Find the distance of the image from object \(O\), formed by the combination of lenses in the figure : (in \(cm\))

In a scries \(LCR\) resonance circuit, if we change the resistance only, from a lower to higher value

A nucleus \(A\), with a finite de -broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de -Broglie wavelength \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : Body \('P'\) having mass \(M\) moving with speed \('u'\) has head-on collision elastically with another body \('Q'\) having mass \('m'\) initially at rest. If \(m< < M,\) body \('Q'\) will have a maximum speed equal to \('2u'\) after collision. Reason \(R\) : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below:

Capacitance of an isolated conducting sphere of radius \(R_{1}\) becomes \(n\) times when it is enclosed by a concentric conducting sphere of radius \(R_{2}\) connected to earth. The ratio of their radii \(\left(\frac{ R _{2}}{ R _{1}}\right)\) is:

In the given figure, the block of mass \(m\) is dropped from the point ' \(A\) '. The expression for kinetic energy of block when it reaches point ' \(B\) ' is ................

In photoelectric effect, the stopping potential \(\left(\mathrm{V}_0\right) \mathrm{v} / \mathrm{s}\) frequency \((\nu)\) curve is plotted.
( h is the Planck's constant and \(\phi_0\) is work function of metal )
(A) \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) is linear.
(B) The slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) curve \(=\frac{\phi_0}{\mathrm{~h}}\)
(C) h constant is related to the slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) line.
(D) The value of electric charge of electron is not required to determine \(h\) using the \(V_0 \mathrm{v} / \mathrm{s} \nu\) curve.
(E) The work function can be estimated without knowing the value of \(h\).
Choose the correct answer from the options given below :

Given below are two statements : Statement \(I\) : When the white light passed through a prism, the red light bends lesser than yellow and violet. Statement \(II\) : The refractive indices are different for different wavelengths in dispersive medium.
In the light of the above statements, choose the correct answer from the options given below :

Let \(A\) and \(E\) be any two events with positive probabilities:
Statement \(- 1\): \(P\left( {E/A} \right) \geq P\left( {A/E} \right)P\left( E \right)\)
Statement \(-2\) : \(P\left( {A/E} \right) \geq P\left( {A \cap E} \right)\)

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter \(0.1\, \mu m\). If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that :

Train \(A\) and train \(B\) are running on parallel tracks in the opposite directions with speeds of \(36\, km / hour\) and \(72 \,km / hour,\) respectively. A person is walking in train \(A\) in the direction opposite to its motion with a speed of \(1.8\, km / hr\). Speed (in \(ms ^{-1}\) ) of this person as observed from train \(B\) will be close to (take the distance between the tracks as negligible)

The number of real solutions of the equation \(3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0\), is

A galaxy is moving away from the earth at a speed of \(286\, kms ^{-1}\). The shift in the wavelength of a red line at \(630\, nm\) is \(x \times 10^{-10}\, m\). The value of \(x ,\) to the nearest integer, is........ [Take the value of speed of light \(c,\) as \(3 \times 10^{8}\) \(\left. ms ^{-1}\right]\)