SECTION – I

(Multiple Correct Answer Type)

This section contains 8 multiple choicequestions. Each question has 4 options (A),(B), (C) and (D) for its answer, out of whichONE OR MORE than ONE option can becorrect.Marking scheme: +4 for all correct options &+1 partial marks, 0 if not attempted and –2 inall wrong cases.

1. Two non – collinear forces of equalmagnitude and oppositely directed areacting on a body. Which of the followingstatements is/are correct?A) The resultant torque of the two forces

about any point in the plane of theforces is same

B) The resultant torque of the two forcesabout any axis in the plane of the forcesis same

C) The resultant torque of the two forcesabout any point in space is same

D) The resultant torque of the two forcesabout any axis in space is same

2. The figure showselectronic wave functionfor a hydrogen atom.A) The quantum number

of this state is 6B) The wavelength of

this electron is 6r0.(r0 is radius of ground state)

C) Can go to ground state by emitting 3different photons

D) On de excitation it emits atleast one linein infrared region of spectrum.

3. A charged particleenters into a regionwhich offers a resis-tance against itsmotion and a uni-form magnetic fieldexists in the region.The particle traces a spiral path as shownin figure. Which of the following state-ment(s) is/are correct?A) Component of magnetic field in the

plane of spiral is zeroB) The particle enters the region at Q C) If magnetic field is outward, then the

particle is positively charged

D) If magnetic field is outward, then theparticle is negatively charged

4. An infinitely long current carrying thickcylindrical conductor of radius R has a

Rcylindrical cavity of radius . The axis of 2

Rthe cylindrical cavity is at a distance 2

from the axis ofthe cylindricalconductor. A cur-rent with currentdensity J flowsalong the lengthof the conductor.The magneticfield at a point ‘P’ at a distance 2R from theaxis of the cylinder is (point ‘P’ is on theplane containing both the axes)

0JRA) Magnetic field at P is

120JR

B) Magnetic field at P is 6

C) Magnetic field on the axis of the cavity isnon – zero

D) Magnetic field on the axis of theconductor is non – zero

5. Two different coils have self inductance8mH and 2mH. The current in one coil isincreased at a constant rate. The current inthe second coil is also increased at thesame constant. At a certain instant of time,the power given to the two coils is thesame. At that time the current, the inducedvoltage and the energy stored in the firstcoil are I1, V1 and W1 respectively.Corresponding values for the second coil atthe same instant are I2, V2 and W2respectively. Then:

I1 1 I1A) = B) = 4I2 4 I2W2 V2 1

C) = 2 D) = W1 V1 4

6. In figure shown, the springconstant is k, the mass of theupper block is m and that of thelower block is 3 m. The upperblock is depressed down from itsequilibrium position by a dis-tance and released at t = 0.Which of the following are correct?A) If = 5 mg/k, then the lower block

losses constant with the ground

B) If = 7 mg/k, then the lower blocklosses constant with the ground

C) If = 7 mg/2k, then the minimumnormal reaction on 3 m from ground isless than mg

15 mgD) If = , then the minimum normal

4 kreaction on 3 m from ground is less thanmg

7. A thin uniform rod is supported by a verticalstring and by a hinge H is at equilibrium asshown in figure. In space gravity varies as

xg

= g0 (1 + ) ( j

) m/s2. Vessel is L

completely filled with water. Density ofmaterial of rod is two times the density ofwater. ‘L’ is the length of rod. Rod is free torotate about the hinge ‘H’. Mass of rod ‘m’kg.

mg0A) Initially tension in string is 25B) Initially tension in string is mg012

C) Just after cutting string angular

5g0accelerating of rod is 4L

D) Just after cutting string angular g0accelerating of rod is 2L

SECTION - II

(Integer Answer Type)This section contains 5 questions. The

answer is a single digit integer ranging from0 to 9 (both inclusive).Marking scheme: +3 for correct answer, 0 ifnot attempted and 0 in all other cases.8. A rod is given an angular acceleration

from rest so that it rotates in horizontalplane about a vertical axis. It has a smallring at a distance r from the axis of rotation.The friction coefficient between the ring

and the rod is . Neglecting gravity. Thetime after which the ring will start to slip on

1the rod is sec. Then find the value of nn

(Take = 3 rad s2 and = 1/3)9. Two identical balls

A and B, each ofmass 0.1 kg, areattached to twoidentical masslesssprings. The springmass system isconstrained to move inside a rigid smoothpipe bent in the form of circle as shown infigure. The pipe is fixed in a horizontalplane. The centres of the balls can move ina circle of radius 0.08 m. Each spring hasa natural length of 0.08 m and springconstant 0.1 N/m. Initially, both the balls

are displaced by an angle = rad12

with respect to the diameter PQ of thecircle (as shown in fig.) and released fromrest. If the frequency of oscillation of ball

xB is Hz, then find the value of x.

10. Figure shows two coherent sources S1 andS2 vibrating in same phase. AB is anirregular wire lying at a far distance fromthe source S1 and S2. Let /d = 10-3,BOA = 0.12. How many bright spots willbe seen on the wire, including points A andB?

11. Intensity of gravitational field E

in space ata point depends on co-ordinates (x, y, z) of

xi yj

the point as E

= . If the total massx2 + y2

m inside an imaginary sphere of radius a awith its centre at origin is n times

2G[G universal gravitational constant], thenn is

12. A neutron having kinetic energy 12.5 eVcollides with a hydrogen atom at rest.Neglect the difference in mass betweenthe neutron and the hydrogen atom andassume that the neutron does not leave itsline of motion. Find the possible kineticenergy (in eV) of the neutron after the event.

No. of Questions: 54 Max. Marks: 183 Time: 3 Hrs.

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PHYSICS

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