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The characteristic X-ray radiation is emitted, when

A steel ball falls from a height h on a floor for which the coefficient of restitution is e. The height attained by the ball after two rebounds is

A battery consists of $n$ number of identical cells having internal resistance connected in series. The terminals of the battery are short circuited and the current $I$ is measured.

Which of the following graphs shows correct relationship between $I$ and $n$?

A small
telescope has an objective lens of focal length 140 cm and an
eyepiece of focal length 5.0 cm. What is the magnifying power of the
telescope for viewing distant objects when

(a)
the
telescope is in normal adjustment (i.e., when the final image

is at infinity)?

(b)
the final image is formed at the least distance of distinct vision

(25 cm)?

suppose the rod with the balls A and B of the previous problem is clamped at the centre in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collides with B and sticks to it. (a) Find the angular momentum and the angular speed of the system just after the collision. (b) What should be the minimum value of h so that the system makes a full rotation after the collision.

A person can see the objects lying between 25 cm and 10 m from his eye. His vision can be corrected by using lens of power:

The equation of a transverse wave on a stretched string is given by $y=0.05\sin 2\pi (\frac{t}{0.002}-\frac{x}{0.1})$, where $x$ and $y$ are expressed in metre and $t$ in second. The speed of the wave is

A composite rod of mass '2m' $\&$ length '2l' consists of two identical rods joined end to end at P. The composite rod is hinged at one of its ends and is kept horizontal. If it is released from rest, ·Find its angular speed when it becomes vertical

The path difference between two wave fronts emitted by coherent sources of wavelength $5460\mathring{A}$ is $2.1\mu \text{m}.$The phase difference between the wave fronts at that point is- (in $\text{radians}$)

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights $h_{sph}$ and $h_{cyl}$ on the incline. The ratio $\frac{h_{sph}}{h_{cyl}}$ is given by:

As shown in the figure a ball is moving with a velocity $u=6\hat{i}+\hat{j}$ and it collides with a vertical wall which is parallel to the vector $\hat{j}$. If the coefficient of restitution between the ball and the wall is $0.5$ and mass of the ball is $m=1\text{kg}$. Find the impulse that acts on the ball.

When light is travelling from denser medium to air at an angle of incidence $\Theta$ , a part of light is reflected and rest is refracted . The refractive index of denser medium is $\frac{\sqrt{7}}{2}$ and the angle between reflected and refracted ray is ${90}^0$.

Find the value of angle $\Theta$

Two particles, each of mass m and speed v, travel in opposite directions along parallel lines separated by a distance d. Show that the vector angular momentum of the two particle system is the same whatever be the point about which the angular momentum is taken.

Find the integrals of the functions.
$\int co{s}^{4}2xdx.$

The monkey B shown in figure is holding on to the tail of the monkey A which is climbing up a rope. The masses of the monkeys A and B are 5 kg and 2 kg respectively. If A can tolerate a tension of 30 N in its tail, what force should it apply on the rope in order to carry the monkey B with it ? Take g = 10 $m/s^2$.

Wavelength of light required to excite an electron in an hydrogen atom from level $n=1$ to $n=2$ will be:

(Given: Planck's constant $\left(h\right)=6.62\times {10}^{-34}\text{Js}$, speed of light $\left(c\right)=3\times {10}^8{\text{ms}}^{-1}$)

Two balls of equal masses are projected upwards simultaneously, one from the ground with initial velocity $50{\text{ms}}^{-1}$, and the other from a $40\text{m}$ tower with initial velocity of $30{\text{ms}}^{-1}.$The maximum height attained by their COM will be:

($g=10{\text{ms}}^{-2}$)

A harmonic wave is travelling on string $1$. At the junction with string $2$, it is partly reflected and partly transmitted. The linear mass density of string $2$ is $9$ times that of string $1$, and that the boundary between the two strings is at $x=0$. If the expression for the incident wave is

$y_i=\left(3\text{cm}\right)\cos \left[\right(3.14{\text{cm}}^{-1})x-(314{\text{rad s}}^{-1}\left)t\right]$. What is the expression for the transmitted waves?

The activity of a sample of a radioactive material is $A_1$ at time $t_1$ and $A_2$ at time $t_2(t_2>t_1)$. If its mean is life T, then

If in the circuit, power dissipation is 150W then R is

A circular platform is free to rotate in a horizontal plane about a vertical axis passing through its centre. A tortoise is sitting at the edge of the platform. Now, the platform is given an angular velocity ${\omega }_0$. When the tortoise moves along a chord of the platform with a constant velocity (with respect to the platform), the angular velocity of the platform $\omega \left(t\right)$ will vary with time $t$ as

The ceiling of a hall is $40m$ high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of $56m{s}^{-1}$ without hitting the ceiling of the ball is

(Take $g=9.8m/s^2$)

In the system shown in figure blocks A and B have mass $m_1=2kgand{m}_2=\frac{26}{7}$ kg respectively. Pulley having moment of inertia I = 0.11 kg $m^2$ can rotate without friction about a fixed axis. Inner and outer radii of pulley are a = 10 cm and b = 15 cm respectively. B is hanging with the thread wrapped around the pulley, while A lies on a rough inclined plane.





Coefficient of friction being $\mu =\frac{\sqrt{3}}{10}$

$\begin{array}{cc}ColumnI& ColumnII\\ P.\text{Tension in the thread connecting block A}& w.26N\\ Q.\text{Tension in the thread connecting block B}& x.2\frac{m}{s^2}\\ RaccelerationofA& \\ R.\text{Acceleration of A}& y.3\frac{m}{s^2}\\ S.\text{Acceleration of B}& z.17N\end{array}$

Twelve resistors each of resistance $r$ are connected together so that each lies along the edge of the cube as shown in the figure. The equivalent resistance between points $1$ and $3$ is

A force $F=2\text{N}$ acts at a distance $x=0.5\text{m}$ above the centre of a thin spherical shell of mass $m=3\text{kg}$ and radius $R=2\text{m}$. Find out the linear acceleration $\left(a\right)$ and angular acceleration $\left(\alpha \right)$ of the shell.

A particle of mass m, kinetic energy $K$ and linear momentum $p$ collides head on elastically with another particle of mass $2m$ at rest. Match the following (after collision) –



$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) momentum of first particle}& \text{(P)}\frac{4}{3}p\\ \text{(B) momentum of second particle}& \text{(Q)}\frac{8K}{9}\\ \text{(C) Kinetic energy of first particle}& \text{(R)}-\frac{p}{3}\\ \text{(D) Kinetic energy of second particle}& \left(S\right)\frac{K}{9}\end{array}$



Which of the following option has the correct combination considering column-I and column-II

In Fig. $\left(a\right)$ and Fig. $\left(b\right)$, two air-cored solenoids $P$ and $Q$ have been shown.

They are placed near each other. In Fig. $\left(a\right)$, when $I_P$ , the current in $P$, changes at the rate of $5\text{A/s}$, an emf of $2\text{mV}$ is induced in $Q$. The current in $P$ is then switched off, and a current changing at $2\text{A/s}$ is fed through $Q$ as shown in diagram. What emf will be induced in solenoid $P$?

A body cools from ${80}^{\circ }\text{C}$ to ${50}^{\circ }\text{C}$ in $5\text{min}$. If the temperature of the surroundings is ${20}^{\circ }\text{C}$ then calculate the time it takes to cool from ${60}^{\circ }\text{C}$ to ${30}^{\circ }\text{C}$.

A particle is projected from the bottom of an inclined plane of angle ${30}^{\circ }$ with a velocity of $30\text{m/s}$ at an angle of ${60}^{\circ }$ with the horizontal. Find the distance travelled by the particle along the plane before it hits the plane.

Four rods of same material having the same cross section and length have been joined as shown. The temperature of the junction of the rods will be

In
Young’s double-slit experiment using monochromatic light of
wavelengthλ,
the intensity of light at a point on the screen where path difference
is λ,
is K units.
What is the intensity of light at a point where path difference is
λ /3?

A plane wave is represented by

$x=1.2sin(314t+12.56y)$

Where x and y are distances measured along in x and y direction in meters and t is time in seconds. This wave has

[MP PET 1991]