\(27\) identical drops are charged at \(22\, V\,\,each.\) They combine to form a bigger drop. The potential of the bigger drop will be............ \(V.\)

In a metre-bridge when a resistance in the left gap is \(2\ \Omega\) and unknown resistance in the right gap, the balance length is found to be \(40\ \mathrm{cm}\). On shunting the unknown resistance with \(2\ \Omega\), the balance length changes by _______.

A sinusoidal voltage of peak value \(283\, V\) and angular frequency \(320/s\) is applied to a series \(LCR\) circuit. Given that \(R\, = 5\,\Omega \) , \(L\,= 25\, mH\) and \(C\, = 1000\, \mu F\). The total impedance, and phase difference between the voltage across the source and the current will respectively be

A hydrogen atom changes its state from \(n=3\) to \(\mathrm{n}=2\). Due to recoil, the percentage change in the wave length of emitted light is approximately \(1 \times 10^{-\mathrm{n}}\). The value of \(\mathrm{n}\) is _______. [Given \(\mathrm{Rhc}=13.6 \mathrm{eV}, \mathrm{hc}=1242 \mathrm{eV} \mathrm{nm}\), \(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}\), mass of the hydrogen atom \(\left.=1.6 \times 10^{-27} \mathrm{~kg}\right]\)

Consider a light ray travelling in air is incident into a medium of refractive index \(\sqrt{2 n}\). The incident angle is twice that of refracting angle. Then, the angle of incidence will be

In a Vernier Calipers. \(10\) divisions of Vernier scale is equal to the \(9\) divisions of main scale. When both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of \(zero\) of the main scale and \(4^{\text {th }}\) Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to \(1\,mm\). While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between \(30\) and \(31\) divisions of main scale reading and \(6^{\text {th }}\) Vernier scale division exactly. coincides with the main scale reading. The diameter of the spherical body will be \(.......cm\)

The magnetic field of a plane electromagnetic wave is given by \(\overrightarrow{ B }=2 \times 10^{-8} \sin \left(0.5 \times 10^{3} x +1.5 \times 10^{11} t \right) \hat{ j } T\) The amplitude of the electric field would be.

Bag \(B_1\) contains 6 white and 4 blue balls, Bag \(B_2\) contains 4 white and 6 blue balls, and Bag \(B_3\) contains 5 white and 5 blue balls. One of the bags is selected at random and a ball is drawn from it. If the ball is white, then the probability, that the ball is drawn from Bag \(B_2\), is :

Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

Let \( S=\{(m,n): m, n\in\{1,2,3,.....,50\}\} \). If the number of elements (m, n) in S such that \( 6^{m}+9^{n} \) is a multiple of 5 is p and the number of elements (m, n) in S such that \( m+n \) is a square of a prime number is q, then \( p+q \) is equal to :

A deviation of \(2^{\circ}\) is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are \(0.02\) and \(0.03\) respectively and refractive index for yellow light for these glasses are \(1.5\) and \(1.6\) respectively. The refracting angles for crown glass prism will be \(........\,^{\circ}\) (in degree) (Round off to the Nearest Integer)

Two closed vessels of same volume are joined through a narrow tube and both vessels are filled with air of pressure \(90\) kPa and temperature \(400\) K. Keeping the temperature of one vessel constant at \(400\) K the second vessel temperature is raised to \(500\) K. The final pressure in the vessels is _______ kPa.

A projectile fired at \(30^{\circ}\) to the ground is observed to be at same height at time \(3 s\) and \(5 s\) after projection, during its flight. The speed of projection of the projectile is \(.........\,ms ^{-1}\)(Given \(g=10\,m s ^{-2}\) )