A parallel plate capacitor whose capacitance \(C\) is \(14\, pF\) is charged by a battery to a potential difference \(V =12\, V\) between its plates. The charging battery is now disconnected and a porcelin plate with \(k =7\) is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of \(..........pJ\). (Assume no friction)

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

Three charges \(Q, +q\) and \(+q\) are placed at the vertices of a right -angle isosceles triangle as shown below. The net electrostatic energy of the configuration is zero, if the value of \(Q\) is

For a uniformly charged ring of radius \(R\), the electric field on its axis has the largest magnitude at a distance \(h\) from its centre. Then value of \(h\) is

If the r.m.s. speed of chlorine molecule is \(490\,m / s\) at \(27^{\circ}\,C\), the r.m.s. speed of argon molecules at the same temperature will be \(......\,m/s\) (Atomic mass of argon \(=39.9\,u\), molecular mass of chlorine \(=70.9\,u )\)

A conical pendulum of length \(1\,m\) makes an angle \(\theta \, = 45^o\) w.r.t. \(Z-\) axis and moves in a circle in the \(XY\) plane.The radius of the circle is \(0.4\, m\) and its centre is vertically below \(O\). The speed of the pendulum, in its circular path, will be ..... \(m/s\) (Take \(g\, = 10\, ms^{-2}\))

A tube of length \(L\) is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is \(2 \mathrm{~m} / \mathrm{s}\), then velocity of water leaving the point (2) will be

The truth table for the circuit given in the fig is

The sum and product of the mean and variance of a binomial distribution are \(82.5\) and \(1350\) respectively. They the number of trials in the binomial distribution is.

The values of \(\mathrm{m}, \mathrm{n}\), for which the system of equations \( x+y+z=4 \) \( 2 x+5 y+5 z=17 \) \( x+2 y+m z=n\) has infinitely many solutions, satisfy the equation :

The \(V-I\) characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is

Consider the following two statements : Statement \(I\) : For any two non-zero complex numbers \(\mathrm{z}_1, \mathrm{z}_2\) \(\left(\left|z_1\right|+\left|z_2\right|\right)\left|\frac{z_1}{\left|z_1\right|}+\frac{z_2}{\left|z_2\right|}\right| \leq 2\left(\left|z_1\right|+\left|z_2\right|\right)\) and Statement \(II\) : If \(\mathrm{x}, \mathrm{y}, \mathrm{z}\) are three distinct complex numbers and a, b, c are three positive real numbers such that \(\frac{a}{|y-z|}=\frac{b}{|z-x|}=\frac{c}{|x-y|}\), then \(\frac{\mathrm{a}^2}{\mathrm{y}-\mathrm{z}}+\frac{\mathrm{b}^2}{\mathrm{z}-\mathrm{x}}+\frac{\mathrm{c}^2}{\mathrm{x}-\mathrm{y}}=1\) Between the above two statements,

An electrical power line, having a total resistance of \(2 \Omega\), delivers \(1 \,kW\) at \(220\, V\). The efficiency of the transmission line is approximately \(.......\%\)