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A ball rolls off the top of a stairway horizontally with a velocity of $4.5{\text{ms}}^{-1}$. Each step is $0.2\text{m}$ high and $0.3\text{m}$ wide. If $g$ is $10{\text{ms}}^{-2}$, then the ball will strike the $n^{th}$ step where $n$ is equal to

A velocity selector is used to select $\alpha$- particles of energy $200\text{keV}$ from a beam containing particles of several energies. The electric field strength is $900\text{kv/m}$. What must be the value of magnetic field strength ?

If the angles of dip at two places are ${45}^{\circ }$ and ${30}^{\circ }$ respectively, then the ratio of vertical components of earth's magnetic field at the two places will be

The maximum range of a bullet fired from a toy pistol mounted on a car at rest is $R_0=40\text{m}$. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity $v=20\text{m/s}$ on a horizontal surface ?

$($ Take $g=10{\text{m/s}}^2)$

The contact force between $2\text{kg}$ and $3\text{kg}$ block placed on an inclined plane as shown in the figure will be

Three particles each of mass m, are placed at the corners of an equilateral triangle of side a, as shown in the figure. The position vector of the centre of mass is

Find the current flowing through the resistance $R_1$ of the circuit shown in the figure. The resistance are equal to $R_1=10\Omega ,R_2=20\Omega$ and $R_3=30\Omega$ and the potentials of points $1,2$ and $3$ are given as $V_1=10\text{V},V_2=6\text{V}$ and $V_3=5\text{V}$.

A horizontal heavy uniform bar of weight 'W' is supported at its ends by two men. At the instant, one of the men lets go off his end of the rod, the other feels the force on his hand changed to

In the series $LCR$ circuit shown, the readings of voltmeter and ammeter respectively are

Write down the output at $X$, for the inputs,

$A=0,B=0\text{and}A=1,B=1$.

In the figure shown below, $W_{AB}$ and $W_{CD}$ are workdone during process $AB$ and $CD$. Which of the following options is correct?

A man of mass 50 kg starts moving on the earth and acquires a speed of 1.8 m/s.With what speed does the earth recoil ? Mass of earth=$6\times {10}^{24}kg$.

If $f(a+b+1-x)=f\left(x\right)$ $\forall x\in R,$ where $a$ and $b$ are fixed positive real numbers, then $\frac{1}{a+b}\underset{a}{\overset{b}{\int }}x\left[f\right(x)+f(x+1\left)\right]dx$ is equal to

A particle moves in a circle of radius 4 m clock wise at constant speed of $2m{s}^{-1}$. If $\hat{x}$ and $\hat{y}$ are unit vectors along x and y axes, respectively, the centripetal acceleration of the particle at the instant half way between PQ is given by

Two inductors whose self-inductances are of $20\text{mH}$ and $30\text{mH}$ respectively are connected together in parallel opposing. Their mutual inductance is given as $5\text{mH}$. Calculate the total inductance of the parallel combination.

The value of integral $\int \frac{dx}{x(\ln x{)}^3}$ is

(where $C$ is constant of integration)

The near point and far point of a person are $40\text{cm}$ and $200\text{cm}$ respectively. Find the power of the lens, he/she should use while reading a book kept at distance $25\text{cm}$.

The ratio of densities of nitrogen and oxygen is 14:16. The temperature at which the speed of sound in nitrogen will be same as that in oxygen at ${55}^{\circ }C$ is

Which of the following is not an application of eddy currents?

A square -shaped copper coil has edges of length 50 cm and contains 50 turns. It is placed perpendicular to a 1.0 T magnetic field. It is removed from the magnetic field in 0.25 s and restored in its original place in the next 0.25 s. Find the magnitude of the average emf induced in the loop during (a) its removal, (b) its restoration and (c) its motion.

Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is${120}^0$. The resultant amplitude will be

The Bode asymptotic magnitude plot of a minimum phase system is shown in the figure.



If the system is connected in a unity negative feedback configuration, the steady state error of the closed loop system, to a unit ramp input is

1. 0.5

Electrons
are emitted with zero velocity from a metal surface when it is
exposed to radiation of wavelength 6800 Å.
Calculate threshold frequency ()
and work function (W₀)
of the metal.

The potential energy for a force field $\overrightarrow{F}$ is given by $U(x,y)=\sin (x+y)$. The force acting on the particle of mass $m$ at $(0,\frac{\pi }{4})$ is (in $N$)

In the following figures (i) and (ii), all the surfaces are smooth, string is massless and pulley is ideal. The mass of rope is $m$ in both the cases. If $T_1$ and $T_2$ be the tensions at the mid points of the ropes in figure (i) and figure (ii) respectively, then $T_1:T_2$ is

The torque (N-m) required to drive a machine is as shown in figure. It takes 2 seconds to complete 1 cycle whereas the motor supplying the power is running at a speed of 300 rpm. The size of the flywheel to be attached on the motor shaft to limit the fluctuations of speed with 1% on either side of the mean speed is