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If an electron enters into a space between the plates of a parallel plate capacitor at an angle $\alpha$ with the plates and leaves at an angle $\beta$ to the plates. The ratio of its kinetic energy while entering the capacitor to that while leaving will be

If $y=e^{2^x}-\cos \left(\ln x\right)$, then $\frac{dy}{dx}$ is

The equation of a simple harmonic progressive wave is given by

y = 8sin (0.628x – 12.56t)

where x and y are in cm and t is in second.

Find the phase difference in degrees between two particles at a distance of 2.0cm apart at any instant.

A light and a heavy body have equal kinetic energy. Which one has a greater momentum ?

The velocity at the maximum height of a projectile is $\frac{1}{2}$ times its initial velocity of projection $\left(u\right)$. Its range on the horizontal plane is

Find the moment of inertia of a non-uniform rod having mass per unit length $\lambda ={\lambda }_0(1+\frac{x}{L})$ about an axis $\perp$ to the length of the rod and passing through an end point $L$. Length of the rod is $L$ and $m$ is mass of the rod.

Four condensers each of capacity 4μF are connected as shown in figure. V_P-V_Q=15volts . The energy stored in the system is [CPMT 1976, 89]

The unit vector along $\overrightarrow{A}=2\hat{i}+3\hat{j}$ is

As shown in figure, a loop-the-loop track of radius $r=10\text{m}$. A box starts sliding from a platform at a distance $h$ above the top of the loop and goes around the loop without falling off the track. Find the minimum value of $h$ for successful looping. (Assume friction is negligible at all surfaces).

For component of vector $\overrightarrow{P}=\hat{i}+2\hat{j}-3\hat{k}$ values are in column - II, then the correct match is:

$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{a)}& \text{X-axis}& \text{p)}& 1\\ \text{b)}& \text{Along vector}& \text{q)}& \sqrt{14}\\ & \overrightarrow{q}=\hat{i}+2\hat{j}+\frac{5}{3}\hat{k}& & \\ \text{c)}& \text{Along vector}& \text{r)}& 0\\ & \overrightarrow{r}=2\hat{i}+4\hat{j}-6\hat{k}& & \\ \text{d)}& \text{Along vector}& \text{s)}& \sqrt{7}\\ & \overrightarrow{s}=\frac{\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{14}}& & \end{array}$

A wire PQRS shown in Fig. carries a current l. The radius of the circular part of the wire r. The magnetic field at the centre O of the circular part of the wire is given by

What is the relation between Modulus of rigidity$\left(G\right),$ Youngs modulus $\left(Y\right)$ and Bulk modulus$\left(B\right)$ ?

A river is flowing at a speed of $10\text{m/s}$. A man standing on the bank of the river wants to reach the opposite side of the river through the shortest path. Find the angle with the bank of the river, at which the man should swim in order to reach the opposite side. Speed of man with respect to river water is $20\text{m/s}$.

The average acceleration vector for a particle having a uniform circular motion is

How many times a diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half?

Which of the given 2 vectors are same?

A ball is projected from point $A$ with velocity $10\text{m/s}$ perpendicular to the inclined plane as shown in figure. Range of the ball on the inclined plane is equal to $\frac{N}{3}\text{m}$. Then, $N$ is equal to

A stone is dropped from a balloon going up with a uniform velocity of $5.0\text{m/s}$. If the balloon was $50\text{m}$ high when the stone was dropped, find its height when stone hits the ground.

The coefficient of volumetric expansion of mercury is $8\times {10}^{-5}{}^{\circ }C$. A thermometer bulb has a volume ${10}^{-6}{m}^3$ and cross section of stem is $0.004c{m}^2$. Assuming that bulb is filled with mercury at $0^{\circ }C$, then the length of the mercury column at ${100}^{\circ }C$ is:

Convert the angles in radians

i. ${120}^{\circ }$

ii. ${270}^{\circ }$

Two particles A and B are thrown vertically upward with velocity, $5m/s$ and $10m/s$ respectively ($g=10m/s^2$). Find separation between them after one second.

A lamina lies in $y-z$ plane having moment of inertia about $x$ axis $I_x=6M{R}^2$ and moment of inertia about $y-$ axis $I_y=3M{R}^2$. Then, the moment of inertia of the lamina about $z$ axis is

A particle is executing linear simple harmonic motion about the origin x = 0. Which of the graphs shown in the figure represents the variation of the potential energy function U(x) versus displacement x?

An iron ball of mass $m=50\text{gm}$ falls from a height of $h_1=5\text{m}$ and rises upto $h_2=3.2\text{m}$ after colliding with the horizontal surface. If the time of contact with the surface is $\Delta t=0.02\text{s},$ find the average contact force$\left(\text{Newtons}\right)$ exerted on the ball by the horizontal surface. Take $g=10{\text{m/s}}^2$.

For the figure

On interchanging, the resistances, the balance point of a meter bridge shifts to left by $10\text{cm}$. The resistance of their series combination is $1k\Omega$. How much was the resistance on the left slot before interchanging the resistances?

A spring when stretched by 2 mm its potential energy becomes 4 J. If it is stretched by 10 mm, its potential energy is equal to

A sound wave of frequency 100 Hz is travelling in air. The speed of sound in air is 350 m s${}^{-1}$. By how much is the phase changed at a given point in 2.5 ms?

Three constant forces are applied on a body that are given as $\overrightarrow{F_1}=3\hat{i}\text{N},\overrightarrow{F_2}=4\hat{j}\text{N},\overrightarrow{F_3}=6\hat{k}\text{N}$.

If these forces displace the body by $5\text{m}$ in negative $y$-axis direction from the origin, then total work done by the forces is

If ${\log }_{10}2=0.3010$ and ${\log }_{10}3=0.4771$, then find the approximate value of ${\log }_{10}192$

We wish to obtain a capacitance of $5\mu F$, by using some capacitors, each of $2\mu F$. Then, the minimum number of capacitors required is

A hollow sphere of mass $M$ and radius $R$ is initially at rest on a horizontal rough surface. It moves under the action of a constant horizontal force $F$ as shown in figure.





The linear acceleration $\left(a\right)$ of the sphere is :

A large tank filled with water to a height 'h' is to be emptied through a small hole at the bottom. The ratio of time taken for the level of water to fall from h to h/2 and from h/2 to zero is

Shape of a transverse wave at time $t=t_0$ is shown in the figure given below.



At $x=x_0$ and time $t=t_0$, slope of the wave curve is $5$. Find the ratio of particle velocity to the wave velocity at $x=x_0$.

A particle is moving in a circle and its angular velocity is given as $\omega =\pi t$ where $\omega$ is in radians and $t$ is in seconds. Find the average angular velocity at the end of one half circle.

Unit vector perpendicular to both$\overrightarrow{A}$ and $\overrightarrow{B}$ is

A disc of mass M and radius R is rolling with angular speed $\omega$ on a horizontal plane as shown. The magnitude of angular momentum of the disc about the origin O is

The gas which obeys Boyle's law for maximum range of temperature is

The phase difference between the displacement and acceleration of particle executing $\text{S.H.M.}$ $\left(\text{in radian}\right)$ is

The refracting angle of prism is A and refractive index of material of prism is cot $\frac{A}{2}$ The angle of minimum deviation is

In the figure the string has a mass $4.5\text{g}$. How much time will it take for a mass for a traverse disturbance produced at the floor to reach the pulley? (Take $g=10{\text{ms}}^{-2}$)

Find the force on diapole p placed at a distance r from an onother dipole $p_0$

The velocity of water waves $v$ may depend upon their wavelength $\lambda$ the density of water $\rho$ and the acceleration due to gravity g. The method of dimensions gives the relation between these quantities as

Find the acceleration of a system consisting of a solid cylinder of mass $m$ and radius $R$ and a plank of mass $M$ placed on a smooth surface if it is pulled with a force $F$ as shown in the figure. Given that sufficient friction is present between the cylinder and the plank surface to prevent sliding of the cylinder.

Position vector of a particle is given as $\overrightarrow{r}=(\frac{4}{3}{t}^{\frac{3}{2}}\hat{i}-\frac{t^2}{2}\hat{j}+2t\hat{k})m$. Magnitude of acceleration at $t=1\text{sec}$ is:

A light ray from air is incident (as shown in figure) at one end of a glass fiber (refractive index $\mu =1.5$) making an incidence angle of ${60}^{\circ }$ on the lateral surface, so that it undergoes a total internal reflection. How much time would it take to traverse the straight fiber of length 1 km

Which of the following is the correct unit for heat capacity?