The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time \(0\) to \(10\,s\) is

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\): A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason \(R\): For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below

A plano-convex lens (focal length \(f_2,\) refractive index \(\mu _2,\) radius of curvature \(R\) ) fits exactly into a plano-concave lens (focal length \(f_1,\) refractive index \(\mu _1,\) radius of curvature \(R\) ). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be

The de Broglie wavelength of a proton and \(\alpha\) -particle are equal. The ratio of their velocities is ...... .

For ac circuit shown in figure, \(\mathrm{R}=100 \mathrm{k} \Omega\) and \(\mathrm{C}=100 \mathrm{pF}\) and the phase difference between \(\mathrm{V}_{\text {in }}\) and \(\left(V_B-V_A\right)\) is \(90^{\circ}\). The input signal frequency is \(10^x \mathrm{rad} / \mathrm{sec}\), where ' x ' is ______.

Unpolarised light of intensity \(32\,Wm ^{-2}\) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \(3\,Wm ^{-2}\), then the angle between pass axis of first two polaroids is \(............\,^{\circ}\)

If \(2\) mole of an ideal monoatomic gas at temperature \(T\), is mixed with \(6\) mole of another ideal monoatomic gas at temperature \(2T\) then the temperature of mixture is :

The displacement of a particle, executing simple harmonic motion with time period \(T\), is expressed as \(x(t)= A \sin \omega t\), where \(A\) is the amplitude. The maximum value of potential energy of this oscillator is found at \(t=T / 2 \beta\). The value of \(\beta\) is ___________.

Young's moduli of the material of wires \(A\) and \(B\) are in the ratio of \(1: 4\), while its area of cross sections are in the ratio of \(1: 3\). If the same amount of load is applied to both the wires, the amount of elongation produced in the wires \(A\) and \(B\) will be in the ratio of [Assume length of wires \(A\) and \(B\) are same]

In the Young's double slit experiment the intensity produced by each one of the individual slits is \(I_0\). The distance between two slits is 2 mm . The distance of screen from slits is 10 m . The wavelength of light is \(6000\) Å. The intensity of light on the screen in front of one of the slits is _________ .

From the circuit given below, the capacitance between terminals \(A\) and \(B\) shown in the circuit is ______ \(\mu\)F.
(take \(C_1=C_2=C_3=1\) \(\mu\)F and \(C_4=2\) \(\mu\)F.)

Refer the figure given below. \(\mu_1\) and \(\mu_2\) are refractive indices of air and lens material. The height of image will be _______ cm.

A heating element has a resistance of  \(100\,\Omega \) at room temperature. When it is connected to a supply of  \(220\,V,\)  a steady current of \(2\,A\)  passes in it and temperature is \(500\,^oC\) more than room temperature. What is the temperature coefficient resistance of the heating element?