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Two sitar strings A and B playing the note ‘Ga’ are slightly out of tune and produce beats of frequency 6 Hz. The tension in the string A is slightly reduced and the beat frequency is found to reduce to 3 Hz. If the original frequency of A is 324 Hz, what is the frequency of B?

Suppose the entire system of the previous question is kept inside an elevator which is coming down with an acceleration a< g. Repeat parts (a) and (b).

Three block $A,B\text{and}C$ are lying on a smooth horizontal surface, as shown in the figure. $A$ and $B$ have equal masses, $m$ while $C$ has mass $M$. Block $A$ is given an initial speed $v$ towards $B$ due to which it collides with $B$ perfectly inelastically. The combined mass collides with $C$, also perfectly inelastically ${\frac{5}{6}}^{th}$ of the initial kinetic energy is lost in the whole process. What is the value of $\frac{M}{m}?$

An ideal gas has a molar heat capacity $C_v$ at constant volume. It undergoes a process given by $T=T_0{e}^{\frac{\alpha }{V}}$, where $T_0$ and $\alpha$ are constants. Find the molar heat capacity of the gas as a function of $V$.

In a series $LCR$ circuit, the voltage across the resistor, capacitor and inductor is $10\text{V}$ each. If the capacitor is short-circuited, the voltage across the inductor will be



​​​​​​​$[$1 Mark$]$

A uniform disc of mass m and radius R is pivoted at its centre O with its plane vertical as shown in figure, A circular portion of disc of radius $\frac{R}{2}$ is removed from it. The time period of small oscillations of remaining portion about O is

The volume of parallelopiped with vectors $\overrightarrow{a}+2\overrightarrow{b}-\overrightarrow{c},\overrightarrow{a}-\overrightarrow{b},\overrightarrow{a}-\overrightarrow{b}-\overrightarrow{c}$ as coterminous edges is $k\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right],$ then $k$ is

A radioactive isotope is being produced at a constant rate A. The isotope has a half life T. Initially, there are no nuclei and after a time, t>>T, the number of nuclei becomes a constant. The value of this constant is:

1. 0.707

A cart of mass $M=100kg$ is at rest over a smooth horizontal surface. A boy of mass $m=50kg$ is standing over the cart. If he jumps from the cart with a horizontal velocity of $20m{s}^{-1}$, the final velocity of the cart is :

The work functions of metals A and B are in the ratio 1 : 2. If light of frequencies f and 2f are incident on the surfaces of A and B respectively, the ratio of the maximum kinetic energies of photoelectrons emitted is (f is greater than threshold frequency of A, 2f is greater than threshold frequency of B)

What is the implied subject in the given sentence?

Turn off the tap!

A circular loop of radius $0.3\text{cm}$ lies parallel to a much bigger circular loop of radius $20\text{cm}$. The centre of the smaller loop is on the axis of the bigger loop. The distance between their centres is $15\text{cm}$. If a current of $2.0\text{A}$ flows through the bigger loop, then the magnetic flux linked with the smaller loop is

A small square loop of wire of side l is placed inside a large square loop of side L $(L\gg l)$. The loops are coplanar and their centres coincide. The mutual induction of the system is proportional to

If ${\lambda }_0$ and $\lambda$ be the threshold wavelength and the wavelength of incident light respectively, the velocity of photo-electrons ejected from the metal surface is:

A player caught a cricket ball of mass 150 gm moving at a rate of 20 m/s. If the catching process be completed in 0.1 s, then the force of the blow exerted by the ball on the hands of the player is

A positive charged particle of charge $q$ and mass $m$ is projected with speed $v$ perpendicular to a uniform magnetic field $B$ as shown in the figure. Neglecting gravity, calculate the $x-$coordinate of the point on the screen at which the charged particle will hit.



Take, $d=\frac{R\sqrt{3}}{2};$ where $R=\frac{mv}{qB}$

The ratio of intensities between two coherent sound sources is $9:1$. The difference of loudness in decibels $\left(\text{dB}\right)$ between maximum and minimum intensities when they interfere in space is

A ball falls on an inclined plane of inclination $\theta$ from a height h above the point of impact and makes a perfectly elastic collision.Where will it hit the plane again ?

The value of tension in a long, thin metal wire has been changed from $T_1$ to $T_2$. The lengths of the metal wire at two different values of tension $T_1$ and $T_2$ are $l_1$ and $l_2$ respectively. The actual length of the metal wire is :

The figure shows a circuit that contains four identical resistors with resistance $R=2.0\Omega$. Two identical inductors with inductance $L=2.0\text{mH}$ and an ideal battery with emf $E=9\text{V}$. The current$\left(i\right)$ just after the switch ${}^{\prime }{s}^{\prime }$ is closed will be:

If there were a smaller gravitational effect, which of the following forces do you think would alter in some respect

The objective lens of a compound microscope produces magnification of $10$. In order to get an overall magnification of $100$ when image is formed at $25cm$ from the eye, the focal length of the eye piece should be

A ball is thrown vertically upwards with a speed $v$ from a height $h$ metre above the ground. The time taken for the ball to hit ground is

1. 4

A particle moves along the parabolic path y = $a{x}^2$ in such a way that the x-component of the velocity remains constant, say c. The acceleration of the particle is :

Three vectors $A$, $B$ and $C$ satisfy the relation $A\cdot B=0$ and $A\cdot C=0$. Then the vector $A$ is parallel or anti-parallel to

A spring balance reads $W_1$ when a ball is suspended from it. A weighing machine reads $W_2$when a tank of liquid is kept on it. When the ball is immersed in the liquid, the spring balance reads $W_3$ and the weighing machine reads $W_4$. Then, which of the following are not correct?

A positive charged particle of mass $m$ and charge $q$ is released from rest in a region having $\overrightarrow{E}=E_0\hat{i}$ and $\overrightarrow{B}=B_0\hat{j}$ from origin. The net force on the particle at any time $t$ if its velocity at this moment is $\overrightarrow{v}=v_x\hat{i}+v_z\hat{k}$ :



$[E_0$ and $B_0$ are constants$]$