A diatomic gas has an initial internal energy of \(80 \mathrm{cal}\). A work of \(18 \mathrm{cal}\) is done on the gas and the gas releases heat energy of \(42 \mathrm{~J}\). The final internal energy of the gas is

The self-inductance of a coil is \(50 \mathrm{mH}\). When a current of 1 A passing through the coil, reduces to zero at a steady rate in \(0.1 \mathrm{~s}\), then find the self-induced emf.

A charge \(q\) is spread uniformly over an isolated ring of radius \(R\). The ring is rotated about its natural axis with an angular velocity \(\omega\). Magnetic dipole moment of the ring is

A \(4 \mu \mathrm{F}\) capacitor is charged by a \(200 \mathrm{~V}\) battery. It is then disconnected from the supply and is connected to another uncharged \(2 \mu \mathrm{F}\) capacitor. During the process, loss of energy (in \(\mathrm{J}\) ) is

An achromatic combination of lenses produces

The radiation of energy ' \(E\) ' falls normally on a perfectly reflecting surface. The momentum transferred to the surface is

A body cools down from \(52.5^{\circ} \mathrm{C}\) to \(47.5^{\circ} \mathrm{C}\) in \(5 \mathrm{~min}\) and from \(47.5^{\circ} \mathrm{C}\) to \(42.5^{\circ} \mathrm{C}\) in \(7.5 \mathrm{~min}\). Then, the temperature of the surroundings is

If \(\mathrm{A}(1,2,3), \mathrm{B}(2,3,-1), \mathrm{C}(3,-1,-2)\) are the vertices of a triangle ABC, then the direction ratios of the bisector of \(\triangle \mathrm{ABC}\) are

The set of all real values of \(x\) such that \(f(x)=\sqrt{\frac{[x]-1}{[x]^2-[x]-6}}\) is a real valued function is

A spring of spring constant \(200 \mathrm{Nm}^{-1}\) is initially stretched by 10 cm from the unstretched position. The work to be done to stretch the spring further by another 10 cm is

The angle between the straight lines represented by \(\left(x^2+y^2\right) \sin ^2 \alpha=(x \cos \alpha-y \sin \alpha)^2\) is

Which of the following reactions are not feasible?
I. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CH}_2 \frac{\mathrm{HCl}}{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2} \longrightarrow \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl}\)
II. \(\mathrm{C}_6 \mathrm{H}_6+\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{Cl} \stackrel{\mathrm{AlCl}_3}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}\left(\mathrm{CH}_3\right)_2\)
III. \(\mathrm{CH}_3 \mathrm{CHClCH}_2 \mathrm{Cl} \underset{\Delta}{\stackrel{\mathrm{KOH}}{\longrightarrow}} \mathrm{CH}_3 \mathrm{C} \equiv \stackrel{+}{\mathrm{CH}}\)
IV. \(\mathrm{CH}_3 \mathrm{CH}=\mathrm{CHCH}_3 \stackrel{\mathrm{KMnO}_4 / \mathrm{H}^{+}}{\longrightarrow} \mathrm{CH}_3 \mathrm{COOH}\)

Let \(\overrightarrow{\mathrm{a}}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}\) and \(\overrightarrow{\mathrm{b}}=\hat{\mathrm{i}}-2 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}\) be two vectors. If \(A_1\) is the area of the quadrilateral having \(\vec{a}, \vec{b}\) as its diagonals and \(A_2\) is the area of the parallelogram having \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) as its two adjacent sides, then \(\mathrm{A}_1 \cdot \mathrm{A}_2=\)