SOH

HBrconc (P)

OH Product ‘P’ is – CH2Br CH2OH

(a) (b) OH Br CH2Br CH2Br

(c) (d) Br

Space for rough work

Silver Line Prestige School PCB/XII/code-M

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35. Which is not formed as an intermediate in alkaline hydrolysis of

2-chlro nitrobenzene Cl OH O N (a) O Cl OH O N (b) O

Cl OH O N (c) O

Cl OH O N (d) O

36. Hydrolysis methyl acetate in aqueous

solution has been studied by titrating

acetic acid against NaOH. At 25°C rate constant of this pseudo first order reaction (as concentration of water remain constant (55 mol/lit) during the course of reaction) was found to be

2 ×10–3 minute–1, value of K′ in the equation.

r = K′ [CH3COOCH3] [H2O] is – (a) 3.6 × 10–5 minute–1 (b) 3.6 × 10–5 lit mol–1 minute –1

(c) 2 × 10–3 minute-1

(d) 2 × 10–3 lit mol–1 minute–1 37. The rate constant of a reaction

A → B is 0.05 mol lit sec–1, rate of reaction after 10 seconds if initially 2 moles of A are taken in a 10 lit flask. (a) 0.05 mol lit sec–1 (b) 0.01 mol lit sec–1 (c) 0.1 mol lit sec–1

(d) 0.02 mol lit sec–1

38.

Correct reactivity as well cause in above table is for – (a) (i), (iii) & (iv) (b) (ii), (iii) & (iv) (c) (i) & (iv) (d) All (i), (ii), (iii) & (iv)

39. A 10° rise in temperature will increase rate of which of the following reaction by highest factor

(a) A → B EA = 25 kJ

(b) X →Y EA = 50 kJ

(c) M → N EA = 75 kJ

(d) P → Q EA = 100 kJ

40. For the reaction N2(g) + 3H2(g) → 2NH3. If rate of formation of NH3 is 3.4 gm/sec, what is rate of disappearance of H2. (a) – 5.1 gm/sec (b) 5.1 gm/sec (c) – 0.6 gm/sec (d) 0.6 gm/sec

41. On increasing temperature rate of

which reaction will not increase (a) A zero order reaction (b) A first order exothermic reaction (c) A first order endothermic reaction (d) Rate of all reactions increases on increasing the temperature

Reactivity Cause

(i) Br < I

for SN1

Bond energy of

C – Br > C – I

(ii) Br < I

for SN2

Leaving group

I– > Br

–

Cl

(iii) < CH3Cl

reactivity for NH3

C – Cl bond in

benzene carry

partial double

character due to

resonance

CH3 – CH – Br CH – Br

(iv) <

reactivity for SN1

H

C is more

carbocation

due to

more number of

resonance

structure

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Silver Line Prestige School PCB/XII/code-M

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42. The gaseous reaction

A (g) → 2B(g) + C (g) is found to be first – order with respect to A . if the reaction is started with pA = 90 mm Hg, the pressure after 10 min is found to be 180 mmHg. The rate constant of the reaction is (a) 1.15 x 10-3 s-1 (b) 2.30 x 10-3 s-1

(c) 3.45 x 10-3 s-1 (d) 0.0693 sec-1

43. The half life period of two first order

reactions are in the ratio of 3 : 2 if ‘t1’ is time required for 25% completion of first reaction & t2 is the time required for 75% completion of the second reaction the ratio of t1/t2 = ?

(log 1.333 = 0.1249) (a) 0.311 : 1 (b) 0.420 : 1 (c) 0.273 : 1 (d) 0.119 : 1

44. What percentage of the fraction of

molecules will cross over the energy barrier for activation energy 19.16 kJ at 1000 K temperature (a) 90% (b) 80% (c) 20% (d) 10%

45. For the reaction

A → B KA = 1015 e-2000/T and for the reaction

C → D KC = 1014 e-1000/T the temperature at which Ka = Kc is – (a) 1000 K (b) 2000 K (c) 2000/2.303 (d) 1000/2.303

46. For the reaction A(g) → B(g), the following data was obtained at 300 K. the rate law is – (a) r = K [A]0 (b) r = K [A]1 (c) r = K [A]2 (d) r = K [A]3

47. In which cell the emf remain constant

throughout the life (a) Leclanche cell (b) Mercury cell (c) Ni-Cd battery (d) Fuel Cell

48. For the reaction 2NO(g) + 2H2(g) → N2(g) + 2 H2O(g) the following data were obtained –

Rate law is – (a) r = K [NO] [H2] (b) r = K [NO]2 [H2] (c) r = K [NO] [H2]2 (d) r = K [NO]2 [H2]2

49. For the reaction A → B the rate

constant at 500 K is 5 × 10–3 sec–1. If this reaction is carried out in presence of catalyst at 500 K, the value of new rate constant would be, if Arrhenius factor remain constant and catalyst decrease the activation energy by 19.16 kJ/mol

(a) 0.5 (b) 0.05 (c) 0.005 (d) 0.0005 50. The emf of the following hydrogen

electrode at 298 K is 0.236 V. The pH of HCl solution is – Pt H2 H+

1 atm HCl Solution (a) 2 (b) 3 (c) 4 (d) 1 51. Zn Zn++ Cu++ Cu 0.1 M 0.1M ZnSO4 CuSO4 If ZnSO4 solution is diluted to 10 times to its initial volume the emf of cell will (a) Increase by 59.1 milli volt (b) Increase by 29.5 milli volt (c) Decrease by 59.1 milli volt (d) Decrease by 29.5 milli volt 52. Total number of structural isomers of

molecular formula C4H6 are (a) 8 (b) 9 (c) 10 (d) 11

t (sec) 0 100 200 300

PA in

Pascal 5 × 10

3 4 × 10

3 3 × 10

3 2 × 10

3

Ex

p [NO] ×××× 10

-4

Mol lit-1

[H2] ×××× 10–3

mol lit–1

410

][ −×−

dt

NOd

mol lit–1

minutes–1

1 1.5 4.0 4.4

2 1.5 2.0 2.2

3 0.5 2.0 0.244

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Silver Line Prestige School PCB/XII/code-M

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53. A lead storage battery holds 5 lit which is 24.5 w/w H2SO4 solution of density 1.3 gm/ml. It was used for 96500 sec by which H2SO4 became 12.25% w/w with density 1.1 gm ml–1 if volume of H2SO4 remained practically constant, the constant current which was withdrawn from battery is –

(a) 9.4 amp (b) 4.8 amp (c) 7.6 amp (d) 18.8 amp

54. During electrolysis of acidulated water using platinum electrode in total 22.4 lit of gaseous mixture (H2 & O2) was evolved at S.T.P. Number of Faraday used are –

(a) F3

2 (b) F

3

1

(c) F3

4 (d) 2 F

55. In an aqueous solution of salt of an oxoacid of chlorine a current of 9.65 amp was passed for 1000 sec by which 224 ml of Cl2(g) was evolved at S.T.P. The salt should be –

(a) NaOCl (b) NaClO2 (c) NaClO3 (d) NaClO4

56. In which case on passing electricity (electrolysis) pH of solution will not change – (I) Aqueous solution of NaCl using platinum electrode (II) Aqueous solution of CuSO4 using copper electrodes (III) Aqueous solution of ZnSO4 using platinum electrode

(a) I & II (b) II & III (c) I & III (d) all I, II & III 57. A cubic cell having edge length one

meter was filled with 1 mol of an electrolyte. The resistance of this cell was found to be 50 ohm. The molar conductivity of electrolyte is –

(a) 2 × 10–2 S m2 mol–1

(b) 2 × 10–3 S m2 mol–1

(c) 2 × 10–1 S m2 mol–1 (d) 20 S m2 mol–1

58. CH3

υh

Cl2 (P)

CH3

3

2

FeCl

Cl (Q)

CH3

3

2

FeCl

Cl (R)

OCH3 P, Q & R were added in aqueous NaOH solution separately at 298 K. Then (a) Reaction will occur only in case of P & R (b) Reaction will occur only in case of P & Q (c) Reaction will occur only in case of Q & R (d) Reaction will occur only in case of P

59. For the reaction

A2 + B2 → C The mechanism is A2 A + A

A + B2 → AB2 (slow)

AB2 + A → C The rate law reaction is – (a) r = K [A] [B2] (b) r = K [B2] (c) r = K [A2]1/2 [B2] (d) r = K [A2] [B2] 60. CH2NH2

templowSOH

NaNO

,42

2 A 22ClCu B

NH2 Compound ‘B’ is – CH2Cl Cl (a) (b) Cl Cl

CH2OH CH2Cl (c) (d) Cl NH2

Space for rough work

Silver Line Prestige School PCB/XII/code-M

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PART –C MATHEMATICS

This part of the paper contains 30 MCQ in all, divided in sections A, B, C & D. Section - I contains only one correct choice out of four for each question, Section – II can have one or more than one correct choice, Section – III contains exactly two correct choices. Section – IV has its own instructions. Marking is +4/-1

61. If x = a(cos θ + θsinθ), y = a(sinθ –

θcosθ) is a parametric equation of y =

f(x). If p(θ) denotes length of the perpendicular from origin to the curve

then θd

d p(θ) is

(a) a sec θ (b) a tan θ (c) zero (d) none of these

62. If 122

=+b

y

a

x and 1

22

=+d

y

c

x cut

orthogonally then (a) a – b = c – d (b) a + b = c + d (c) ac = bd (d) none 63. All points of the curve

y2 = 4 a(x + a sin a

x) at which

tangents are parallel to X axis lie on (a) circle (b) parabola (c) straight line (d) none 64. If f(x) = x3 – x2 + x + 1 and g(x) defined

as g(x) = Maximum f(t) ; 0 ≤ t ≤ x

0 ≤ x ≤ 1 = 3 – x for x > 1 then (a) f(x) is continuous in (0, 2) (b) f(x) is differentiable in (0, 2) (c) f(x) is not differentiable at ‘2’ points in [0, 2] (d) none

65. If (2x)7 (3y)3 = (2x + 3y)10 then dx

dy is

(a) y

x

3

2 (b)

x

y

(c) x

y

3

7 (d) none of these

66. If f(x) = x3 + sin π x and ‘g’ inverse of

‘f’ then g′ (1) is

(a) 2 – π

(b) 3 – π

(c) π−3

1

(d) 3

1

67. The line ax + by + c = 0 is a normal to

xy = 1. Then (a) a > 0, b = 0

(b) a × b < 0

(c) a × b > 0 (d) none

68. If f(x) = sin–1 2x 21 x− and

f′(x) = 21

2

x− then

(a) 2

1

2

1<<− x (b)

2

1

2

1≤≤− x

(c) – 1 ≤ x ≤ 1 (d) none of these

69. If f(x) = xx

1

, g (x) =

x

x

1, x ≠ 0

Then

(a) f′ (e) = g′ (b) f′ = g′(e)

(c) f′ = g′(e) (d) none of these

70. The domain of f(x) = ||2

1||

x

x

−

− is

(a) (–2, –1] U [1, 2] (b) (–2, –1] U [1, 2)

(c) (– ∞, –2) U (2, ∞) U [–1, 1] (d) none of these 71. The function f(x) = – 2x3 + 21 x2 – 60 x + 41 is

(a) Strictly positive in [– ∞, 1]

(b) Strictly negative in ( – ∞, 1) (c) neither strictly positive nor strictly

negative in (– ∞, 1) (d) f(x) decreases in (2 ,5)

e

1

e

1

e

1

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Silver Line Prestige School PCB/XII/code-M

Page - 10

x → 1

y → 0

72. A man is standing on a straight bridge over a river and an other man on boat is in the river just below the man on the bridge. If the first man starts walking at a uniform speed of 4m/min and the boat moves perpendicular to the bridge at the speed 5m/minute. The rate at which both are separated from each other after 4 minutes, given that height of the bridge above the boat is 3 mts is

(a) utemts min/665

164

(b) utem min/655

162

(c) utemt min/755

166

(d) none of these 73. The reasonable approximation of

(8.01)4/3 + (8.01)2 is (a) 80.2167 (b) 80.1867 (c) 80.0867 (d) none of these

74. If y = f(x), qdx

ydp

dx

dy==

2

2

, then 2

2

dy

xd is

(a) 3p

q−

(b) 2p

q−

(c) 3p

q

(d) p

q2

75. If y2 + x2 + 2ax + 2by = K2 then

2

2

2/32

1

dx

yd

dx

dy

+

is

(a) K

(b) 222baK −−−

(c) 222baK ++−

(d) none of these

76. A man starts moving on a circular track, starts from A. The source of light is at the centre of the track. A force is along a tangent to the track at A. If the speed of the man is 30 Km/Hr. The speed with which the shadow of the man moves on the force at the instant when man has

moved 8

1 th of the track is

(a) 40 (b) 60 (c) 80 (d) none of these

77. If 2x = y1/5 + y –1/5 and 2

22 )1(

dx

ydx −

+ λx dx

dy = µ y

Then

(a) λ = 1, µ = 5

(b) λ = 1, µ = 25

(c) λ = 5, µ = 25 (d) None

78. If y = dxc

bxa

+

+ then

(a) 3

32

2

2

.23dx

yd

dx

dy

dx

yd=

(b) 3

32

2

2

.32dx

yd

dx

dy

dx

yd=

(c) dx

dy

dx

yd

dx

yd.32

2

2

3

3

=

(d) none of these

79. The function y = e|x| , x ∈R is –

(a) differentiable for all x∈R (b) increases for all x (c) non differentiable at finite number of paints (d) none of these

80. Lim 123

3

−− yx

y as (x, y) → (1, 0)

on y = x–1, is (a) 0 (b) 1

(c) 3

1

(d) none of these

Space for rough work

Silver Line Prestige School PCB/XII/code-M

Page - 11

Section – II

81. (a) If f is even function then the number of real roots of

f(x) =

+

+

2

1

x

xf are 4

(b) If f(x) = x

x

+

−

1

1, x > 0 then least value

of f(f(x)) + f

xf

1 is

2

1

(c) The domain of

f(x)= )cos(loglog 4/13 xa + is ‘R’ then

Range of values of a is φ set

(d) If f(x) = 3

2

−

−

x

x from 3−R to 1−R

then ‘f’ is a bijection 82. (a) The number of integral values of ‘n’

so that 3π is period of

cosnxsin n

x5 are eight

(b) The number of points where f(x) defined as f(x) = x2 – 5x + 7 when x is rotational and = 1 when x is irrational is continuous are, ‘2’ only

(c) Limx→0

−

x

x

x

x tansin= – 1

When [.] denotes greatest integer function (d) The value of ‘m’ so that x3 – mx2 + 3x – 11 is invertible

function lies in (– ∞, –3] U [0, α)

83. If f(x) = cot –1 2

3

31

3

x

xx

−

− and

g(x) = cos–1 2

2

1

1

x

x

+

− then

limx→a

<<

−

−

2

10,

)()(

)()(a

agxg

afxf is

(a) )1(2

32a+

(b) 2

3

(c) )1(2

32x+

(d) 2

3−

84. If t2 – tx + 1 = 0 and t2 – ty – 1 = 0

Then 2

2

dx

yd

(a) 3

4

y− (b)

3)1(

42

3

−−

t

t

(c) 3

22

y

xy − (d) none of these

Section – III

85. If f(x) = x p (ln|x| + cos ) , x ≠ 0 is

differentiable at x = 0. Then (a) ‘p’ must be even integer (b) p is any real number > 2

(c) p can be even integer ≥ 2 (d) p is any real number > 1 86. If 4a + 2b + c = 0 then f(x) = 3 ax2 + 2bx + c = 0 has atleast one root in (a) (0, 2) (b) (1, 3) (c) (–2, 2 ) (d) (2, 3) 87. (a) tan–1 (sin x + cos x) increases in

2,

4

ππ

(b) ln (1 + x) > x

x

+1 , x > 0

(c) ln (1 + x) > x , x > 0

(d) if 0 < β < α < 2

π

Then α – β > sin α – sin β

88. limit 1 + cos2m(n!πx) is

m → ∞, n → ∞ (a) 2 when x is rational and 1 when x is irrational (b) 2 when x is irrational and 1 when x is irrational (c) is continuous for all rational x (d) is discontinuous for all rational x

x

1

Space for rough work

Silver Line Prestige School PCB/XII/code-M

Page - 12

Section – IV This section contains 1 question. This question

contains statements given in two columns, which

have to be matched. Statements in Column I are

labelled as i, ii, iii and iv whereas statements in

Column II are labelled as p, q, r and s. The answer to

this question have to be appropriately bubbled as

illustrated in the following example.

If the correct matches are i-q, i-r, ii-p,

ii-s, ii – t, iii-r, C-s and iv-q, then the correctly

bubbled matrix will look like the following. P Q R S T

i

ii

iii

iv

89. If f(x) = 65

562

2

+−

+−

xx

xx, x ≠ 2, x ≠ 3

Then match the statements of column I with the correct statement of column II Column - I (A) If –1 < x < 1 then (B) If 1 < x < 2 then (C) If 3 < x < 5 then (D) If x > 5 then Column - II (p) 0 < f(x) < 1 (q) f(x) < 0 (r) f(x) > 1 (s) f(x) < 1 90. If [.], |x| represent G.I.F and modules

function resp. the match the function in Column I with the correct statement of Column II

Column - I (A) x |x|

(B) || x

(C) x + [x] (D) |x – 1| + | x + 1|

Column - I (p) Continuous in (–1, 1) (q) differentiable in (–1, 1) (r) strictly increasing in (–1, 1) (s) not differentiable at least on pt. in (–1, 1)

Space for rough work