The current flowing through the \(1 \Omega\) resistor is \(\frac{\mathrm{n}}{10} \ A.\) The value of \(n\) is _______.

According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :-

Two blocks of masses \(m\) and \(M,(M \gt m)\), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
(\(\mu=\) coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is \(\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}\)
(B) The acceleration of the blocks is \(\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}}\) (\(\mathrm{x}=\) displacement of the blocks from the mean position)
(C) The magnitude of the frictional force on the upper block is \(\frac{m \mu|x|}{M+m}\)
(D) The maximum amplitude of the upper block, if it does not slip, is \(\frac{\mu(M+m) g}{k}\)
(E) Maximum frictional force can be \(\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}\).
Choose the correct answer from the options given below:

A collimated beam of light of diameter 2 mm is propagating along x -axis. The beam is required to be expanded in a collimated beam of diameter 14 mm using a system of two convex lenses. If first lens has focal length 40 mm , then the focal length of second lens is _________ mm.

Match List - \(I\) with List - \(II\).

List - \(I\) \((Number)\)	List - \(II\) \((Significant figure)\)
\((A)\) \(1001\)	\((I)\) \(3\)
\((B)\) \(010.1\)	\((II)\) \(4\)
\((C)\) \(100.100\)	\((III)\) \(5\)
\((D)\) \(0.0010010\)	\((IV)\) \(6\)

Choose the correct answer from the options given below :

The least count of the main scale of a screw gauge is \(1\, mm\). The minimum number of divisions on its circular scale required to measure \(5\,\mu m\) diameter of a wire is

The voltage and the current between \(A\) and \(B\) points shown in the circuit are _____.

A card from a pack of 52 cards is lost. From the remaining 51 cards, \(n\) cards are drawn and are found to be spades. If the probability of the lost card to be a spade is \(\frac{11}{50}\), the n is equal to

An \(\alpha\) particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be.

The image of the line \(\frac{{x - 1}}{3} = \frac{{y - 3}}{1} = \frac{{z - 4}}{{ - 5}}\) in the plane \(2x - y + z + 3 = 0\)  is the line :

The number of elements in the set \(\left\{A=\left(\begin{array}{ll}a & b \\ 0 & d\end{array}\right): a, b, d \in\{-1,0,1\}\right.\) and \(\left.(I-A)^{3}=I-A^{3}\right\}\) where \(I\) is \(2 \times 2\) identity matrix, is :

Let \(f : R \rightarrow R\) be continuous function satisfying \(f ( x )+ f ( x + k )= n\), for all \(x \in R\) where \(k >0\) and \(n\)is a positive integer. If \(I _{1}=\int\limits_{0}^{4 n k} f ( x ) dx\) and \(I _{2}=\int\limits_{- k }^{3 k } f ( x ) dx\), then

In a Young's double slit experiment two slits are separated by \(2\, mm\) and the screen is placed one meter away. When a light of wavelength \(500 \,nm\) is used, the fringe separation will be ........ \(mm\)