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NARAYANA JUNIOR COLLEGE

SR IIT ALL STREAMS ADV MODEL DPT Date: 12/04/2016

PHYSICS SINGLE ANSWER QUESTIONS

1. Find the radius of gyration of a cylinder of mass M radius r and length 2r about an axis

passing through its centre and perpendicular to its symmetry axis

A) 12

r B)

3

12r C)

7

12r D)

10

12r

2. A cylinder of mass ‘m’ suspended by two strings wrapped around the cylinder one near each

ends. The free ends of the strings being attached to hooks on the ceiling, such that the

length of the cylinder is horizontal. From the position of rest, the cylinder is allowed to roll

down as suspension strings unwind in same sense, calculate the tension in the each string.

A) 1

3mg B)

1

6mg C)

1

9mg D)

1

12mg

3. A force F is applied tangential at the topmost point of a sphere of mass M and radius R. If the

ground is rough enough to prevent sliding, find the frictional force acting on the sphere.

A) 1

7F B)

2

7F C)

3

7F D)

4

7F

2r

r

Axis of Rotation


2

4. An equilateral triangle ABC formed from a uniform wire has two small identical beads

initially located at A. The triangle is set rotating about the vertical axis AO. Then the beads

are released from rest simultaneously and allowed to slide down, one along AB and other

along AC as shown, Neglecting frictional effects, the quantities that are conserved as the

beads slides down.

A) Angular velocity and total energy (kinetic and potential)

B) Total angular momentum and total energy

C) Angular velocity and moment of inertia about the axis of rotation.

D) Total angular momentum and moment of inertia about the axis of rotaion.

5. A cylinder of mass m and radius r rolls down a circular track from point A as shown in the

figure. Assume that the friction is just sufficient to support rolling. Velocity of the cylinder at

point A was zero. Assume r R . The reaction by the ground on the cylinder at point B is

A) 7

3mg B)

4

3mg C)

5

3mg D)

2

3mg


3

6. Four identical rods of mass 6M kg each are welded at their ends to form a square and then

welded to a massive ring having mass 4m kg having radius 1R m . If the system is allowed

to roll down the incline of inclination 030 , assuming there is no slipping find the minimum

value of friction coefficient to prevent slipping.

A) 5

7 B)

5

12 3 C)

5 3

7 D)

7

5 3

7. A uniform smooth rod is placed on a smooth horizontal floor is hit by a particle moving on

the floor at a distance / 4l from one end. Velocity of particle was perpendicular to length of

rod. Then the distance travelled by the centre of the rod after collision when it has completed

three revolutions will be [ 0e and l is the length of the rod]

A) 2 l B) l

C) / 2l D) Can’t be determined

8. A ball of mass m and radius R rolling without slipping on a rough horizontal surface collides

elastically with a smooth wall (inclined as shown) and comes back. It eventually starts pure

rolling in back ward direction. The work done by friction in the whole process i.e., starting

from pure rolling in forward direction and ultimately pure rolling in backward direction is

A) is zero B) is surely positive

C) is surely negative D) may be positive, negative or zero

9. A solid sphere is rolling purely on a rough horizontal surface (coefficient of kinetic friction =

) with speed of centre = u . It collides inelastically with a smooth vertical wall at a certain

moment, the coefficient of restitution being ½. The sphere will begin pure rolling after a time.

A) 3 /(7 )u g B) 2 /(7 )u g


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C) 3 /(5 )u g D) 2 /(5 )u g

10. A yo-yo arranged as shown, rests on a frictionless surface. When a force F is applied to the

string, the yo-yo:

A) moves to the left and rotates counterclockwise

B) moves to the right and rotates counterclockwise

C) moves to the left and rotates clockwise

D) moves to the right and rotates clockwise

11. Velocity of the centre of smaller cylinder is v . If there is no slipping anywhere, then the

velocity of the centre of larger cylinder is:

A) 2v B) v C) 3 / 2v D) / 2v

12. A system of uniform cylinders and plates is shown. All the cylinders are identical and there is

no slipping at any contact. Velocity of lower & upper plates is v and 2v respectively as shown.

Then the ratio of angular speeds of the upper cylinders to lower cylinders is

A) 1/3 B) 3 C) 1 D) 2

13. A thin uniform rod AB of mass M and length L is hinged at one end A to the horizontal floor.

Initially it stands vertically. It is allowed to fall freely on the floor in the vertical plane by

giving a small disturbance. The angular velocity of the rod when its end B strikes the floor is

A) g

L B)

2g

L C)

3g

L D)

g2

L


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14. A disc of mass M and radius R is rolling with angular speed on a horizontal plane as

shown in Figure. The magnitude of angular momentum of the disc about the origin O is

(Friction is sufficient so no slipping takes place)

A) 21MR

2 B)

2MR C) 23MR

2 D)

22MR

15. A thin wire of length L and uniform linear mass density is bent into a circular loop with

centre at O as shown in figure. The moment of inertia of the loop about the axis XX is

A) 3

2

L

8

B)

3

2

L

16

C)

3

2

5 L

16

D)

3

2

3 L

8

SECTION – II

Multiple Correct Answer Type

___________________________________________________________________________

This section contains 5 multiple correct answer(s) type questions. Each question has 4 choices

(A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

___________________________________________________________________________

16. The moment of inertia of a thin square plate ABCD of uniform thickness about an axis

passing through the center O and Perpendicular to the plate is ------

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


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where 1 2 3 4I I I I are respectively the moments of inertia about axcs 1,2,3 and 4 which are in

the plane of the plate.

17. If a rigid body is subjected to two forces 1 2 3 4f i i k acting at (3,3,4) and

2 2 3 4f i i k acting at (1,0,0) then which of the following is (are) true?

A) The body is in translatory equilibrium

B) The body is under the influence of a couple only

C) The body is under the influence of a single force

D) The body is under the influence of a force to gether with a couple.

18. In the figure, the blocks have masses1 2M and M 1 2M M and acceleration a. The pulley P

has a radius r and some mass the string does not slip on the pulley

A) The two sections of the string have unequal tensions

B) The two blocks have accelerations of equal magnitude

C) The angular acceleration of P is ‘ar’

D) Angular acceleration of the pulley is zero.


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19. A particle of mass M is projected from ground with an initial speed u and angle of projection

as shown in fig.

A) Average torque on a projectile during the time of flight about the point of projection is

zero

B) Average torque on a projectile during the time of flight about the point of projection is

2 sin 2

2

Mu

C) The torque produced by gravity on the particle at the highest point about the point of

projection is not zero

D) The torque produced by gravity on the particle at the highest point about the point of

projection is zero

20. A uniform rod of length l and mass 2m rests on a smooth horizontal table. A point of mass m

moving horizontally at right angle to the rod with velocity v collides with one end of the rod

and sticks to it, then:

A) Angular velocity of the system after collision is /v l

B) Angular velocity of the system after collision is / 2v l

C) The loss in kinetic energy of the system as a whole as a result of the collision is 2 / 6mv

D) The loss in kinetic energy of the system as a whole as a result of the collision is 27 / 24mv

CHEMISTRY

SINGLE ANSWER QUESTIONS

21.


8

A) 2 B) 3 C) 4 D) 5

22. The electrophilic aromatic substitution proceeds through a

A) Free radical B) Sigmacomplex C) Benzyne D) Carbene

23. Heating benzene in a large excess of 80% 2 4D SO in 2D O results in what products

A) 6 5 3C H SO D B)

6 5C H OD C) 6 5C H D D)

6 6C D

24. Which of the following organic chlorides will not give a friedel craft alkylation product when

heated with Benzene and 3AlCl ?

A) 3 3CH CCl B)

2 2CH CHCH Cl C) 3 2CH CH Cl D)

2CH CHCl

25. The compound ‘X’ in the reaction

A)

B)

C)

D)

26. For the coagulation of 100 ml of arsenous sulphide solution 5 ml of 1M NaCl is required. The

coagulation value of NaCl is

A) 48.1 B) 38.1 C) 49.5 D) 47.6

27. Gold number of gelatin is 0.01. Find the amount of gelatin to be added to 1000 ml of a

colloidal Sol of gold to prevent its coagulation before adding 1 ml of 10% NaCl solution.

A) 2 mg B) 4 mg C) 1 mg D) 5 mg

28. At 400 K the energy of activation of a reaction is decreased by 0.8 Kcal in the presence of

catalyst hence the rate will be


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A) Increased by 2.73 times B) Increased by 1.18 times

C) Decreases by 2.7 times D) Increased by 6.26 times

29. Which of the following is most effective for coagulation of 2 3AS S Sol

A) 3 6K Fe CN B) 4 6

K Fe CN C) 2CaCl D)

2 4Na SO

30. Activators are generally metal ions. The catalytic activity of amylase increases in the presence

of

A) Na B)

2Ca C)

2Cu D) 2Mn

31. How many moles of 3 4Th NO should be dissolved in 15 moles of water so that vapour

pressure of water is reduced by 40%

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

32. HP of 0.1 M monobasicacid is measured to be 2. Its osmotic pressure at a given temperature

‘T’ K is

A) 0.1 RT B) 0.11 RT C) 1.1 RT D) 0.01 RT

33. To 10 ml of 1M 2BaCl solution 5 ml of 0.5 M 2 4K SO is added.

4BaSO is precipitated what

will happen?

A) Freeezing point is increased B) Freezing point is decreased

C) Boiling point is lowered D) Freezing point remains same

34. An aqueous solution of methanol in water has vapour pressure

A) less than that of water B) Equal to that of water

C) More than that of water D) Equal to that of methanol

35. The osmotic pressure of an aqueous solution of a non electrolyte is 18.8 atm at 015 C what

will be the vapour pressure of this solution at 0100 C (Density of water at 0100 C is 1g / cc)

A) 0.958 atm B) 3.26 atm C) 6.23 atm D) 7.12 atm

SECTION – II





10

36. The vapour pressure of a solution depends upon

A) Surface area B) Temperature

C) Mole fraction of solvent D) degree of dissociation of solute


11

37. Which of the following forms an ideal solution?

A) Ethyl bromide + Ethyl Iodide B) Ethyl alcohol + water

C) Chloroform + Benzene D) Benzene + Toluene

38. For an electrophilic substitution reaction, the presence of a halogen atom in the benzene ring

A) Deactivates the ring by inductive effect B) Deactivates the ring by resonance

C) Increases the charge density at ortho and para positions relative to metaposition by

resonance.

D) Directs the incoming electrophile to metaposition by increasing the charge density at

metaposition

39. Which of the following acts as negative catalyst?

A) Ethanol in oxidation of chloroform B) Tetra ethyl lead used as antiknocking agent

C) Glycerol in the decomposition of 2 2H O

D) Fe in the formation of ammonia by habers process

40. Which of the following is / are correct about Freundlich adsorption isotherm for gases and

solutions

A) 1

nx

KCm B)

1x bp

m a

C) log log logx

k n pm D)

1log log log

xk c

m n

MATHEMATICS

SINGLE ANSWER QUESTIONS

41. Let

2

2 21 1 1

x dxf x

x x

and 0 0f . Then the value of 1f will be

A) log 1 2 B) log 1 24

C) log 1 2

4

D) None of these

42. cos 4 1

cot tan

xdx

x x

is equal to


12

A) 21 11 sec 2 cos 2

2 4n x x c B) 21 1

1 sec 2 cos2 4

n x x c

C) 21 11 cos 2 cos 2

2 4n x x c D) 21 1

1 cos 2 cos2 4

n x x c

43. If 2

3tan tan ,

cos sin 2

dxa x b x c

x x then

A) 2 1

,5 5

a b B) 2

, 55

a b

C) 2 1

,5 5

a b D) 2

, 55

a b

44. If /2 2

1 2

0

cos

1 cos

xI dx

x

,

/2 2

2 2

0

sin

1 sin

xI dx

x

,

/2 2 2

3 2 2

0

1 2cos sin

4 2cos sin

x xI dx

x x

then

A) 1 2 3I I I B)

3 1 2I I I C) 1 2 3I I I D) None of these

45.

0

2,

2

x t

tdt where . denotes the greatest integer function, and x R , is equal to

A) 1

2 11 2

xx

n B)

12

1 2

xx

n

C) 1

21 2

xx

n D)

12 1

1 2

xx

n

46. Let :f R R be a continuous function and 2f x f x is true .x R If 1 3,f then

value of 1

1

f f x dx

is equal to

A) 6 B) 0 C) 3 3f D) 2 0f

47. The value of /2

0

sin 2 ,x dx

where 0, is

A) 1 cos B) 1 cos C) 1 D) cos

48. The value of

1/2

lim tan tan ........ tan2 2 2

n

n

n

n n n

is


13

A) e B) 2e C) 1 D) 3e


14

49. If nA is the area bounded by y x and ny x , ,n N then

2 3, .......... nA A A

A)

1

1n n B)

1

2 1n n n C)

1

1

2 1n n n D)

2

1

2 1n n n

50. The area of the region bounded by 2 2 2 3 0x y x and 1y x is

A) 1 .2

sq units B) 2 .sq units C) 4 .sq units D) .

2sq units

51. The area bounded by the loop of the curve 2 2 24 4y x x is

A) 7 / 3 .sq units B) 8 / 3 .sq units C) 11/ 3 .sq units D) 16 / 3 .sq units

52. The form of the differential equation of the central conics 2 2 1ax by is

A) dy

x ydx

B) 0dy

x ydx

C)

2 2

2

dy d y dyx xy y

dx dx dx

D) None of these

53. The equation of the curve which is such that the portion of the axis of x cut off between the

origin and tangent at any point is proportional to the ordinate of that point is

A) logx y a b x B) 2log x by a

C) 2 logx y a b y D) None of these

54. An object falling from rest in air is subject not only to the gravitational force but also to air

resistance. Assume that the air resistance is proportional to the velocity with constant of

proportionality as 0k , and acts in a direction opposite to motion 29.8 /g m s . Then

velocity cannot exceed.

A) 9.8 / /k m s B) 98 / /k m s C) /9.8

km s D) None of these


15

SECTION – II




55. The population of a country increases at a rate proportional to the number of inhabitants. f is

the population which doubles in 30 years, then the population will triple in approximately

A) 30 years B) 45 years C) 48 years D) 54 years

56. If 0

2 ,

x

g x t dt then

A) g x x x B) g x is monotonic

C) g x is differentiable at x = 0 D) 'g x is differentiable at x = 0

57. If f x is integral over 1,2 , then 2

1

f x dx is equal to

A) 1

1lim

n

nr

rf

n n

B) 2

1

1lim

n

nr n

rf

n n

C) 1

1lim

n

nr

r nf

n n

D) 2

1

1lim

n

nr

rf

n n

58. If tA is the area bounded by , ,i ix a y b i N where 1

3

2i i ia a b and

1 1 1, 0, 32,2

ii

bb a b then

A) 3 128A B) 3 256A

C) 2

1

8lim 32

3

n

in

i

A

D) 2

1

4lim 16

3

n

in

i

A

59. If cos 4 1

,cot tan

xdx Af x B

x x

then

A) 1

8A B)

1

2B

C) f x has fundamental period 2

D) f x is an odd function


16

60. The graph of the function y f x passing through the point 0,1 and satisfying the

differential equation cos cosdy

y x xdx

is such that

A) it is a constant function B) it is periodic

C) It is neither an even nor an odd function D) It is continuous and differentiable for all x

NARAYANA JUNIOR COLLEGE

SR IIT ALL STREAMS ADV MODEL DPT Date: 12/04/2016

PHYSICS

1 – 10 C B C B A B A C A B

11 – 20 B B C C D A, B, C A A, B B, C A, C

CHEMISTRY

21 – 30 C B D D B D C A C A

31 – 40 B B B A A B, C, D A, D A, C A, B, C A, D

MATHEMATICS

41 – 50 B C B C A A C C D A

51 – 60 D C A A C A, B, C B, C A, C A, C A, B, D


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HINTS

PHYSICS

1.

22 2 2

22

1 1 1 12

4 12 4 12

7 7

12 12

I mR mL mr m r

mrmK K r

2.

2 &2

1 1

4 2

2 1

3 6

mg T ma TR I

HenceT Ma mg ma

a g T mg

3.

22

5

9

10 3

7 7

F f Ma

FR fR MR

R

Fso a Hence f F

M

4. No torque acts on the system so the angular momentum will remain conserved. Also if no

external force does any work, hence the total energy remain conserved.

a

F

f

f


18

5. Acceleration = 2

n

Va

R and nN mg ma ;

22

2

1( ) 1

2

Kmg R mv

r

6.

222( 2)

412 2

M R RI M mR

2 2 2820 .

3I MR mR kg m … (i)

(4 ) sin (4 )M m g f M m a

.a

f R IR

…. (ii)

Solving (i) and (ii)

7

24

ga

5

20 28 cos3012 3

f a g

7. iF dt MV and 2

4 12i

l MlFdt

So, 3

lV

6

23

lV t l

8. Conceptual

9. Conceptual

10. Conceptual

11. In the figure 1C and 2C are IC of two cylinders. In the absence of slipping between plank and

cylinders, point 1A and 2A have same velocity.


19

Angular velocity of larger cylinder is 2

4 2

v v

R R

(2 )2

CM

vv R v

R

12. In the absence of slipping, velocities of contact points of upper cylinders and lower cylinders

are respectively.

3

2

ABup

v v

R AB ,

2

CDlower

v v

CD R

3up

lower

13. Loss is PE = gain in rotational KE. As the centre of mass of the rod falls through a distance

L/2, the loss in mgL

PE = 2

Gain in 2

2 21 1 mLKE = Iω = ω

2 2 3

Equating the two, we have mgL mL ω

2 6

Or 3g

L, which is choice c

14. Let OC = Rc and let vc be the velocity of the centre of mass of the disc. The linear

momentum of the centre of mass is Pc = Mvc. If Lc is the angular momentum of the disc

about C, then the angular momentum about origin O is


20

0 c c cMagnitudeL = I ω +R × Mv sinθ

2

c c

1MR ω + MR v sin θ

2

2

c

1I = MR

2

21MR ω + MR Rω

2

c cR sin θ = R and V = Rω 23= MR ω

2

15. Let m be the mass of the loop and r its radius. The moment of inertia of the loop about ax

axis passing through the centre O is

2

0

1I = mr

2

From the parallel axes theorem, the moment of inertiabout XX’ is

2 2 2 2

0

1 3I = I + mr = mr + mr = mr

2 2

The mass of the loop, m = pL and radius r = L/2 π

Hence

2 3

2

3 3ρLI = ρL =

2 2 8

L

SECTION – II


___________________________________________________________________________

This section contains 5 multiple correct answer(s) type questions. Each question has 4

choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.

_________________________________________________________________________

16. Conceptual

17. Conceptual

18. Conceptual

19. Conceptual


21

20. W.r.t centre of mass frame.

From law of conservation of momentum 13mv mv

1

3

vv ( 1v - velocity of C.M)

From law of conservation of angular momentum w.r.t to centre of mass of the system

2 221 1(2 )

23 12 6 3

mvL m L L L vm m

L

Loss in K.E = 222 1 1 11 1 1

(3 )2 2 2

f iK K mv m v I

Where

2 221 (2 )

212 6 3

m L L LI m m

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