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Water is filled in $\text{U}$ shaped tube up to height $H$ on both sides. If we displace a liquid column of any one side by $x\text{cm}$. What is the time period of oscillation of liquid column ?

Mass of water per unit length $=50\text{g}$.

For which of the following substances, resistance decreases with the increase in temperature?
(a) copper (b) mercury (c) carbon (d) platinum.

If in a stationary wave the amplitude corresponding to antinode is $4\text{cm}$, then the amplitude corresponding to a particle of medium located exactly midway between a node and an antinode is

Two different liquid films of surface tensions $T_1\&T_2$ and are held between three concentric wires of radii a, b and c as shown in the figure. The outermost and the innermost wires are fixed Neglecting gravity, the tension in the middle wire is

What is the dimension of angular acceleration ?

The vector $a\hat{i}+b\hat{j}+c\hat{k}$ is the external angle bisector of the angle between the vectors $\hat{i}+\hat{j}$ and $\hat{j}+\hat{k}.$ if

1. 8

A fixed ended beam is subjected to a load W at $\frac{1}{3}rd$ span as shown in figure. The collapse load is:

A block of mass $m=1\text{kg}$ is at rest with respect to a rough wedge placed in a lift as shown. The the lift starts moving up from rest with an acceleration of $a=2{\text{m/s}}^2$ and the block remains at rest with respect to wedge. Then in $4\text{seconds}$ of motion (if $\theta ={30}^{\circ }$ and $g=10{\text{m/s}}^2$) work done on block.





$\begin{array}{cccc}& \text{Column-I}& & \text{Column-II}\\ \text{(A)}& \text{By gravity (in magnitude)}& \text{(P)}& 144\text{J}\\ \text{(B)}& \text{By normal reaction}& \text{(Q)}& 32\text{J}\\ \text{(C)}& \text{By frictional force}& \text{(R)}& 160\text{J}\\ \text{(D)}& \text{By all the forces}& \text{(S)}& 48\text{J}\end{array}$

Which of the following is the only corect combination?

An elevator and its load have a total mass of $800\text{kg}$. If the elevator, originally moving downward at $10\text{m/s}$, is brought to rest with constant deceleration in a distance of $25\text{m}$, the tension in the supporting cable will be ($g=10{\text{m/s}}^2$)

A ball moving at a speed of $3\text{m/s}$ approaches a wall moving towards it with a speed of $3\text{m/s}$. After the perfectly elastic collision, the speed of the ball will be

An air capacitor of capacitance $20\mu \text{F}$ is connected to a battery of $20\text{V}$. Now the space between its plates is completely filled with an insulator $(K=2)$. The magnitude of induced charge on the dielectric is

A small block of mass $m$, having charge $q$ is placed on frictionless inclined plane making an angle $\theta$ with the horizontal. There exists a uniform magnetic field $B$ parallel to the inclined plane but perpendicular to the length of spring. If $m$ is slightly pulled on the inclined in downward direction and released, the time period of oscillation will be (assume that the block does not leave contact with the plane)

If $i={90}^{\circ },$ find minimum value of angle of prism $A$ in degrees for which emergence is not possible:

Four particles each of mass $500\text{g}$ are placed at the four corners of a rectangle $ABCD$ with sides of length $5\text{m}$ and $10\text{m}$. What is the ratio of moment of inertia of the system when $AB$ is the axis to when $BC$ is the axis?

A ball of mass $0.2\text{k}g$ rests on a vertical post of height $5\text{m}$. A bullet of mass $0.01\text{kg}$ travelling with a velocity $V\text{m/s}$ in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of $20\text{m}$ and the bullet at a distance of $100\text{m}$ from the foot of the post. The initial velocity $V$ of the bullet is,

The thermal efficiency of an air-standard Brayton cycle in terms of pressure ratio $r_p$ and $\gamma (=c_p/c_v)$ is given by

Two infinitely long conducting parallel rails are connected through a capacitor $C$ as shown in the figure. A conductor of length $l$ is moved with constant speed $V_0$. Which of the following graph truly depicts the variation of current through the conductor with time?

Two litres of water at initial temperature of ${27}^{\circ }\text{C}$ is heated by a heater of power $1\text{kW}$ in a kettle. If the lid of the kettle is open, then heat energy is lost at a constant rate of $160\text{J/s}$. The time in which the temperature will rise from ${27}^{\circ }\text{C}$ to ${77}^{\circ }\text{C}$ is (specific heat of water $=4.2\text{kJ/kg}$).

Find the current through $2\text{V}$ battery.

A Proton and an Alpha particle are accelerated through the same potential difference enter in a region of uniform magnetic field with their velocities perpendicular to the field they also have same Kinetic energy. compare the radii of circular path followed by them

For a Prism of refractive index $\mu$ , if $C<A\le 2C$, where $C$ is critical angle and $A$ is angle of prism. Find the value of angle of incidence, $i_0$ for which if,

$0\le i<i_0\to$$\text{TIR}$ occurs, ray does not come out of $\text{BC}$.

And if $i_0<i\le {90}^{\circ }\to$ Ray emerges from face $\text{BC}$.



[Assume, $i$ be the angle of incidence of incident ray as shown in the figure below]

In the given circuit,the potential difference $(V_x-V_y)$ between the points $x$ and $y$ when capacitors reach steady state is___

A long metal rod of length $l$ and relative density $\sigma$ is held vertically with its lower end just touching the surface of water. The speed of the rod when it just sinks in water is given by

A uniform rod of mass $5\text{kg}$ and length $3\text{m}$ is held at an angle $\theta ={37}^{\circ }$ with the horizontal as shown in the figure. The potential energy of the rod is (in $\text{J}$)

A man applies a constant force of $5\text{N}$ on an object of mass $2\text{kg}$ and displaces it by $5\text{m}$. The object was initially at rest. The final velocity of object is

In Young's double slit experiment, the fringes are formed at a distance of $1\text{m}$ from double slit of separation $0.12\text{mm}$. Given $\lambda =6000\stackrel{\circ }{A}$. Then the distances of 3rd dark band from the centre of the screen and 3rd bright band from the centre of the screen will be respectively

A block of mass 2.0 kg is moving on a friction less horizontal surface with a velocity of 1.0 m/s below figure towards another block of equal mass kept at rest.The spring constant of the spring fixed at one end is 100 N/m.Find the maximum compression of the spring.

The two blocks shown in the figure are not attached. The minimum magnitude of the horizontal force $F$ required to keep the smaller block from slipping down the larger block is -

[Take $g=10{\text{m/s}}^2$]

A particle starts from rest and travels a distance $l$ with uniform acceleration, then moves uniformly over a further distance $2l$ and finally comes to rest after moving a further distance $3l$ under uniform retardation. Assuming entire motion to be rectilinear motion the ratio of average speed over the journey to the maximum speed on its ways is