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

A mass of \(50\,g\) of water in a closed vessel, with surroundings at a constant temperature takes \(2\, minutes\) to cool from \(30\,^oC\) to \(25\,^oC\). A mass of \(100\,g\) of another liquid in an identical vessel with identical surroundings takes the same time to cool from \(30\,^oC\) to \(25\,^o C\). The specific heat of the liquid is .......... \(kcal/kg\) (The water equivalent of the vessel is \(30\,g\).)

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 particle starts from origin at \(t=0\) with a velocity \(5 \hat{i} \mathrm{~m} / \mathrm{s}\) and moves in \(x-y\) plane under action of a force which produces a constant acceleration of \((3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2\). If the \(x\)-coordinate of the particle at that instant is \(84 \mathrm{~m}\), then the speed of the particle at this time is \(\sqrt{\alpha} \mathrm{m} / \mathrm{s}\). The value of \(\alpha\) is___________.

A ball is thrown vertically upward with an initial velocity of \(150\,m / s\). The ratio of velocity after \(3\,s\) and \(5\,s\) is \(\frac{x+1}{x}\). The value of \(x\) is \(...........\) Take \(\left(g=10\,m / s ^2\right)\)

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension \(70 \mathrm{dyn} / \mathrm{cm}\) and glass water contact angle \(\simeq 0^{\circ}\)) with \(30^{\circ}\) inclined with vertical. The length of water risen in the capillary is ________ cm.
\(\left(\right.\) Take \(\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\)

A long solenoid is formed by winding \(70\) turns \(cm ^{-1}\). If \(2.0\,A\) current flows, then the magnetic field produced inside the solenoid is \(.......\times 10^{-4}\,T\) \(\left(\mu_0=4 \pi \times 10^{-7}\,TmA ^{-1}\right)\)

The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \(\mathrm{h} / \sqrt{2 m E}\) The dimensional formula for Planck's constant is _______.

In the reported figure, heat energy absorbed by a system in going through a cyclic process is \(......\,\pi J\)

A clock has a continuously moving second's hand of \(0.1\, m\) length. The average acceleration of the tip of the hand (in units of \(ms ^{-2}\) ) is of the order of

Three rays of light, namely red (R), green (G) and blue (B) are incident on the face \(PQ\) of a right angled prism PQR as shown in figure. The refractive indices of the material of the prism for red, green and blue wavelength are \(1.27, 1.42\) and \(1.49\) respectively. The colour of the ray(s) emerging out of the face \(PR\) is:

Figure shows the circuit that contains three resistances (9 Ω each) and two inductors (4 mH each). The reading of ammeter at the moment switch K is turned ON, is__________ A.

The charge flowing in a conductor changes with time as \(Q ( t )=\alpha t -\beta t ^2+\gamma t ^3\). Where \(\alpha, \beta\) and \(\gamma\) are constants. Minimum value of current is :