In a microscope the objective is having focal length \(f_0=2 cm\) and eye-piece is having focal length \(f_{ e }=4 cm\). The tube length is 32 cm . The magnification produced by this microscope for normal adjustment is _________ .

The magnetic field in a travelling electromagnetic wave has a peak value of \(20\ n T\). The peak value of electric field strength is......\(Vm^{-1}\)

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

As show in the figure, in steady state, the charge stored in the capacitor is....... \(\times 10^{-6}\,C\).

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). \(Assertion\) \(A\) : Number of photons increases with increase in frequency of light. \(Reason\) \(R\) : Maximum kinetic energy of emitted electrons increases with the frequency of incident radiation. In the light of the above statements, choose the most appropriate answer from the options given below :

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by \(50 \%\). The percentage change in voltage sensitivity of the galvanometer will be \(..........\%\)

The electric field of an electromagnetic wave in free space is represented as \(\vec{E}=E_0 \cos (\omega t-k z) \hat{i}\). The corresponding magnetic induction vector will be _______.

If the distances of the point (1, 2, a) from the line \(\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}\) along the lines
\(L_{1}:\frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}\) and
\(L_{2}:\frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}\) are equal,
then \(a+b+c\) is equal to

The magnetic field at the center of current carrying circular loop is \(B _{1}\). The magnetic field at a distance of \(\sqrt{3}\) times radius of the given circular loop from the center on its axis is \(B_{2}\). The value of \(B_{1} / B_{2}\) will be.

Let \(\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}\) be a thrice differentiable function such that \(f(0)=0, f(1)=1, f(2)=-1, f(3)=2\) and \(f(4)=-2\). Then, the minimum number of zeros of \(\left(3 f^{\prime} f^{\prime \prime}+f f^{\prime \prime \prime}\right)(x)\) is ...........

Equation of the tangent to the circle, at the point \((1 , -1)\) whose centre is the point of intersection of the straight lines \(x - y = 1\) and \(2x + y= 3\) is

A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of \(10\,cm\). The separation between the two lenses is \(2\,cm\). The focal lengths of the component lenses

The set of all values of \(\mathrm{k}\,>\,-1\), for which the equation \(\left(3 x^{2}+4 x+3\right)^{2}-(k+1)\left(3 x^{2}+4 x+3\right)\) \(\left(3 x^{2}+4 x+2\right)+k\left(3 x^{2}+4 x+2\right)^{2}=0\) has real roots is: