PART-I ((MCQs) (COMPULSORY)

Q.1. (i)Select the best option/answer and fill in the appropriate Circle on the OMR Answer Sheet. (20x1=20)

(ii) Answers given anywhere, other than OMR Answer Sheet, shall not be considered.

1. The square of the orbital period of a planet is:

(a)Directly proportional to the cube of the semi-major axis of its orbit.

(b)Directly proportional to the cube of the semi-minor axis of its orbit.

(c)Inversely proportional to the cube of the semi-major axis of its orbit.

(d)Inversely proportional tothe cube of the semi-minor axis of its orbit. (e)None of these

2. If the velocity of the particlebecomes doubled then its K.E:

(a)Becomes doubled (b)Reduces to half (c)Becomes four times (d)None of these

3. The P.E of a simple harmonic oscillator is:

(a)21 kx2 (b)21kx2 (c)kx2

(d)kx (e)None of these

4. Two car racers are 100 Kmaway from each other.They drive their cars at 40 Km/h and 60 Km/h

respectively towards each other. After 15 minutes they will be at a distance of:

(a)25 Km (b)50 Km (c)60 Km (d)75 Km (e)None of these

5. The equation of adiabatic change is:

(a)PV

r

= K (b)P

r

V = K (c)(PV)

r

= K (d)None of these

6. By exerting a certain amount of pressure on an ice block, you:

(a)Rise its melting point (b)Lower its melting point

(c)Make it melting at 0

o

C only (d)None of these

7. Mercury thermometer can be usedto measure temperature upto:

(a)250

o

C (b)100

o

C (c)360

o

C (d)500

o

C (e)None of these

8. Three Vectors C and B A

, not in the same plane make a Parallelepiped. The volume of Parallelepiped is:

(a) C B A

) ( (b) C B A

) . ( (c) C B A

. ) ( (d) C B A

) . ( (e)None of these

9. The moment arm ) 4 ( m r

and force ) 10 ( N F

make an angle of 30

0

about the turning point. The

torque produced will be:

(a)40 N.m (b)20 N.m (c)34.6 N.m (d)None of these

10. In total internal reflection the refracted ray makes an angle of with the normal.

(a)0

o

(b)90

o

(c)180

o

(d)None of these

11. Solar eclipse occurs when:

(a)Earth is between sun and moon (b)Sun is between moon and earth

(c)Moon is between earth and sun (d)None of these

12. Light is dispersed into different colours when passing through a glass prism because:

(a)Refraction of light occurs in glass (b)Refractive index of different colours is different

(c)Glass is denser than air (d)None of these

13. A ball is thrown with a velocity of ) / (

ˆ 8 Sec m j . The acceleration (m/Sec

2

)is

)

ˆ ˆ

(

ˆ 2 ˆ 4 vectors unit are j and i j i . The displacement after 5 seconds:

(a)52m (b)68m (c)82m (d)None of these

14. The time period of a Second’s pendulum is 2 Sec. The mass of the Spherical bob of Second’s pendulum

is 50g and is empty. If it is replaced by another solid bob of same radius but mass 100g then its time

period will be:

(a)8 Sec. (b)4 Sec. (c)1 Sec. (d)2 Sec. (e)None of these

15. The equation of the displacement of a harmonic oscillator is x=3 Sinwt + 4 Coswt

(m)

. The amplitude of

the particle will be:

(a)1m (b)5m (c)7m (d)12m (e)None of these

16. One m

3

is equivalent to:

(a)1000 liters (b)100 liters (c)10 liters (d)None of these

17. The frequency of Second’s pendulum is:

(a)2 hertz (b)1 hertz (c)0.5 hertz (d)None of these

18. The gradient of Scalar Potential is:

(a)Scalar quantity (b)Vector quantity (c)Neither Scalar nor Vector (d)None of these

19. Beats are produced because of:

(a)Interfrence of sound waves (b)Refraction of sound waves

(c)Diffraction of sound waves (d)None of these

20. The sound waves are:

(a)Longitudinal (b)Transverse (c)Electromagnetic (d)None of these

PART-II

NOTE: (i) Part-IIis to be attempted on the separate Answer Book.

(ii)Candidate must write Q. No.in the Answer Bookin accordance with Q. No.in the Q. Paper.

(iii)Attempt ONLY FOUR questions from PART-II. ALL questions carry EQUAL marks.

(iv) Extra attempt of any question orany part of the attempted question will not be considered.

(v) Use of Calculator is allowed.

Q.No.2. (a)The Vectors .

ˆ

2 ˆ 2 ˆ

,

ˆ

3 ˆ ˆ 2 k j i B k j i A

Find the magnitudes of

B A B A

. , & and Projection of B

on . A

(b)Prove that ). . ( ) . ( ) ( B A C C A B C B A

(c)Are the units vectors in the cylindrical and spherical coordinate system constant

vectors? Explain.

(2,2,3,3)

(6)

(4)

Q.No.3. (a)State Kepler’s laws of planetary motion and prove

(i) Law of Areas (ii) Law of periods.

(b)Use Maxwell’s equations to derive the electromagnetic wave equation.

(2,4,4)

(10)

Q.No.4. (a)What is Doppler’s effect? Derive expressions of frequency of sound heard by

observer when:

(i) The observer moving towards a stationary source

(ii) The source is moving towards a stationary observer.

(b)A stationary observer detects sound offrequency 250 hertz emitted from a source

at rest. He detects soundof frequency 750 hertz when source is moving towards

him with constant velocity. Determine velocity of sound.

(Velocity of sound = 341 m/Sec.)

(2,6,6)

(6)

Q.No.5. (a)Describe the Young’s double slit experiment and find the conditions of

constructive and destructive interference.

(b)The double slit arrangement is illuminated by light of wavelength 546nm, the

slits are 0.12mm apart and the screen on which the interference pattern appears is

55cm away. What is angular position of first maxima? What is linear distance

between 3

rd

and 4

th

maxima?

(10)

(4,6)

Q.No.6. (a) Describe the Postulates of relativity. Show the relativistic effecton mass, length

and time.

(b)What is the total energy E of a 2.53 Mev electron? When an energy is used as an

adjective, it refers to the Kinetic energy of the particle, here K= 2.53 Mev.

(3,3,3,3)

(8)

Q.No.7. (a)Derive the expressions of position and time coordinates in frame S relative to S

(Lorentz Transformation).

(b)Derive the Bernoulli’s equation of a steady flow.

(12)

(8)

Q.No.8. Write notes on any TWOof the following:

(a)Travelling and Standing Waves.

(b)LASER, its production and applications.

(c)Laws of thermodynamics.

(10 each) (20)

Q.1. (i)Select the best option/answer and fill in the appropriate Circle on the OMR Answer Sheet. (20x1=20)

(ii) Answers given anywhere, other than OMR Answer Sheet, shall not be considered.

1. The square of the orbital period of a planet is:

(a)Directly proportional to the cube of the semi-major axis of its orbit.

(b)Directly proportional to the cube of the semi-minor axis of its orbit.

(c)Inversely proportional to the cube of the semi-major axis of its orbit.

(d)Inversely proportional tothe cube of the semi-minor axis of its orbit. (e)None of these

2. If the velocity of the particlebecomes doubled then its K.E:

(a)Becomes doubled (b)Reduces to half (c)Becomes four times (d)None of these

3. The P.E of a simple harmonic oscillator is:

(a)21 kx2 (b)21kx2 (c)kx2

(d)kx (e)None of these

4. Two car racers are 100 Kmaway from each other.They drive their cars at 40 Km/h and 60 Km/h

respectively towards each other. After 15 minutes they will be at a distance of:

(a)25 Km (b)50 Km (c)60 Km (d)75 Km (e)None of these

5. The equation of adiabatic change is:

(a)PV

r

= K (b)P

r

V = K (c)(PV)

r

= K (d)None of these

6. By exerting a certain amount of pressure on an ice block, you:

(a)Rise its melting point (b)Lower its melting point

(c)Make it melting at 0

o

C only (d)None of these

7. Mercury thermometer can be usedto measure temperature upto:

(a)250

o

C (b)100

o

C (c)360

o

C (d)500

o

C (e)None of these

8. Three Vectors C and B A

, not in the same plane make a Parallelepiped. The volume of Parallelepiped is:

(a) C B A

) ( (b) C B A

) . ( (c) C B A

. ) ( (d) C B A

) . ( (e)None of these

9. The moment arm ) 4 ( m r

and force ) 10 ( N F

make an angle of 30

0

about the turning point. The

torque produced will be:

(a)40 N.m (b)20 N.m (c)34.6 N.m (d)None of these

10. In total internal reflection the refracted ray makes an angle of with the normal.

(a)0

o

(b)90

o

(c)180

o

(d)None of these

11. Solar eclipse occurs when:

(a)Earth is between sun and moon (b)Sun is between moon and earth

(c)Moon is between earth and sun (d)None of these

12. Light is dispersed into different colours when passing through a glass prism because:

(a)Refraction of light occurs in glass (b)Refractive index of different colours is different

(c)Glass is denser than air (d)None of these

13. A ball is thrown with a velocity of ) / (

ˆ 8 Sec m j . The acceleration (m/Sec

2

)is

)

ˆ ˆ

(

ˆ 2 ˆ 4 vectors unit are j and i j i . The displacement after 5 seconds:

(a)52m (b)68m (c)82m (d)None of these

14. The time period of a Second’s pendulum is 2 Sec. The mass of the Spherical bob of Second’s pendulum

is 50g and is empty. If it is replaced by another solid bob of same radius but mass 100g then its time

period will be:

(a)8 Sec. (b)4 Sec. (c)1 Sec. (d)2 Sec. (e)None of these

15. The equation of the displacement of a harmonic oscillator is x=3 Sinwt + 4 Coswt

(m)

. The amplitude of

the particle will be:

(a)1m (b)5m (c)7m (d)12m (e)None of these

16. One m

3

is equivalent to:

(a)1000 liters (b)100 liters (c)10 liters (d)None of these

17. The frequency of Second’s pendulum is:

(a)2 hertz (b)1 hertz (c)0.5 hertz (d)None of these

18. The gradient of Scalar Potential is:

(a)Scalar quantity (b)Vector quantity (c)Neither Scalar nor Vector (d)None of these

19. Beats are produced because of:

(a)Interfrence of sound waves (b)Refraction of sound waves

(c)Diffraction of sound waves (d)None of these

20. The sound waves are:

(a)Longitudinal (b)Transverse (c)Electromagnetic (d)None of these

PART-II

NOTE: (i) Part-IIis to be attempted on the separate Answer Book.

(ii)Candidate must write Q. No.in the Answer Bookin accordance with Q. No.in the Q. Paper.

(iii)Attempt ONLY FOUR questions from PART-II. ALL questions carry EQUAL marks.

(iv) Extra attempt of any question orany part of the attempted question will not be considered.

(v) Use of Calculator is allowed.

Q.No.2. (a)The Vectors .

ˆ

2 ˆ 2 ˆ

,

ˆ

3 ˆ ˆ 2 k j i B k j i A

Find the magnitudes of

B A B A

. , & and Projection of B

on . A

(b)Prove that ). . ( ) . ( ) ( B A C C A B C B A

(c)Are the units vectors in the cylindrical and spherical coordinate system constant

vectors? Explain.

(2,2,3,3)

(6)

(4)

Q.No.3. (a)State Kepler’s laws of planetary motion and prove

(i) Law of Areas (ii) Law of periods.

(b)Use Maxwell’s equations to derive the electromagnetic wave equation.

(2,4,4)

(10)

Q.No.4. (a)What is Doppler’s effect? Derive expressions of frequency of sound heard by

observer when:

(i) The observer moving towards a stationary source

(ii) The source is moving towards a stationary observer.

(b)A stationary observer detects sound offrequency 250 hertz emitted from a source

at rest. He detects soundof frequency 750 hertz when source is moving towards

him with constant velocity. Determine velocity of sound.

(Velocity of sound = 341 m/Sec.)

(2,6,6)

(6)

Q.No.5. (a)Describe the Young’s double slit experiment and find the conditions of

constructive and destructive interference.

(b)The double slit arrangement is illuminated by light of wavelength 546nm, the

slits are 0.12mm apart and the screen on which the interference pattern appears is

55cm away. What is angular position of first maxima? What is linear distance

between 3

rd

and 4

th

maxima?

(10)

(4,6)

Q.No.6. (a) Describe the Postulates of relativity. Show the relativistic effecton mass, length

and time.

(b)What is the total energy E of a 2.53 Mev electron? When an energy is used as an

adjective, it refers to the Kinetic energy of the particle, here K= 2.53 Mev.

(3,3,3,3)

(8)

Q.No.7. (a)Derive the expressions of position and time coordinates in frame S relative to S

(Lorentz Transformation).

(b)Derive the Bernoulli’s equation of a steady flow.

(12)

(8)

Q.No.8. Write notes on any TWOof the following:

(a)Travelling and Standing Waves.

(b)LASER, its production and applications.

(c)Laws of thermodynamics.

(10 each) (20)

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