A nucleus of mass \(M\) at rest splits into two parts having masses \(\frac{M^{\prime}}{3}\) and \(\frac{2 M^{\prime}}{3}\left(M^{\prime} < M\right)\). The ratio of de Broglie wavelength of two parts will be.

When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will be.

A parallel beam of monochromatic light of wavelength \(600 \mathrm{~nm}\) passes through single slit of \(0.4 \mathrm{~mm}\) width. Angular divergence corresponding to second order minima would be _______ \(\times 10^{-3} \mathrm{rad}\).

A student measures the time period of \(100\) oscillations of a simple pendulum four times. The data set is  \(90\;s\) ,\(91\;s \), \(95\;s\) and \(92\;s\). If the minimum division in the  measuring clock is \(1\;s\), then the reported mean time should be

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are :
\(\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2\) and \(\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}\). The free ends of rods A and B are maintained at \(400 \mathrm{~K}, 200 \mathrm{~K}\), respectively. The temperature of rods interface is ________ K, when equilibrium is established.

Two resistances are given as \(R _1=(10 \pm 0.5)\,\Omega\) and \(R_2=(15 \pm 0.5)\, \Omega\). The percentage error in the measurement of equivalent resistance when they are connected in parallel is

A force is applied to a steel wire ' \(A\) ', rigidly clamped at one end. As a result elongation in the wire is \(0.2\,mm\). If same force is applied to another steel wire ' \(B\) ' of double the length and a diameter \(2.4\) times that of the wire ' \(A\) ', the elongation in the wire ' \(B\) ' will be \(............\times 10^{-2}\,mm\) (wires having uniform circular cross sections)

A ball is thrown vertically upwards with a velocity of \(19.6\,ms ^{-1}\) from the top of a tower. The ball strikes the ground after \(6\,s\). The height from the ground up to which the ball can rise will be \(\left(\frac{ k }{5}\right) m .\) The value of \(k\) is ..... (use \(g =9.8\,m / s ^{2}\))

A butterfly is flying with a velocity \(4 \sqrt{2} \,{m} / {s}\) in North-East direction. Wind is slowly blowing at \(1\) \({m} / {s}\) from North to South. The resultant displacement of the butterfly in \(3\, seconds\) is \(....\,{m}.\)