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An AC source of frequency f is fed across a resistor R and a capacitor C in series. The current flowing in the circuit is I. If now the frequency of source is changed to $\frac{f}{3}$, without any change in magnitude of voltage, the current in the circuit is found to halved. The ratio of reactance to resistance at the original frequency f will be

The volume of a gas increases by $10{\text{m}}^3$, when it is subjected to a constant pressure of $2\times {10}^5\text{Pa}$. The amount of work done by the gas is

A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through ${60}^{\circ }$, the torque needed to maintain the needle in this position will be

Two waves of equal frequencies, have their amplitudes in the ratio of $4:5$. They are superimposed on each other. Calculate the ratio of maximum and minimum intensity of the resultant wave.

Two rods $\text{AB}$ and $\text{CD}$ of the same mass and lengths $1\text{m}$ and $\frac{3}{2}\text{m}$ are joined at ${}^{\prime }{\text{O}}^{\prime }$ to form an $L$-shaped frame $\text{AOD}$ as shown in figure. Assuming $COM$ of a rod is at the mid point of the rod, the location of centre of mass of the $L$-shaped frame from the point of intersection ${}^{\prime }{\text{O}}^{\prime }$ is

The value of acceleration due to gravity is $g_1$ at a height $h=\frac{R}{2}$ ($R=$ radius of the earth) from the surface of the earth. It is again equal to $g_1$ and a depth $d$ below the surface. The ratio $\left(\frac{d}{R}\right)$ equals

A solid sphere of radius $R$, acquires a terminal velocity $v_1$ when falling (due to gravity) through a viscous fluid, having a coefficient of viscosity $\eta$. The sphere is broken into $27$ identical solid spheres. If each of these spheres acquires a terminal velocity, $v_2$, when falling through the same fluid, the ratio $\left(\frac{v_1}{v_2}\right)$ equals:

22 g of $C{O}_2$ at ${27}^{\circ }C$ is mixed with 16g of $O_2$ at ${37}^{\circ }C.$ The temperature of the mixture is

A circular hole of radius $\frac{a}{2}$ is cut out of a circular disc of radius ${}^{\prime }{a}^{\prime }$ shown in the figure. The centroid of the remaining circular portion with respect to point ${}^{\prime }{O}^{\prime }$ will be :

Under what observations do the wave theory of light appears to fail

Two drops of same radius are falling through air with steady velocity $v$. If the two drops coalesce, what would be the terminal velocity?

When two tuning forks, fork $A$ and fork $B$ are sounded together, $4$ beats per second are heard. When the tuning fork $B$ is loaded with wax then $6$ beats per second are heard. If the frequency of fork $A$ is $200\text{Hz}$ then what was the original frequency of fork $B$?

A block of $4kg$ is suspended from the ceiling through a massless spring of spring constant $k=100N/m$. If $4kg$ is replaced by $8kg$, what would be the ratio of elongation in 1st case to 2nd case?

The mean length of an object is $5\text{cm}$. Which of the following measurements is most accurate?

A slit of width $a$ is illuminated by parallel monochromatic light of wavelength $\lambda .$ The value of $a$ at which the first minimum of the diffraction pattern will from at $\theta ={30}^{\circ }$ is

A person was moving at a uniform speed, but suddenly he comes to rest. What will be his acceleration at rest?

A conducting loop of area $5.0c{m}^2$ is placed in a magnetic field which varies sinusoidally with time as $B=B_{0}sin\omega t$ where $B_0=0.20T$ and $\omega =300s^{-1}$. The normal to the coil makes an angle of ${60}^{\circ }$ with the field. Find (a) the maximum emf induced in the coil, (b) the emf induced at $\tau =\left(\frac{\pi }{900}\right)s$ and (c)the emf induced at $t=\left(\frac{\pi }{600}\right)s$.

A particle is moving in a circle of radius R with constant speed v, if radius is double then its centripetal force to keep the same speed should be

Test dimensionally if the equation $v^2=u^2$ + 2ax may be correct.

Simplify:$\frac{sin\alpha }{(1+cos\alpha )}+\frac{(1+cos\alpha )}{sin\alpha }$

The circuit has two oppositely connect ideal diodes in parallel. What is the current following in the circuit?

lf all the particles of a system lie in a cube, is it necessary that the centre of mass be in the cube?

A body moves with constant angular velocity on a circle. Magnitude of angular acceleration

A small object is placed $50cm$ to the left of a thin convex lens of focal length $30cm$ . A convex spherical mirror of radius of curvature $100cm$ is placed to the right of the lens at a distance of $50cm$. The mirror is titled such that the axis of the mirror is at a angle $\theta ={30}^{\circ }$ to the axis of the lens, as shown in the figure.

If the origin of the coordinate system is taken to be at the centre of the lens, the coordinates $\left(incm\right)$ of the point $(x,y)$ at which the image is formed are