Q13. The magnetic field in a plane electromagnetic wave is $\mathrm { B } _ { \mathrm { y } } = \left( 3.5 \times 10 ^ { - 7 } \right) \sin \left( 1.5 \times 10 ^ { 3 } x + 0.5 \times 10 ^ { 11 } t \right) \mathrm { T }$. The corresponding electric field will be :
(1) $E _ { y } = 10.5 \sin \left( 1.5 \times 10 ^ { 3 } x + 0.5 \times 10 ^ { 11 } t \right) \mathrm { Vm } ^ { - 1 }$
(2) $E _ { z } = 1.17 \sin \left( 1.5 \times 10 ^ { 3 } x + 0.5 \times 10 ^ { 11 } t \right) \mathrm { Vm } ^ { - 1 }$
(3) $E _ { y } = 1.17 \sin \left( 1.5 \times 10 ^ { 3 } x + 0.5 \times 10 ^ { 11 } t \right) \mathrm { Vm } ^ { - 1 }$
(4) $E _ { z } = 105 \sin \left( 1.5 \times 10 ^ { 3 } x + 0.5 \times 10 ^ { 11 } t \right) \mathrm { Vm } ^ { - 1 }$

Q14. An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :
(1) the electron will continue to move with uniform
(2) the electron will be accelerated along the axis. velocity along the axis of the solenoid.
(3) the electron path will be circular about the axis.
(4) the electron will experience a force at $45 ^ { \circ }$ to the axis and execute a helical path.

Q14. In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :
(1) outside the cable
(2) inside the outer conductor
(3) inside the inner conductor
(4) in between the two conductors

Q14. A series LCR circuit is subjected to an ac signal of $200 \mathrm {~V} , 50 \mathrm {~Hz}$. If the voltage across the inductor $( \mathrm { L } = 10 \mathrm { mH } )$ is 31.4 V , then the current in this circuit is $\_\_\_\_$ .
(1) 68 A
(2) 63 A
(3) 10 A
(4) 10 mA

Q14. Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below:
(1) Statement I is false but Statement II is true
(2) Statement I is true but Statement II is false
(3) Both Statement I and Statement II are true
(4) Both Statement I and Statement II are false

Q14. In the given electromagnetic wave $\mathrm { E } _ { \mathrm { y } } = 600 \sin ( \omega \mathrm { t } - \mathrm { kx } ) \mathrm { Vm } ^ { - 1 }$, intensity of the associated light beam is (in $\mathrm { W } / \mathrm { m } ^ { 2 } : \left( \right.$ Given $\left. \epsilon _ { 0 } = 9 \times 10 ^ { - 12 } \mathrm { C } ^ { 2 } \mathrm {~N} ^ { - 1 } \mathrm {~m} ^ { - 2 } \right)$
(1) 243
(2) 729
(3) 972
(4) 486

Q14. A LCR circuit is at resonance for a capacitor $C$, inductance $L$ and resistance $R$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:
(1) Zero
(2) same
(3) halved
(4) double

Q14. A coil of negligible resistance is connected in series with $90 \Omega$ resistor across $120 \mathrm {~V} , 60 \mathrm {~Hz}$ supply. A voltmeter reads 36 V across resistance. Inductance of the coil is :
(1) 0.286 H
(2) 0.76 H
(3) 2.86 H
(4) 0.91 H

Q14. Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :
(1) Both Statement I and Statement II are true
(2) Statement I is true but Statement II is false
(3) Both Statement I and Statement II are false
(4) Statement I is false but Statement II is true

Q14. The following figure represents two biconvex lenses $L _ { 1 }$ and $L _ { 2 }$ having focal length 10 cm and 15 cm [Figure] respectively. The distance between $L _ { 1 } \& L _ { 2 }$ is :
(1) 10 cm
(2) 35 cm
(3) 25 cm
(4) 15 cm

Q15. In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below :
(1) A, B and C only
(2) A and B only
(3) B, C and D only
(4) A, B and D only

Q15. Arrange the following in the ascending order of wavelength: A. Gamma rays $\left( \lambda _ { 1 } \right)$ B. $x$ - rays $\left( \lambda _ { 2 } \right)$ C. Infrared waves $\left( \lambda _ { 3 } \right)$ D. Microwaves $\left( \lambda _ { 4 } \right)$ Choose the most appropriate answer from the options given below
(1) $\lambda _ { 4 } < \lambda _ { 3 } < \lambda _ { 1 } < \lambda _ { 2 }$
(2) $\lambda _ { 2 } < \lambda _ { 1 } < \lambda _ { 4 } < \lambda _ { 3 }$
(3) $\lambda _ { 1 } < \lambda _ { 2 } < \lambda _ { 3 } < \lambda _ { 4 }$
(4) $\lambda _ { 4 } < \lambda _ { 3 } < \lambda _ { 2 } < \lambda _ { 1 }$

Q15. Two conducting circular loops $A$ and $B$ are placed in the same plane with their centers coinciding as shown in [Figure] figure. The mutual inductance between them is :
(1) $\frac { \mu _ { 0 } \pi b ^ { 2 } } { 2 a }$
(2) $\frac { \mu _ { o } } { 2 \pi } \cdot \frac { b ^ { 2 } } { a }$
(3) $\frac { \mu _ { 0 } } { 2 \pi } \cdot \frac { a ^ { 2 } } { b }$
(4) $\frac { \mu _ { 0 } \pi a ^ { 2 } } { 2 b }$

Q15.

	List-I		List-II
	EM-Wave		Wavelength Range
(A)	Infra-red	(I)	$< 10 ^ { - 3 } \mathrm {~nm}$
(B)	Ultraviolet	(II)	400 nm to 1 nm
(C)	X-rays $S$	(III)	1 mm to 700 nm
(D)	Gamma rays	(IV)	1 nm to $10 ^ { - 3 } \mathrm {~nm}$

(1) (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
(2) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
(3) (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
(4) (A)-(I), (B)-(III), (C)-(II), (D)-(IV)

Q15. Electromagnetic waves travel in a medium with speed of $1.5 \times 10 ^ { 8 } \mathrm {~m} \mathrm {~s} ^ { - 1 }$. The relative permeability of the medium is 2.0 . The relative permittivity will be:
(1) 2
(2) 4
(3) 5
(4) 1

Q15. In finding out refractive index of glass slab the following observations were made through travelling microscope 50 vernier scale division $= 49 \mathrm { MSD }$; 20 divisions on main scale in each cm For mark on paper $\mathrm { MSR } = 8.45 \mathrm {~cm} , \mathrm { VC } = 26$ For mark on paper seen through slab MSR $= 7.12 \mathrm {~cm} , V C = 41$ For powder particle on the top surface of the glass slab $\mathrm { MSR } = 4.05 \mathrm {~cm} , \mathrm { VC } = 1$ (MSR = Main Scale Reading, $\mathrm { VC } =$ Vernier Coincidence) Refractive index of the glass slab is :
(1) 1.52
(2) 1.35
(3) 1.42
(4) 1.24

Q15. Critical angle of incidence for a pair of optical media is $45 ^ { \circ }$. The refractive indices of first and second media are in the ratio:
(1) $1 : \sqrt { 2 }$
(2) $\sqrt { 2 } : 1$
(3) $2 : 1$
(4) $1 : 2$

Q15. The position of the image formed by the combination of lenses is : [Figure]
(1) 15 cm (right of second lens)
(2) 30 cm (left of third lens)
(3) 15 cm (left of second lens)
(4) 30 cm (right of third lens)

Q15. A plane EM wave is propagating along $x$ direction. It has a wavelength of 4 mm . If electric field is in $y$ direction with the maximum magnitude of $60 \mathrm { Vm } ^ { - 1 }$, the equation for magnetic field is :
(1) $\mathrm { B } _ { z } = 2 \times 10 ^ { - 7 } \sin \left[ \frac { \pi } { 2 } \times 10 ^ { 3 } \left( x - 3 \times 10 ^ { 8 } \mathrm { t } \right) \right] \hat { \mathrm { k } } \mathrm { T }$
(2) $\mathrm { B } _ { z } = 60 \sin \left[ \frac { \pi } { 2 } \left( x - 3 \times 10 ^ { 8 } \mathrm { t } \right) \right] \hat { \mathrm { k } } \mathrm { T }$
(3) $\mathrm { B } _ { x } = 60 \sin \left[ \frac { \pi } { 2 } \left( x - 3 \times 10 ^ { 8 } \mathrm { t } \right) \right] \mathrm { i } \hat { T }$
(4) $\mathrm { B } _ { z } = 2 \times 10 ^ { - 7 } \sin \left[ \frac { \pi } { 2 } \left( x - 3 \times 10 ^ { 8 } \mathrm { t } \right) \right] \hat { \mathrm { k } } \mathrm { T }$

Q15. UV light of 4.13 eV is incident on a photosensitive metal surface having work function 3.13 eV . The maximum kinetic energy of ejected photoelectrons will be:
(1) 4.13 eV
(2) 3.13 eV
(3) 1 eV
(4) 7.26 eV

Q16. The electric field in an electromagnetic wave is given by $\overrightarrow { \mathrm { E } } = \hat { i } 40 \cos \omega ( \mathrm { t } - z / \mathrm { c } ) \mathrm { NC } ^ { - 1 }$. The magnetic field induction of this wave is (in SI unit) :
(1) $\overrightarrow { \mathrm { B } } = \hat { k } \frac { 40 } { \mathrm { C } } \cos \omega ( \mathrm { t } - z / \mathrm { c } )$
(2) $\vec { B } = \hat { j } 40 \cos \omega ( t - z / c )$
(3) $\overrightarrow { \mathrm { B } } = \hat { i } \frac { 40 } { \mathrm { C } } \cos \omega ( \mathrm { t } - z / \mathrm { c } )$
(4) $\overrightarrow { \mathrm { B } } = \hat { j } \frac { 40 } { \mathrm { C } } \cos \omega ( \mathrm { t } - z / \mathrm { c } )$

Q16. The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum of the minimum intensity in the interference pattern is:
(1) $1 : 1$
(2) $4 : 1$
(3) $9 : 1$
(4) $16 : 1$

Q16. An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of $12 \mu \mathrm {~F}$. The maximum displacement current between the plates of the capacitor is nearly :
(1) 10 A
(2) 12 A
(3) 8 A
(4) 13 A

Q16. Given below are two statements : Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement II : The refractive indices are different for different wavelengths in dispersive medium. In the light of the above statements, chose the correct answer from the options given below:
(1) Statement I is false but Statement II is true
(2) Statement I is true but Statement II is false
(3) Both Statement I and Statement II are true
(4) Both Statement I and Statement II are false

Q16. In photoelectric experiment energy of 2.48 eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V . Work function of the photo sensitive material is :
(1) 1.68 eV
(2) 2.48 eV
(3) 1.98 eV
(4) 0.5 eV