The dimensional formula of latent heat is _______.

A solid sphere of mass ' \(m\) ' and radius ' \(r\) ' is allowed to roll without slipping from the highest point of an inclined plane of length ' \(L\) ' and makes an angle \(30^{\circ}\) with the horizontal. The speed of the particle at the bottom of the plane is \(v_1\). If the angle of inclination is increased to \(45^{\circ}\) while keeping \(L\) constant. Then the new speed of the sphere at the bottom of the plane is \(v_2\). The ratio \(v_1^2: v_2^2\) is:

A coil of cross-sectional area  \(A\) having \(n\)  turns is placed in a uniform magnetic field \(B.\)  When it is rotated with an angular velocity \(\omega ,\)  the maximum \(e.m.f.\)  induced in the coil will be

The plot given below is of the average power delivered to an \(LRC\) circuit versus frequency. The quality factor of the circuit is

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is \(25 \%\) of the velocity of light, then the ratio of \(K.E.\) of electron and \(K.E.\) of photon will be:

Light from a point source in air falls on a convex curved surface of radius \(20 \mathrm{~cm}\) and refractive index \(1.5.\) If the source is located at \(100 \mathrm{~cm}\) from the convex surface, the image will be formed at _______ \(\mathrm{cm}\) from the object.

A body travels \(102.5 \mathrm{~m}\) in \(\mathrm{n}^{\text {th }}\) second and \(115.0 \mathrm{~m}\) in \((n+2)^{\text {th }}\) second. The acceleration is what?

Identify the logic operation carried out by the given circuit :-

An electric dipole of moment \(\overrightarrow{\mathrm{p}}=(-\hat{\mathrm{i}}-3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times 10^{-29}\; \mathrm{C} \cdot \mathrm{m}\) is at the origin \((0,0,0) .\) The electric field due to this dipole at \(\overrightarrow{\mathrm{r}}=+\hat{\mathrm{i}}+3 \hat{\mathrm{j}}+5 \hat{\mathrm{k}}\) (note that \(\overrightarrow{\mathrm{r}} \cdot \overrightarrow{\mathrm{p}}=0)\) is parallel to

A uniform sphere of mass \(500\; g\) rolls without slipping on a plane horizontal surface with its centre moving at a speed of \(5.00\; \mathrm{cm} / \mathrm{s}\). Its kinetic energy is

A \(16\  \Omega\) wire is bend to form a square loop. A \(9 \mathrm{~V}\) battery with internal resistance \(1\  \Omega\) is connected across one of its sides. If a \(4\  \mu \mathrm{F}\) capacitor is connected across one of its diagonals, the energy stored by the capacitor will be \(\frac{x}{2} \ \mu \mathrm{J}\). where \(x=\) ________.