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A thin isosceles prism with angle $4^{\circ }$ and refractive index $1.5$ is placed inside a transparent tube with water $(\text{refractive index}=\frac{5}{4})$ as shown. The deviation of light due to prism will be

A resistor of resistance $100\Omega$ is connected to an $AC$ source $E=12\sin 250\pi t$. Find the energy dissipated as heat during $t=0$ to $t=1.0\text{ms}$.

A body of mass $5\text{kg}$ starts from rest and moves in a straight line under the influence of two variable forces $F_1=(10t+\frac{6}{t})\text{N}$ and $F_2=(15-\frac{6}{t})\text{N}$, acting in same direction. Find the power delivered by force $F_1$ at $t=2\text{sec}$.

A particle moves in the $x-y$ plane under the action of a force $\overrightarrow{F}$ such that the value of its linear momentum $\overrightarrow{p}$ at any instant is $\overrightarrow{p}=2(\cos t\hat{i}+\sin t\hat{j})$. The angle $\theta$ between $\overrightarrow{F}$ and $\overrightarrow{p}$ is

Two non - zero vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $|\overrightarrow{A}+\overrightarrow{B}|=|\overrightarrow{A}-\overrightarrow{B}|$. Find angle between $\overrightarrow{A}$ and $\overrightarrow{B}$?

If $\underset{-\pi /4}{\overset{3\pi /4}{\int }}\frac{e^{\pi /4}dx}{(e^x+e^{\pi /4})(\sin x+\cos x)}=k\underset{-\pi /2}{\overset{\pi /2}{\int }}\sec xdx$, then the value of $k$ is

The work functions of metals A and B are in the ratio 1 : 2. If light of frequencies f and 2f are incident on the surfaces of A and B respectively, the ratio of the maximum kinetic energies of photoelectrons emitted is (f is greater than threshold frequency of A, 2f is greater than threshold frequency of B)

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\lambda =600nm$ are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $d=1.8mm$. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $\Delta \theta$. Which of the following options is/are correct?

Question: A particle moving in a straight line covers half the distance with speed of 2m/s. The other half of the distance is covered in two equal time intervals with speed of 4.5 m/s and 3.5/ms respectively. The average speed of the particle during this motion is what

A rod of mass $m$ and resistance $r$ is placed on fixed, smooth and resistanceless conducting rails which is closed by a resistance $R$ and it is projected with an initial velocity $u$. Find its velocity at any instant as a function of time $\left(t\right)$.

A conducting rod of mass m and length l is placed over a smooth horizontal surface. A uniform magnetic field B is acting perpendicular to the rod. Charge q is suddenly passed through the rod and it acquires an initial velocity υ on the surface, then q is equal to

$|\overrightarrow{A}|=4units$

$|\overrightarrow{B}|=10units$ If angle between $\overrightarrow{A}$ & $\overrightarrow{B}$ is ${60}^{\circ }$ then find $\overrightarrow{A}$ . $\overrightarrow{B}$.

Five equal forces of 10 N each are applied at one point and all are lying in one plane. If the angles between them are equal, the resultant force will be

Water in a bucket is whirled in a vertical circle with a string attached to it. The water does not fall down even when the bucket is inverted at the top of its path. We conclude that in this position.

A body initially moving with a velocity of $4{\text{ms}}^{–1}$, attains a velocity of $20{\text{ms}}^{–1}$ in $4s$ . The acceleration of the body is:

(Assume constant acceleration)

In the figure shown, find the maximum amplitude of the system, so that there is no slipping between any of the blocks.

The figure represents four positions of a current carrying loop in a uniform magnetic field directed towards the right. $\hat{n}$ represents the direction of area vector of the loop. The correct order of potential energy is

Convert $\frac{\pi }{3}$ radians to degrees.

A bar of uniform cross-section and having a length $l$ is hanging from the roof. What will be the elongation in bar due to self weight if $\gamma$ is the specific weight of the bar and $Y$ is the young's modulus of elasticity?

A thin Non-conducting rod is bent into a semicircle of radius $r$. A charge $+Q$ is uniformly distributed along the upper half and a charge $-Q$ is uniformly distributed along the lower half, as shown in figure. Find the electric field $E$ at $\text{P}$.

The momentum of a photon of energy hv will be

Two guns $A$ and $B$ can fire bullets at speeds $1\text{km/s}$ and $2\text{km/s}$ respectively, they are fired in all possible directions. The ratio of maximum areas covered by the bullets fired by the two guns, on the ground is:

What is the output Y in the following circuit when all the three inputs A, B, C are first $0$ and then $1$ ?