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Projection of $\overrightarrow{A}=\hat{i}-\hat{j}+2\hat{k}$ along $\overrightarrow{B}=-\hat{k}$ is

Find the change in internal energy of the system from state P to R, while moving from $P\to Q\to R$, if heat added to the system for the process $PQ$ and $QR$ is $300\text{J}$ each.

A stone weighing $1\text{kg}$ is whirled in a vertical circle at the end of a rope of length $0.5\text{m}$. Stone completes the vertical circle with minimum possible speed. The velocity of the stone midway, when the string is horizontal is (Take $g=10{\text{m/s}}^2)$

If G = 8, FOG = 31, then what is FRONT equal to?

What is the slope of the line passing through the points $(-2,3)$ and $(2,7)$

Power supplied to a particle of mass $5\text{kg}$ varies with time as $P=\frac{4t^3}{5}\text{W}$, where $t$ is in $\text{seconds}$. If the velocity of the particle at $t=0$ is zero, then what will be the velocity of the particle at $5\text{seconds}$?

In a Young’s double slit experiment, the fringes are displaced by a distance x when a glass plate of refractive index 1.5 is introduced in the path of one of the beams. When this plate is replaced by another plate of same thickness, the shift of fringes is $\left(\frac{3}{2}\right)x$. The refractive index of second plate is

Two infinite sheets carrying current per unit length (Surface current density) $10\text{A/m}$ each in opposite directions. What is the magnetic field at point $P$.

A uniform magnetic
field of 3000 G is established along the positive z-direction.
A rectangular loop of sides 10 cm and 5 cm carries a current of 12 A.
What is the torque on the loop in the different cases shown in Fig.
4.28? What is the force on each case? Which case corresponds to
stable equilibrium?

Determine the de-Broglie wavelength(in angstrom) associate with He Atom at $500K$.

A body P strikes head-on with another body Q of mass that is 'p' times that of body P and moving with a velocity that is $\frac{1}{q}$ of the velocity of body P. If the body P comes to rest, the coefficient of restitution is

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

The radius of a circular current carrying coil having a single turn is $R$. At what distance from the centre of the coil on its axis, the intensity of magnetic field will be $\frac{1}{2\sqrt{2}}$ times the intensity of magnetic field at the centre ?

A small object is placed at the centre of the bottom of a cylindrical vessel of radius $3\text{cm}$ and height $4\text{cm}$ filled completely with water. Consider the ray leaving the vessel through its edge. Suppose this ray and the ray along the axis of the vessel are used to trace the image. Find the ratio of real depth to the apparent depth under the assumptions taken. Refractive index of water $=1.33$.

A magnetic needle lying parallel to a magnetic field requires $W$ units of work to turn it through ${60}^{\circ }$. The torque required to maintain the needle in this position will be

Given vector $\overrightarrow{A}=2\hat{i}+3\hat{j}$, the angle between $\overrightarrow{A}$ and y-axis is

Consider a source of sound S, and an observer/detector D. The source emits a sound wave of frequency $f_0$. The frequency observed by D is found to be

Displacement is always less than or equal to ______

A block of mass $10\text{kg}$ is moving in x-direction with a constant speed of $10\text{m/s}$. It is subjected to a retarding force $F=(-0.1x)\text{N}$ during its travel from $x=20\text{m}$ to $x=30\text{m}$. Its final kinetic energy will be

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The charge flown through a circuit in the time interval between t and t+dt is given by $dq=e^{-t/\tau }dt$, where $\tau$ is a constant. Find the toatal charge flown through the circuit t = 0 to t = $\tau$

The radioactivity of a sample is X at time $t_1$ and Y and a time $t_2$. If the mean life time of the specimen is $\tau$, the number of atoms that have disintigrated in the time interval $t_1-t_2$ is

From a tower of height $H$, a particle is thrown vertically upwards with a speed $u$. The time taken by the particle to hit the ground, is $n$ times that taken by it to reach the highest point of its path. The relation between $H$,$u$ and $n$ is

A wire of length l is bent in the form of a circular loop and is suspended in a region of a uniform magnetic field . When a steady current I is passed through the loop, the maximum torque experienced by it is