The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea \((7.8\, mm)\). This surface separates two media of refractive indices \(1\) and \(1.34\). Calculate the distance from the refracting surface at which a parallel beam of light will come to focus.......\(cm\)

Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to \(A\) and \(T,\)  respectively. At time \(t=0\) one particle has displacement \(A\) while the other one has displacement \(\frac {-A}{2}\) and they are moving towards each other. If they cross each other at time \(t,\) then \(t\) is

A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities \(\rho_1\) and \(\rho_{2^{\prime}}\), respectively. The frequency of \(9^{\text {th }}\) harmonic of closed tube is identical with \(4^{\text {th }}\) harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is \(\rho_1: \rho_2=1: 16\), then the length of the open tube is :

For a nucleus \({ }_Z^A X\) having mass number \(A\) and atomic number \(Z\) \(A.\) The surface energy per nucleon \(\left(b_s\right)=a_1 A^{2 / 3}\) \(B.\) The Coulomb contribution to the binding energy \(b_c=-a_2 \frac{Z(Z-1)}{A^{4 / 3}}\) \(C.\) The volume energy \(b_v=a_3 A\) \(D.\) Decrease in the binding energy is proportional to surface area. \(E.\) While estimating the surface energy, it is assumed that each nucleon interacts with \(12\) nucleons, \(\left(a_1, a_2\right.\) and \(a _3\) are constants) Choose the most appropriate answer from the options given below:

A current of \(6\, A\) enters one corner \(P\) of an equilateral triangle \(PQR\) having \(3\) wires of resistance \(2 \,\Omega\) each and leaves by the corner \(R\). The currents \(i_{1}\) in ampere is ........ .

A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\)

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

An \(n.p.n\) transistor with current gain \(\beta=100\) in common emitter configuration is shown in figure. The output voltage of the amplifier will be\(.....V\)

A mirror is used to produce an image with magnification of \(\frac{1}{4}\). If the distance between object and its image is 40 cm , then the focal length of the mirror is ________

A displacement current of \(4.0\) A can be set up in the space between two parallel plates of \(6\) \(\mu\)F capacitor. The rate of change of potential difference across the plates of the capacitor is nearly \(\alpha \times 10^6\) V/s. The value of \(\alpha\) is __________.

If \({E}\) and \({H}\) represents the intensity of electric field and magnetising field respectively, then the unit of \(E/H\) will be :

A helicopter flying horizontally with a speed of \(360 \mathrm{~km} / \mathrm{h}\) at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is :
(use acceleration due to gravity \(\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\) and neglect air resistance)