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The electric field intensity at points $P$ and $Q$ in the shown arrangement, are in the ratio

A body is whirled in a horizontal circle of radius 20 cm. It has angular velocity of 10 rad/s. What is its linear velocity at any point on circular path

A heater is designed to operate with a power of $1000\text{W}$ in a $100\text{V}$ line. It is connected, in combination with a resistance $R$, to a $100\text{V}$ main supply as shown in Figure. What should be the value of $R$ such the heater may operate with a power of $62.5\text{W}$?

A concave lens made of material of refractive index 1.6 is immersed in a medium of refractive index 2.0. The two surfaces of the concave lens have the same radius of curvature 0.2 m. The lens will behave as a

1. 2.25

A gas in an airtight container is heated from ${25}^{\circ }C$ to ${90}^{\circ }C$. The density of the gas will:
( Consider there is a negligible expansion of container)

The density of an ideal gas at $27{}^{o}C$ and pressure of 1 atm is $1.8\times {10}^{-3}g/c{m}^3,$ find the number of molecules in $90g$ of gas.

A boy releases a $0.5\text{kg}$ ball along the frictionless floor with the speed of $20\text{m/s}$. The ball is deflected by an obstacle on the way. After the deflection, it moves with $5\%$ of its initial kinetic energy. What is the final speed of the ball?

In a metre bridge set up with null deflection in galvanometer, find $\alpha$ of material of wire.

In column 1 different setup for Young’s double slit experiment is given. Distance between two slits S1 and S2 is ‘d’ and between slits and screen is ‘D’ in every setup. In column 2 location of central maxima is given. In column 3 path difference $\Delta P$ is given at point P which is $\theta$ angle above MO line (d << D)

Which of the following is correct, when a glass slab of thickness t and refractive index $\mu$ is placed in front of $S_1$.

Two balls of masses $5\text{kg}$ and $10\text{kg}$ are at the positions shown in figure. The track on which the balls move is frictionless. Initially, the $10\text{kg}$ ball is kept at rest and the $5\text{kg}$ ball is dropped with speed $v$ from height $5\text{m}$. Assuming the collision between the balls is perfectly elastic, find the value of ${}^{\prime }{v}^{\prime }$ such that the $10\text{kg}$ ball reaches point ${}^{\prime }{C}^{\prime }$.

A bucket tied at the end of a 1.6 m long string is whirled in a vertical circle with constant speed. What should be the minimum speed so that the water from the bucket does not spill, when the bucket is at the highest position (Take g = 10m/$se{c}^2$)

A light ray is incident at ${30}^{\circ }$ on one of the two mirrors that are placed at right angle to each other. Find the angle of reflection for the ray reflected from mirror B.

Vector $A$ and $B$ are as shown in the figure having magnitude of $2$ units each. Find $\overrightarrow{A}+\overrightarrow{B}$.

A bucket full of hot water cools from ${75}^{\circ }\text{C}$ to ${70}^{\circ }\text{C}$ in time $t_1$, from ${70}^{\circ }\text{C}$ to ${65}^{\circ }\text{C}$ in time $t_2$ and from ${65}^{\circ }\text{C}$ to ${60}^{\circ }\text{C}$ in time $t_3$, then

Consider the two following statements A and B and identify the correct choice given in the answers;

(A) In photovlotaic cells the photoelectric current produced is not proportional to the, intensity of incident light.

(B) In gas filled photoemissive cells, the velocity of photoelectrons depends on the wavelength of the incident radiation.

What if in charging by conduction or charging by rubbing, both the bodies were positively or negatively charged already. Then what would have happened?

1. -2

Two charges $Q$ & $-Q$ are kept at some distance, so that electric field at the mid point is $\overrightarrow{E}$. Find the force on $Q$ due to the field of $-Q$. (charges are isolated)

If a particle moving in a straight line which has slope $4$ and passes through $(4,-3)$, then, the equation of the motion is

A block of mass $m$ rests on a horizontal table with coefficient of static friction $\mu$. What minimum force must be applied on the block to drag it on the table?

In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function than X; which one of the following graphs best illustrates the expected results?

The given AC RLC circuit is connected to an AC source of $110\text{V};50\text{Hz}$. The power factor of the circuit is -

The figure shows a conducting circular loop of radius $20\text{cm}$ placed in a uniform magnetic field $1.5\text{T}$ perpendicular to the plane of the loop. A semicircular wire $OP$ is pivoted at the center $O$ and the other end touches the loop at $P$. The center $O$ and a fixed point $Q$, on the loop, are connected by a resistor of $10\Omega$. Resistance of semicircular wire and the circular loop is negligible. Find the current flowing through the resistor, if the semicircular loop is rotating with a constant angular velocity of $5\text{rad/s}$.

A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it ?

The value of $\underset{0}{\overset{\frac{\pi }{2}}{\int }}{\cos }^{2}xdx$ is

A toroid of $N$ turns, mean radius $r$ and cross- sectional radius $a$ is connected across a battery of emf $V$. If the magnetic field inside the core of toroid is $B$, find the value of $V$. Take resistance per unit length of wire equal to $\rho$.

[wires are closely wounded on toroid]

An airplane going at a constant velocity that is trying to bomb a city during the war.Then, which of these is true(Ignoring air drag)

An aircraft moving with a speed of $540\text{km/h}$ is at a height of $6000\text{m}$, just overhead of an anti aircraft gun. If the muzzle velocity of the bullet is $300\text{m/s}$, the firing angle $Q$ from the horizontal for the bullet to hit the aircraft should be

If $\underset{0}{\overset{1}{\int }}\frac{{\tan }^{-1}x}{{\cot }^{-1}(1-x+x^2)}dx$ equals $k,$ then the value of $\frac{1}{k}$ is