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Strain gauge $G_f=2$ and operational amplifier $A_d=2500,A_c=0.25$. For given quarter Wheatstone bridge the strain is

If

A. cos x
+ x sin x

B. x sin
x

C. x cos
x

D. sin x +
x cos x

Suppose our school is $1\text{km}$ away from our house, and we go to school in the morning, and in the afternoon we come back. Then, the total displacement for the entire trip is

Two
particles undergo SHM along parallel lines with the same time period (T) and
equal amplitudes. At a particular instant, one particle is at its extreme
position while the other is at its mean position. They move in the same
direction. They will cross each other after a further time

A particle is moving on a circular path of radius $3cm$ with a time varying speed of $v=3tcm/s$, where $t$ is in seconds. The magnitude of tangential acceleration and the total acceleration of the particle at $t=1s$ is

A small particle of mass $0.36\text{g}$ rests on horizontal turntable at a distance $25\text{cm}$ from the axis of spindle. The turntable is accelarated at a rate of $\alpha =\frac{1}{3}{\text{rad/s}}^2$. The frictional force that the table exerts on the particle $2\text{s}$ after the startup is

An iron rod of volume ${10}^{-4}{m}^3$ and relative permeability 1000 is placed inside a long solenoid wound with 5 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod is

A ball of mass $600\text{g}$ is dropped to the ground from a height of $25\text{m}$. If the energy of the ball reduces by $35\%$ after striking the ground, what is the height to which it rebounds?

A block of ice with mass m falls into a lake. After impact, a mass of ice $\frac{m}{5}$melts. Both the block of ice and the lake have a temperature of 0⁰C. If L represents the latent heat of fusion, the distance the ice falls before striking the surface is

A gas is said to behave like an ideal gas when the relation $\frac{PV}{T}$=constant. When do you expect a real gas to behave like an ideal gas

Find the acceleration of the block of mass $M$ in the situation shown in the figure. All the surfaces are frictionless and the pulley and the string are light.

Two bodies $1$ and $2$ are projected simultaneously with velocities $V_1=2\text{m/s}$ and $V_2=4\text{m/s}$ . The body $1$ is projected vertically up from the top of a cliff of height $h=10\text{m}$ and the body $2$ is projected vertically up from the bottom of the cliff . If the bodies meet, find the time in $\left(s\right)$ of meeting of the bodies.

In a 7-stage ripple counter, the propagation delay of a flip-flop is $50ns$. If the pulse width of the strobe pulse is $50ns$, then the maximum frequency at which the counter will operate reliably is

Two identical conducting rods are first connected independently to two vessels, one containing water at ${100}^{\circ }\text{C}$ and the other containing ice at $0^{\circ }\text{C}$. In the second case, the rods are joined end to end and connected to the same vessels. Let $q_1$ and $q_2$ gram per second be the rate of melting of ice in the two cases respectively. The ratio $\frac{q_1}{q_2}$ is

Which of the following statements is/are correct regarding the refractive index ?

The figure shows four wire loops, with the lengths of either $L$ or $2L.$ All four loops will move through a region of uniform magnetic field of intensity $B$ outward from the plane of paper. The loops will move at the same constant velocity. Rank the four loops according to the increasing magnitude of the emf induced as they move through the field,

1. 1.5

Young's double slit experiment apparatus shown in figure , $D>>d$ and $d=6\lambda$. Find total number of maxima on the screen.

Small droplets of a liquid are usually more spherical in shape than larger drops of the same liquid because

For the given uniformly charged quarter ring, the angle $\theta$ made by the net electric field at the centre with negative x-axis is equal to

A particle is observed from two frames S1 and S2. The graph of relative velocity of S1 with respect to S2 is shown in figure. Let F1 and F2 be the pseudo forces on the particle when seen from S1 and S2 respectively. Which one of the following is not possible?

Water rises to a height of $10\text{cm}$ in a certain capillary tube. Another identical tube when dipped in mercury, the level of mercury is depressed by $3.42\text{cm}$. Density of mercury is $13.6{\text{gm/cm}}^3$. The angle of contact for water in contact with glass is $0^{\circ }$ and mercury in contact with glass is ${135}^{\circ }$. Then the ratio of surface tension of water to that of mercury is:

(use $\frac{0.0342}{\sqrt{2}}=0.024$)

Three semi-conductors are arranged in the increasing order of their energy gap as follows. The correct arrangement is :

Find the magnetic field at ‘o’

A car is moving on a smooth horizontal road. Find the ratio of work done by the engine of the car, in order to change its speed from $0$ to $v$ and $v$ to $2v$.

In problems where only position and nature (not size) of image is asked, do we have to write the magnification of the image as well ?

One cubic meter of mild steel weighs about