One mole of an ideal gas is taken from A to B, from \(B\) to \(C\) and then back to \(A\). The variation of its volume with temperature for that change is as shown. Its pressure at \(\mathrm{A}\) is \(\mathrm{P}_{0}\), volume is \(\mathrm{V}_{0}\), Then, the internal energy

A linear object of height \( 10 \mathrm{~cm} \) is kept in front of a concave mirror of radius of curvature \( 15 \mathrm{~cm} \),
at a distance of \( 10 \mathrm{~cm} \). The image formed is

A cylindrical conductor of diameter \( 0.1 \mathrm{~mm} \) carries a current of \( 90 \mathrm{~mA} \). The current density (in \(\mathrm{Am}^{-2})\) is \( (\pi \simeq 3) \)

A closed organ pipe and an open organ pipe of same length produce 2 beats/second while vibrating in their fundamental modes. The length of the open organ pipe is halved and that of closed pipe is doubled. Then the number of beats produced per second while vibrating in the fundamental mode is

Two capacitors of \( 10 \mathrm{pF} \) and \( 20 \mathrm{pF} \) are connected to \( 200 \mathrm{~V} \) and \( 100 \mathrm{~V} \) sources respectively. If
they are connected by the wire, what is the common potential of the capacitors ?

Light of wavelength \( 600 \mathrm{~nm} \) is incident normally on a slit of width \( 0.2 \mathrm{~mm} \). The angular width of
central maxima in the diffraction pattern is (measured from minimum to minimum)

If the refractive index from air to glass is \(\frac{3}{2}\) and that from air to water is \(\frac{4}{3}\), then the ratio of focal lengths of a glass lens in water and in air is

Match List-I with List-II for the following reaction pattern
Glucose \(\xrightarrow{\text { Reagent }}\) Product \(\longrightarrow\) Structural prediction
\begin{array}{|l|l|l|l|}\hline & \text{List - I (Reagents)} & & \text{List-II (Structural prediction)} \\\hline \text{a}. & \text{Acetic anhydride} & \text{(i)} & \text{Glucose has an aldehyde group} \\\hline \text{b.} & \text{Bromine water} & \text{(ii)} & \text{Glucose has a straight chain of six carbon atoms} \\\hline \text{c.} & \text{Hydroiodic acid} & \text{(iii)} & \text{Glucose has five hydroxyl group} \\\hline \text{d.} & \text{Hydrogen cyanide} & \text{(iv)} & \text{Glucose has a carbonyl group} \\\hline\end{array}

Choose the correct answer from the options given below.

PCR is used for

Find the correct match.

If \(A_n=\left[\begin{array}{cc}1-n & n \\ n & 1-n\end{array}\right]\), then \(\left|A_1\right|+\left|A_2\right|+\ldots\left|A_{2021}\right|=\)

If \(A=\left[\begin{array}{ll}1 & 2 \\ 3 & 4\end{array}\right]\), then \(\mathrm{A}^{-1}\) is equal to

You are given a dipole of charge \(+q\) and \(-q\) separated by a distance 2R. A sphere 'A' of radius ' \(R\) ' passes through the centre of the dipole as shown below and another sphere ' \(B\) ' of radius ' \(2 R\) ' passes through the charge +q . Then the electric flux through the sphere \(A\) is