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Two rods $OA$ and $OB$ of equal length and mass are lying on the $xy$ plane as shown in figure. Let $I_x,I_y$ and $I_z$ be the moment of inertia of the system about $x,y$ and $z$ axis respectively. Then,

Volume of a given amount of gas at ${57}^{\circ }\text{C}$ is $425.8{\text{cm}}^3$. If the temperature is decreased to ${37}^{\circ }\text{C}$ at constant pressure, then the volume of the gas would be :

A metal cube of length $10.0\text{mm}$ at $0^{\circ }\text{C}\left(273\text{K}\right)$ is heated to ${200}^{\circ }\text{C}\left(473\text{K}\right)$. Given its coefficient of linear expansion is $2\times {10}^{-5}{\text{K}}^{-1}$, the percent change in its volume is

A square plate is hinged as shown in figure and it is held stationary by means of a light thread as shown in figure. Then find out the force exerted by the hinge.

With what acceleration ‘$a$’ should the box in the figure descend so that the block of mass $M$ exerts a force $Mg/4$ on the floor of the box?

A $2\text{kg}$ ball is swinging in a vertical circle at the end of an inextensible string $2\text{m}$ long. The angular speed of the ball if the string can sustain a maximum tension of $119.6\text{N}$ is (Take $g=9.8{\text{m/s}}^2$)

The r.m.s. current in an ac circuit is 2 A. If the watt less current be $\sqrt{3}$ A , what is the power factor

What are the dimensions of $a$ and $b$ in the relation $F=a\sqrt{x}+b{t}^2$ where $F$ is force, $x$ is distance and $t$ is time?

Two objects of masses $2\text{kg}$ and $3\text{kg}$ are dropped from a tower of height of $60\text{m}$. The ratio of their kinetic energy when they reach the ground is

The angular velocity of a wheel is 70 rad/sec. If the radius of the wheel is 0.5 m, then linear velocity of the wheel is

Which of the lines in the figure represents the relation between Celsius and Fahrenheit temperatures?

A body of mass $1kg$ is moving with a velocity $\overrightarrow{v}=(10\hat{i}+5\hat{j})m/s.$ What is the angle made by the momentum vector with x-axis?

A girl is standing on ground near a horizontally moving conveyor belt. She throws her suitcase horizontally. Such that the initial velocity of suitcase relative to stationary girl is along dotted line shown in top view of conveyor belt.

Which of the following arrows represents the direction of friction on the bag at the initial moment.

A particle moves in a circle of radius $25cm$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is

The gravitational force between two stones of mass 1 kg each separated by a distance of 1 metre in vacuum is

Find the equivalent resistance of the network shown in figure between the points P and Q.

A charge Q is divided into two parts of q and Q-q. If the coulomb repulsion between them when they are separated is to be maximum, the ratio of $\frac{Q}{q}$ should be

If the ratio of concentration of electrons to that of holes in a semiconductors is $\frac{7}{5}$ and the ratio of currents is $\frac{7}{4}$, what is the ratio of their drift velocities?

The angular velocity of the earth with which it has to rotate so that acceleration due to gravity on ${60}^{\circ }$ latitude becomes zero is (Radius of earth = 6400 At the poles g = 10$m{s}^{-2}$)

A simple pendulum is oscillating without damping. When the bob is at extreme position, acceleration vector is correctly shown by

Electric field in the space is given as $\overrightarrow{E}=2x\hat{i}+y\hat{j}$, then charge enclosed inside cube of side length $2m$ as shown in figure will be

Two trains each $50\text{m}$ long are moving parallel towards each other at speeds $10\text{m/s}$ and $15\text{m/s}$ respectively. Time taken by them to pass each other is

A uniform cylinder of mass $m$ and radius $R$ rolls without slipping down a slope of angle $\theta$ with the horizontal. The cylinder is connected to a spring having spring constant $K$ while the other end of the spring is connected to a rigid support at $P$. The cylinder is released when the spring is unstretched. The maximum distance that the cylinder travel along the plane is

If the radius of curvature of the path of two particles of same masses are in the ratio 1 : 2, then in order to have constant centripetal force, their velocity, should be in the ratio of

An electron starting from rest has a velocity that increases linearly with time as $v=kt$, where $k=2m{s}^{-2}$. The distance travelled in the first 3 seconds will be

The wavelength associated with an electron accelerated through a potential difference of 100 V is nearly

A wind with speed $40\text{m/s}$ blows parallel to the roof of a house. The area of the roof is $250{\text{m}}^2$. Assuming that the pressure inside the house is equal to atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $({\rho }_{\text{air}}=1.2{\text{kg/m}}^3)$

The period of oscillation of a simple pendulum in the experiment is recorded as 2.63 s, 2.56 s, 2.42, 2.71 s and 2.80 s respectively. Find the average absolute error.

Plane polarised light is passed through a polaroid. On viewing through the polaroid we find that when the polaroid is given one complete rotation about the direction of the light, one of the following is observed

[MNR 1993]

The velocity of a particle depends upon as v = a + bt + $c{t}^2$ ; if the velocity is in m/sec, the unit of a will be

Water and mercury are filled in two cylindrical vessels up to same height. Both vessels have a hole in the wall near the bottom. The velocity of water and mercury coming out of the holes are v₁ and v₂ respectively.

If a point $\left(P\right)$ moves along a circle with constant speed. Ratio of its angular speed wrt any point $\left(O\right)$ on circumference to angular speed wrt centre $\left(C\right)$ of the circle is

A super dense particle of mass $\frac{M}{2}$ is projected from the surface of the planet of mass M and radius R. Escape velocity for this particle of mass $\frac{M}{2}$ from surface of planet is

At constant volume, when the temperature of a gas increases by $1^{\circ }\text{C}$, its pressure increases by $0.4\%$. What is its initial temperature ?

A car travels the first half of a distance between two places at a speed of 30 km/hr and the second half of the distance at 50 km/hr. The average speed of the car for the whole journey is

The closed container filled with water is moving with some acceleration as shown in the figure. Then $P_A-P_D$ is :-

Calculate $sin{15}^o.cos{15}^o$.

The temperature coefficient of resistance of a conductor varies as $\alpha \left(T\right)=3T^2+2T$. If $R_0$ is resistance at $T=0$ and $R$ be resistance at $T$ then

Three vectors $\overrightarrow{A},\overrightarrow{B}and\overrightarrow{C}$ are related as $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$. If $\overrightarrow{C}$ is perpendicular to $\overrightarrow{A}$ and the $|\overrightarrow{C}|$ is equal to the $|\overrightarrow{A}|$, what will be the angle between $\overrightarrow{A}and\overrightarrow{B}$?

Which one of the following statements is not true about thermal radiations?

The angle between vectors $\overrightarrow{A}\times \overrightarrow{B}$ and $\overrightarrow{B}\times \overrightarrow{A}$ is

Turpentine oil is flowing through a tube of length ${}^{\prime }{l}^{\prime }$ and radius ${}^{\prime }{r}^{\prime }$ . The pressure difference between the two ends of the tube is $P$. The viscosity of oil is given by $\eta =\frac{P(r^2-x^2)}{4vl}$, where $v$ is the velocity of oil at a radial distance '$x$' from the axis of the tube. The dimensions of $\eta$ are

A N-type semiconductor is

Frequency of photon having energy 66 eV is