Explore topic-wise InterviewSolutions in .

The graph given shows the velocity $v$ versus time $t$ for a body. Which of the following graphs shown represents the corresponding acceleration versus time graph ?

In a common-emitter amplifier, using output resistance of $5000\text{ohm}$ and input resistance of $2000\text{ohm}$, if the peak value of input signal voltage is $10\text{mV}$ and $\beta =50$, then the power gain is

A ray of light is incident on a plane mirror along a vector $(\hat{i}+\hat{j}-\hat{k})$. The normal on the incident point is along $\left(\hat{k}\right)$. The unit vector along the reflected ray will be:

$\int \frac{dx}{\sqrt{2ax-x^2}}$ = $a^{n}si{n}^{-1}[\frac{x}{a}-1]$

The value of n is

The magnetic field at the centre of the circular coil carrying current of 4A is

A fish looking from within water sees the outside world through a circular horizon. If the fish is $\sqrt{7}m$ below the surface of water, then the radius of the circular horizon will be

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

Two forces 3N and 2 N are at an angle q such that the resultant is R. The first force is now increased to 6N and the resultant become 2R. The value of q is

Particles of mass $1\text{kg}$ each are placed along $x-$ axis at $x=1,2,4,8,.....\infty$. Then gravitational force on a mass of $3\text{kg}$ placed at origin is ($G=$ universal gravitational constant)

A position dependent force $F$ is acting on a particle and its force position curve is shown in the figure. Change in kinetic energy of the particle, when its displacement is from $0$ to $5\text{m}$ is

A smooth wire of length $2\pi r$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circlular frame is rotating with angular speed $\omega$ about the vertical diameter $AB$, the bead is at rest with respect to the circular frame at the position shown in the figure. Then, the value of ${\omega }^2$ is equal to:

A particle has potential energy dependent on its position on the $x$ axis, represented by the function $U\left(x\right)=e^{2x}+1$ for all real values of $x$, where $U\left(x\right)$ and $x$ are given in standard units. The force it feels at position $x=1$ is closest to

[Take $e=2.72$]

A particle executing linear $\text{SHM}$ is represented by the equation $x=\text{A cos}\omega t$. Which of the following graphs correctly represent the variation of velocity$\left(v\right)$ with time$\left(t\right)$?

If a body moving in a straight line travels from position $x=-6\text{m}$ to $x=+4\text{m}$ in $4\text{s}$, considering origin at $x=0$. What is the average speed of body in the journey?

A disc of mass $m$ is moving with constant speed $v_0$ on a smooth horizontal table. Another disc of same mass is placed on the table at rest as show in the figure. If collision is elastic then find the velocity of the discs after collision.

[Consider $r<<R$]$(\theta =ta{n}^{-1}\frac{h}{\sqrt{R^2-h^2}})$.

A steel wire of mass $8\text{g}$ and length $160\text{cm}$ is fixed at two ends. The tension in the wire is $50\text{N}$. Find the frequency and wavelength of the fourth harmonic.

A simple pendulum of length $100\text{cm}$ is suspended from the ceiling of a cart which is sliding without friction on an inclined plane of inclination ${60}^{\circ }$. Find the time period of the pendulum.

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

A disc of mass $m$ and radius $r$ is rolling purely on rough surface with velocity $v$. If initially the spring was in natural state, then maximum compression in spring is

A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is $11{\text{kms}}^{–1}$, the escape velocity from the surface of the planet would be

The area of cross-section of the wider tube shown in figure is $800{\text{cm}}^2$. If a mass of $12\text{kg}$ is placed on the massless piston, the difference in heights in the level of water in the two tubes is:

A rod is measured to be of length $50\text{cm}$ at ${10}^{\circ }\text{C}$. Its length measured at ${50}^{\circ }\text{C}$ is $x$. Find $x$, if thermal coefficient of linear expansion of the rod is $2\times {10}^{-5}{/}^{\circ }\text{C}$ and of the scale is $3\times {10}^{-5}{/}^{\circ }\text{C}$.

The orbital angular momentum of a satellite revolving at a distance r from the centre is L. If the distance is increased to 16r , then new angular momentum will be

An ideal fluid is flowing in a pipe in a streamline flow. The pipe has a maximum and minimum diameter of $6.4\text{cm}$ and $4.8\text{cm}$ respectively. Find out the ratio of minimum to maximum velocity.

A wave is propagating in a medium of electric dielectric constant 2 and relative magnetic permeability 50. The wave impedance of such a medium is

Two identical metallic blocks resting on a frictionless horizontal surface are connected by a light metallic spring having the spring constant $100\text{N/m}$ and an unstretched length of $0.2\text{m}$, as shown in figure 1. A total charge $Q$ is slowly placed on the system, causing the spring to stretch to an equilibrium length of $0.3\text{m}$, as shown in figure 2. The value of charge $Q$, assuming that all the charge resides on the blocks and that the blocks are like point charges , is

The equivalent quantity of mass in electricity is

A cycle can bend upto a maximum angle of ${45}^{\circ }$. If the radius of the bend is $10\text{m}$, then what should be the maximum speed of the cyclist so that he does not crash?

Two uniform ropes having linear mass densities $m$ and $4m$ are joined to form a closed loop. The loop is hanging over a fixed frictionless small pulley with the lighter rope above and denser rope below, as shown in the figure. (Figure represents equilibrium position). Now if point $A$ (joint) is slightly displaced in downward direction and released, it is found that the loop performs SHM. Find the time period of oscillation.

$[\text{Take}l=\frac{150}{4{\pi }^2}\text{m},g=10{\text{m/s}}^2]$

Statement 1: Charge density on a solid conductor is always uniform no matter what the shape.

Statement 2: Charges are always on the surface of a conductor and they repel each other so they always arrange to give uniform charge density.

Work done in converting one gram of ice at $-{10}^{\circ }\text{C}$ into steam at ${100}^{\circ }\text{C}$ is -

[Given, specific heat of ice $c_i=0.5{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, specific heat of water $c_w=1{\text{cal g}}^{-1}{}^{\circ }{\text{C}}^{-1}$, latent heat of fusion of ice $L_f=80\text{cal/g}$, & latent heat of vaporization of steam $L_v=540\text{cal/g}$]

In the arrangements shown in figure,masses of each ball are 1 kg and mass of trolley is 4 kg. In the figure shell of mass 1 kg moving horizontally with velocity v = 6 m/sec collides with the ball and get stuck to it .It's maximum deflection of the thread (length 1.5 m) with vertical is:

If motion of a particle is represented by $s=e^t+4^t-\cos t$, then the acceleration of the particle at any time $t$ is

[Hint: Acceleration of the particle is $\frac{d^{2}s}{d{t}^2}$]

Which of these is not a basic assumption (axiom) of the model of electrostatics?

A stone is projected at time t = 0 with a speed $v_0$ and an angle $\theta$ with the horizontal in a uniform gravitational field. The rate of work done (P) by the gravitational force plotted against time (t) will be as

Derivative of $f\left(x\right)=\frac{x^2}{\cos x}$ is

A block of mass $m$ is suspended from a pulley in the form of a circular disc of mass $m$ and radius $R$. The system is released from rest. Find the angular velocity of the disc when the block has dropped by height $h$. [Assume there is no slipping between string & pulley]

A car travelled the first one-third of the distance $d$ at a speed of $20km{h}^{-1}$, the second one-third of the distance at a speed of $40km{h}^{-1}$ and the last one-third of the distance at a speed of $120km{h}^{-1}$. Determine the average speed of the car.

A particle moves under the effect of a force $F=k{x}^2$. Find work done by force when particle displaces from $x=0\text{m}$ to $x=4\text{m}$.

Four particles, each of mass $m,$are kept at the four corners of a square of edge$a.$Moment of inertia of the system about the line perpendicular to the plane of the square and passing through the centre of the square is.

A proton is projected with a velocity ${10}^{7}m/s$ at right angle to a uniform magnetic field of induction 100 mT. The time taken by proton to traverse ${90}^{\circ }$ arc is

A tennis ball is dropped on a horizontal smooth surface. It bounces back after hitting the surface. The force on the ball during the collision is proportional to the degree of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy $K$ with time $t$ most appropriately? The figures are only illustrative and not to scale.

A block is sliding along incline as shown in the figure. If the acceleration of the chamber is $a$ as shown in the figure. The time required to cover a distance $L$ along the incline is:

A boat that has a speed of $5\text{km/hr}$ in still water crosses a river of width $1\text{km}$ along the shortest possible path in $20$ minutes. The velocity of the river water in $\left(\text{km/hr}\right)$ is

Photoelectric effect supports quantum nature of light because

As shown in the figure, a circular sheet is removed from a uniform rectangular sheet. Find the horizontal distance of centre of mass of the remaining sheet from the origin $\text{O}$, after the removal of circular sheet. Use $\pi =\frac{22}{7}$ for calculation.