Match the following - - SECTION – III

SECTION – III

20. Match the following -

− x

y = cos 1 (B) π

−

− x

y = cos (0.28)

(C)

1 x y

− π

− = cos (1) (D) None of these

Paragraph # 2 (Ques. 16 to 18)

Two circles S1 = 0 and S2 = 0 are touching to each other externally at point T, with centre C1, C2 and radii r1 and r2 respectively.

If P and Q be the points of contact of a direct common tangent to the two circles and PQ meets the line joining C1, C2 in S. Tangent at common point T is intersecting to the tangent PQ at R point and to other direct tangent at V point. Let S1= x²+ y²– 6x = 0 and S2= x²+ y²+ 2x = 0.

16. Angle between the two direct tangents is–

(A) 90º (B) 30º

(A) y = 3 x + 3 , y = – 3 x + 3 (B) y =

x – 3 , y = 3

−x – 3

x + 3 , y = 3

−x – 3 (D) None of these

18. A circle S = 0 of radius 1 units rolls on the outside of the circle S2 = 0, touching it externally, locus of the centre of this outer circle is –

(A) Circle (B) Ellipse (C) Parabola (D) None of these

SECTION – IV

Matrix – Match Type

This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. any given statement in Column I can have correct matching with ONE OR MORE statements (s) in column II. The appropriate bubbled corresponding to the answers to these questions have to be darkened as illustrated in the following example : If the correct matches are A – p, s and t; B – q and r;

C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following.

q r

p s

r p q

t s t r

A B C D

p q r s t

19. Match the following-:

Column- I Column- II

(A) The sum of the series

∑

= 10

0 r

20C is r

(p) – ¹⁰C5

(B) The coefficient of x⁵³ in

∑

− − 100

0 r

r r r 100

100C (x 3) 2 is

(q) ¹⁰⁰C4

…..–(¹⁰C9)² + (¹⁰C10)² equals (r) 2¹⁹+ 2 120C10

(D) The value of

95C4 +

∑

= 5 − 1 j

j 3 100 C is

(s) – ¹⁰⁰C53

(t) ¹⁰⁰C47

20. Match the following -

Column -I Column -II

(A) If the lines 1

2 x−

= 1 3 y−

= λ z− 4

and λ x−1=

2 4 y−

= 1 5 z− intersect at (α, β, γ) then λ =

(p) 0

(B) If

∞

→

xlim 4x _



 



 



 



 +

− +

π ₋

2 x

1 tan x

1 =

y² + 4y + 5 then y =

(q) –1

(r) –2

(D) If a = iˆ + jˆ +kˆ, a .b = 1 and a ×b =jˆ–kˆ, then |b | is equal to

(s) 1

(t) –3

PHYSICS

SECTION – I

Straight Objective Type

This section contains 8 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.

1. ABCD is a smooth horizontal fixed plane on which mass m1 = 0.1 kg is moving in a circular path of radius r = 1 m. It is connected by an ideal string which is passing through a smooth hole and connects of mass m2 = 1/ 2 kg at the other end as shown. m2

also moves in a horizontal circle of same radius of 1 m with a speed of 10m/s. If g = 10 m/s² then the speed of m1 is-

m₂ D

m₁

A B

(A) 10m/s (B) 10 m/s

1 m/s (D) None of these

2. A L shaped rod whose one rod is horizontal and other is vertical is rotating about a vertical axis as shown with angular speed ω. The sleeve shown in figure has mass m and friction coefficient between rod and sleeve is µ. The minimum angular speed ω for which sleeve cannot sleep on rod is –

m ω

sleeve

l (A)

µl

ω g

(B)

l µg

= ω

ω l (D) None of these

3. Two solid spherical balls of radius r1 & r2 (r2 < r1), of density σ are tied up with a string and released in a viscous liquid of lesser density ρ and coefficient of viscosity η, with the string just taut as shown. The terminal velocity of spheres is -

(A) r g( ) 9

2 ₂² σ−ρ

η (B) r g( )

2 ₁² σ−ρ η (C)

η ρ

− σ +

+ ( )g

r r

) r r ( 9 2

2 1

13 (D)

η ρ

− σ

−

− ( )g r

r ) r r ( 9 2

2 1

4. A block of mass m is attached to an ideal spring and system lies in vertical plane as shown. Initially the supporting plane is placed so that spring remains in its natural length then the plane is moved very slowly downwards. The graph showing variation of normal reaction applied by mass on supporting plane with distance travelled by block is –

Supporting plane M

(A) ^mg

x N

(B)_mg

x N

(D) None of these

5. A massless container is filled with liquid of density ρ. It contains two holes as shown in figure. Container rests on ground. Area of the two holes are A each.

Container is filled with liquid upto height H. Then –

3H/4 H

H/4

(A)Torque produced by normal force between container & ground about center of gravity is

2 AgH²

ρ into the plane of paper

(B) Torque produced by friction about center of gravity is ρAgH² out of the plane of paper

4 AgH²

ρ into the plane of paper

(D) Torque produced by normal force between container and ground about centre of gravity is zero

6. A B

Two containers A & B contain ideal gases helium and oxygen respectively. Volume of both containers are equal and pressure is also equal. Container A has twice the number of molecules than container B then if vA & vB represent the rms speed of gases in containers A & B respectively, then

(A)

B A

v = 2 (B)

B A

v v = 4

(C)

B A

v = 2 (D)

B A

v v = 8

7. A capacitor is composed of three parallel conducting plates. All three plates are of same area A. The first pair of plates are kept a distance d1 apart and the space between them is filled with a medium of a dielectric ε₁. The corresponding data for the second pair are d2 & ε₂ respectively. What is the surface charge density on the middle plate ?

d1 d2

ε₁ ε₂

(A) _



 



ε +ε ε

2 2 1

0V d1 d (B) _



 



ε +ε ε

−

2 2 1 0V d1 d



 



ε +ε ε

2 2 1 0V d1 d

2 (D) _



 



ε +ε ε

−

2 2 1 0V d1 d 2

8. The mirror of length 2l makes 10 revolutions per minute about the axis crossing its mid point O and perpendicular to the plane of the figure There is a light source in point A and an observer at point B of the circle of radius R drawn around centre O (∠AOB = 90º)

What is the proportion l

R if the observer B first sees the light source when the angle of mirror ψ = 15º ?

R B l

l O

(A) 2 (B) 2

1 (C) 2 2 (D) 2 2

SECTION – II

Multiple Correct Answers Type

This section contains 4 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.

9. A body moves in a circular path of radius R with deceleration so that at any moment of time its tangential and normal acceleration are equal in magnitude. At the initial moment t = 0, the velocity of body is v0 then the velocity of body at any time will be –

(A) v =



 

 + R

t 1 v

0 at time t

(B) v = ^R

S 0e

v ⁻ after it has moved S meter (C) v = v0e^–SR after it has moved S meter (D) None of these

10. A cylinder block of length L = 1m is in two immiscible liquids. Part of block inside liquid(1) is

1m and in liquid (2) is 4

1m. Area of cross-section of block is A. Densities of liquid (1) & (2) are ρ and 2ρ respectively –

Liquid (1) ρ.

2ρ. Liquid (2)

(A) Density of block is 3ρ/4

(B) Force exerted by liquid (1) on block is ρAg/4 (C) Block is depressed so that it is just completely

immersed in liquid (1) and released. A initial acceleration of block is 4/3 g

(D) In case (C) force exerted by liquid (2) on block is 3/2 ρAg

11. R = 10Ω & E = 13 V and voltmeter & Ammeter are ideal then -

c 6V

3Ω b 8V

(A) Reading of Ammeter is 2.4 A (B) Reading of Ammeter is 8.4 A (C) Reading of voltmeter is 8.4 V (D) Reading of voltmeter is 27 V

12. A parallel plate air capacitor is connected to a battery. If plates of the capacitor are pulled further apart, then which of the following statements are correct -

(A) Strength of electric field inside the capacitor remain unchanged, if battery is disconnected before pulling the plate.

(B) During the process, work is done by an external force applied to pull the plates whether battery is disconnected or it remain connected.

(D) None of the above

SECTION – III

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice questions based on a paragraph.

Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE is correct.

Paragraph # 1 (Ques. 13 to 15)

In the shown arrangement, both springs are relaxed.

The coefficient of friction between m2 and m1 is µ.

There is no friction between m1 and surface. If the blocks are displaced slightly they perform SHM together

13. If the small displacement of blocks is x then acceleration of m2 is-

(A)

2 2

m x

k (B)

2 2 1

m x ) k k ( +

m m

k k

2 1

2 1 

 



 +

+ (D) None of these

14. The condition in which frictional force on m2 acts in the direction of its displacement from mean position is –

(A)

2 1 2 1

k k

mm > (B)

2 1 1 2

k k m >m (C)

2 1 2 1

k k

mm = (D) None of these

15. If the condition obtained in Q.15 is met, then the maximum amplitude of oscillation is –

(A)

1 2 2 1

2 1 2

k m k m

) m m ( g m

− +

µ (B)

2 2 1 1

2 1 2

k m k m

) m m ( g m

− + µ

(C)

1 2 2 1

2 1 2

k m k m

) m m ( g m

+ +

µ (D) None of these

Paragraph # 2 (Ques. 16 to 18)

A conducting rod PQ of mass M rotates without friction on a horizontal plane about Ο on circular rails of diameter 'l'. The centre O and the periphery are connected by resistance R. The system is located in a uniform magnetic field perpendicular to the plane of the loop. At t = 0, PQ starts rotating clockwise with angular velocity ω₀. Neglect the resistance of the rails and rod, as well as self inductance.

B O ω

⁰

Q

R P

⊗

16. Magnitude of current as a function of time (A) ⁰ ²e ^t

R 2

Bω l −α (B) ⁰ ²e ² ^t R 16

Bω l −α

Bω l ₋_α (D) ⁰ ²e ² ^t R 8

Bω l ₋ _α

Where α = RM 8

B 3 ²l²

17. Total charge flow through resistance till rod PQ stop rotating .

(A) B 8

0M ω (B)

B 3

0M ω (C)

B 6

ω (D)

B 9

0M ω

18. Heat generated in the circuit by t = ∞ (A)

Ml²ω²₀ (B)

8 Ml²ω²₀

Ml²ω₀² (D)

32 Ml²ω²₀

SECTION – IV

Matrix – Match Type

C – p and q; and D – s and t; then the correct darkening of bubbles will look like the following.

q r

p s

r p q

In document Xtraedge April 2010 (Page 59-63)