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What would be the maximum energy of an X-Ray if an electron is accelerated with a potential difference of 10kV. From this data find out the minimum wavelengths of the X-Ray. (Use hc = 1242 eV-nm)

Two particles, one with constant velocity $50{\text{m s}}^{-1}$ and the other with uniform acceleration $10{\text{m s}}^{-2}$, start moving simultaneously from the same place in the same direction. They will be at a distance of 125 m from each other after

A swimmer wishes to cross a $800\text{m}$ wide river flowing at $6\text{km/hr}$. His speed with respect to water is $4\text{km/hr}$. He crosses the river in shortest possible time. He is drifted downstream on reaching the other bank by a distance of

When a load is attached to the wire, the ratio of increase in elastic energy of the wire to the decrease in gravitational potential energy when load moves downwards by 1 mm, will be

A boy throws a stone in the air, its height at any time is given by $h=-3t^2+12t-4\text{m}$. The maximum height (in $\text{m}$) attained by the stone is

Two blocks are connected by a string, as shown in the figure. They are released from rest. Find the speed after they have moved a distance x. $\mu$ is the coefficient of kinetic friction between the upper block and the surface. Assume that the pulley is massless and frictionless.

Balls are thrown vertically upward in such a way that the next ball is thrown when the previous one is at the maximum height. If the maximum height is $5\text{m}$, the number of balls thrown per minute will be

A nuclear fission is given below

$A^{240}\to B^{100}+C^{140}+Q\left(\text{energy}\right)$.

Let binding energy per nucleon of nuclei $A,B$ and $C$ be $7.6\text{MeV},8.1\text{MeV}$ and $8.1\text{MeV}$ respectively. Value of $Q$ is : (Approximately)

If $S=e^x-\sin x$, find $\frac{d^{2}S}{d{x}^2}$

From a square plate of side $10\text{m}$, a right angled triangle is removed as shown in the figure. The square plate has mass density $2{\text{kg/m}}^2$. Find the centre of mass of the remaining portion. Assume the origin to be at the intersection of $x$ and $y$ axes.

Two particles $A$ and $B$ are projected in air. $A$ is thrown with a speed of $60m/sec$ and $B$ with a speed of $80m/sec$ as shown in the figure.

What is the separation between them after $2sec$?

Sources separated by $20\text{m}$ vibrate according to the equation $y_1=0.06\sin \pi t$ and $y_2=0.02\sin \pi t.$ They send out waves along a rod with speed $3\text{m/s}$. What is the equation of motion of a particle $12\text{m}$ from the first source and $8\text{m}$ from the second? Given $y_1,y_2$ are in metres.

A boy walks uniformally along the sides of a rectangular park of size 400 m× 300 m, starting from one corner to the other corner diagonally opposite. Which of the following statement is incorrect

The graph gives the magnitude B(t) of a uniform magnetic field that exists throughout a conducting loop, perpendicular to the plane of the loop. Rank the five regions of the graph according to the magnitude of the emf induced in the loop, greatest first

A 1kg rod of length 1m is pivoted at its centre and two masses of 5kg and 2kg and are hung from the ends as shown in figure. Find the tension in the supports to the blocks of mass 2kg and 5kg $(g=9.8\frac{m}{s^2})$

A car accelerates with an acceleration of $2{\text{m/s}}^2$ for $20\text{s}$ from rest on a straight path. Then it decelerates with $1{\text{m/s}}^2$ until its velocity becomes zero. The total distance covered by the car is -

A stationary horizontal disc is free to rotate about its axis. When a torque is applied on it, its kinetic energy as a function of $\theta$, where $\theta$ is the angle by which it has rotated, is given as $k{\theta }^2$ (where $k$ is a constant). If its moment of inertia is $I$, then the angular acceleration of the disc is

A ball of mass $2\text{kg}$ is dropped from a height of $20\text{m}$. After striking the ground, the ball bounces back with half of its striking speed. Find the impulse imparted by the normal reaction from the ground. Take $g=10{\text{m/s}}^2$.

What is the Unit of Charge?

Find the slope of the tangent to the curve $y=4x^2-3x-8$ at point $(-3,4)$.

What direction must you swim at to cross the river in minimum time given the crocodiles have left and your maximum velocity is $5\frac{Km}{hr}$ and the velocity of river is $3\frac{Km}{hr}$ in the west direction.

Find the elongation in the spring for the system shown in the figure. ($g=10m/s^2$)

A short bar magnet is moved with constant velocity along the axis of a short coil. The magnet enters into the coil and then leaves it. The variation of induced emf $\left(\epsilon \right)$ with time $\left(t\right)$ is best represented as

A cylinder is given angular velocity ${\omega }_0$ and kept on a horizontal rough surface. The initial velocity is zero. The distance travelled by it before it starts performing pure rolling is: [Assume radius of cylinder $=R$]

The photoelectric work function for a metal surface is 4.125 eV. The cut-off wavelength for this surface is

A long straight wire is parallel to one edge of the loop as shown in the figure. If the current in the long wire varies with time as $I=I_0{e}^{-\frac{t}{\tau }}$, what will be the induced emf in the loop ?

Find the maximum force $F$ to be applied for the system shown, so that the two blocks move together. Given that it accelerates with $2{\text{m/s}}^2$. Take $g=10{\text{m/s}}^2$. $({\mu }_1=0.2,{\mu }_2=0.3)$

Two balls are projected from the same point in directions inclined at ${60}^{\circ }$ and ${30}^{\circ }$ to the horizontal. If they attain the maximum height at the same time, what is the ratio of their velocities of projection?

A particle is projected from a horizontal plane (x-y plane) such that its velocity vector at time $t$ is given by $\overrightarrow{V}=a\hat{i}+(b-ct)\hat{j}$. Its range on the horizontal plane is given by

A motorboat covers a given distance in $6\text{hours}$ moving downstream in a river. It covers the same distance in $10\text{hours}$ moving upstream. The time taken to cover the same distance in still water is

If a displacement vector of $AB$ is $\hat{i}+\hat{j}+2\hat{k}$ and point $A$ having a position vector $2\hat{i}+5\hat{j}+6\hat{k}$, then find the position vector of $B$ ?

A motor cycle driver doubles its velocity when he is having a turn. The force exerted outwardly will be

In an isothermal reversible expansion, if the volume of 96 gm of oxygen at ${27}^{\circ }C$ is increased from 70 litres to 140 litres, then the work done by the gas will be

According to De Broglie the electron in n=3 of Hydrogen atom will look like

A small block of mass 2 kg is kept on a rough inclined surface of inclination $\theta ={30}^{\circ }$ fixed in a lift. The lift goes up with a uniform speed of 1 m$s^{-1}$ and the block does not slide relative to the inclined surface. The work done by the force of friction on the block in a time interval of 2 s is.

A pendulum of mass $m\text{kg}$ has velocity $v$ at point $A$. What is the change in potential energy when the pendulum reaches point $B$ as shown in figure ?

The work function of a metal is $h{v}_0$. Light of frequency v falls on this metal. The photoelectric effect will take place only if

A force $\overrightarrow{F}=3\hat{i}+2\hat{j}+c\hat{k}$ acts on a particle and causes a displacement $\overrightarrow{r}=c\hat{i}+4\hat{j}+c\hat{k}$ meter.

The work done is 36 joule.Find the value of 'c' ?

A target is made of two plates, one of wood and the other of iron. The thickness of the wooden plate is $4\text{cm}$ and that of iron plates is $2\text{cm}$. A bullet fired goes through the wood first and then penetrates $1\text{cm}$ into the iron. A similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\text{cm}$ into the wood. If $a_1$ and $a_2$ be the retardation offered to the bullet by the wood and iron plates respectively, then

The acceleration of a particle is increasing linearly with time t as bt . The particle starts from the origin with an initial velocity $v_o$. The distance travelled by the particle in time t will be

The coefficient of restitution 'e' for a perfectly inelastic collision is

Vectors $\overrightarrow{C}$ and $\overrightarrow{D}$ have magnitudes of 3 and 4 units respectively. What is the angle between the directions of $\overrightarrow{C}$ and $\overrightarrow{D}$ if the magnitude of vector product $\overrightarrow{C}\times \overrightarrow{D}$ is x and y respectively?

(x) 0 (y) 12 units

(i) 0 (ii)$\frac{\pi }{2}$ (iii)$\frac{\pi }{3}$ (iv) $\frac{\pi }{4}$

A closed tube filled with water is rotating about an axis as shown in figure. The pressure difference $P_A-P_C$ is

Find $R_{AB}$ All arms have resistance R.

Which of the following options are correct regarding the molar heat capacity $\left(C\right)$ for the gas whose $PV$ graph is shown below.

Two blocks of masses 40 kg and 20 kg are connected by a wire that has a linear mass density of 1 g/m. These blocks are being pulled across horizontal frictionless floor by horizontal force F that is applied to 20 kg block. A transverse wave travels on the wave between the blocks with a speed of 400 m/s (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. The magnitude of F is

Find the centre of mass of uniform L-shaped lamina (a thin flat plate) with dimensions as shown in figure. The mass of lamina is 3 kg