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16.

Using the expression   $2d \sin\theta=\lambda$, one calculates the values of d by measuring the corresponding angle $\theta$ in the range 0 to 90°.  The wavelength $\lambda$  is exactly known and the error in $\theta$  is constant for all values of $\theta$. As $\theta$  increases from 0°

A) The absolute error in d remains constant

B) The absolute error in d increases

C) The fractional error in d remains constant

D) The fractional error in d decreases

17.

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other.The wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency  f1. An observer in the other vehicle hears the frequency of the whistle to be f2. The speed of sound in still air is  v. The correct statement(s) is (are)

A) If the wind blows from the observer to the source , $f_{2} > f_{1}$

B) If the wind blows from the source to the observer, $f_{2} > f_{1}$

C) If the wind blows from the observer to the source , $f_{2} < f_{1}$

D) If the wind blows from the source to the observer m $f_{2} < f_{1}$

18.

A steady current I flows along an infinitely long hollow cylindrical conductor of radius R. This cylinder is placed coaxially inside an infinite solenoid of radius 2R. The solenoid has n turns per unit length and carries a steady current I. Consider a point p  at a distance r from the common axis . The  correct statement (s)  is (are)

A) In the region 0 < r < R, the magnetic field is non-zero

B) In the region R < r < 2R the magnetic field is along the common axis

C) In the region R < r < 2R , the magnetic field is tangential to the circle of radius r, centered on the axis

D) In the region r >2 R, the magnetic field is non -zero

19.

A  particle of mass m is attached to one end of the mass-less spring of force constant k, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time t=0 with an initial velocity $\mu_{0}$.When the speed of the particle is 0.5 $\mu_{0}$, it collides elastically with a rigid wall. After this collision

A) the speed of the particle when it returns to its equilibrium position is $\mu_{0}$

B) the time at which the particle passes through the equilibrium position for the first time is $t=\pi\sqrt{\frac{m}{k}}$

C) the time at hich the maximum compression of the spring occurs is $t=\frac{4\pi}{3}\sqrt{\frac{m}{k}}$

D) the time at which the particle passes through the equilibrium position for the second time is $t=\frac{5\pi}{3}\sqrt{\frac{m}{k}}$

20.

Two bodies, each of mass M, are kept fixed with a separation of 2L. A particle of mass m is projected from the mid-point of the line joining their centres, perpendicular to the line.The  gravitational constant G .The correct statement(s) is (are)

A) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $4\sqrt{\frac{GM}{L}}$

B) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $2\sqrt{\frac{GM}{L}}$

C) The minimum initial velocity of the mass m to escape the gravitational field of the two bodies is $\sqrt{\frac{2GM}{L}}$

D) The energy of the mass m remain constant

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