The truth table for the circuit given in the fig is

Two long straight wires \(P\) and \(Q\) carrying equal current \(10\,A\) each were kept parallel to each other at \(5\,cm\) distance. Magnitude of magnetic force experienced by \(10\,cm\) length of wire \(P\) is \(F_1\). If distance between wires is halved and currents on them are doubled, force \(F_2\) on \(10\,cm\) length of wire \(P\) will be :

A \(1\) kg block subjected to two simultaneous forces \((2\hat{i} + 3\hat{j} + 4\hat{k})\) N and \((3\hat{i} - \hat{j} - 2\hat{k})\) N is moved a distance of \(25\) m along \((3\hat{i} - 4\hat{j})\) direction. The work done in this process is _____ J.

A stone tide to a string of length \(L\) is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed \(u\). The magnitude of change in its velocity, as it reaches a position where the string is horizontal, is \(\sqrt{ x \left( u ^{2}- gL \right)}\). The value of \(x\) is .............

The position of a particle moving on \(x\)-axis is given by \(x(t)=A \sin t+B \cos ^2 t+C t^2+D\), where \(t\) is time. The dimension of \(\frac{A B C}{D}\) is

Three containers \(\mathrm{C}_{1}, \mathrm{C}_{2}\) and \(\mathrm{C}_{3}\) have water at different temperatures. The table below shows the final temperature \(T\) when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) \(\begin{array}{|c|c|c|c|}\hline \mathrm{C_{1 }} & {\mathrm{C}_{2}} & {\mathrm{C}_{3}} & {\mathrm{T}} \\ \hline {1 l} & {2 l} & {-} & {60^{\circ} \mathrm{C}} \\ \hline {-} & {1 l} & {2 l} & {30^{\circ} \mathrm{C}} \\ \hline  {2 l} & {-} & {1 l} & {60^{\circ} \mathrm{C}} \\ \hline  {1 l} & {1 l} & {1 l} & {\theta} \\ \hline\end{array}\) The value of \(\theta\) (in \(^{\circ} \mathrm{C}\) to the nearest integer) is

Five persons \(P_1, P_2, P_3, P_4\) and \(P_5\) recorded object distance (u) and image distance (v) using same convex lens having power +5 D as \((25,96),(30,62)\), \((35,37),(45,35)\) and \((50,32)\) respectively. Identify correct statement

The number of points in the interval \([2, 4]\), at which the function \(f(x) = \left[x^2 - x - \dfrac{1}{2}\right]\), where \([\cdot]\) denotes the greatest integer function, is discontinuous, is _______.

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between \(A\) and \(B\) is \(.......\Omega\).

\(\operatorname{Lim}_{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}\) is equal to :

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

On the \(x-\)axis and a dsitance \(x\) from the origin, the gravitational field due to a mass distribution is given by \(\frac{A x}{\left(x^{2}+a^{2}\right)^{3 / 2}}\) in the \(x-\)direction. The magnitude of gravitational potential on the \(x-\)axis at a distance \(x,\) taking its value to be zero at infinity, is

If \(\int \frac{\cos x d x}{\sin ^{3} x\left(1+\sin ^{6} x\right)^{2 / 3}}=f(x)\left(1+\sin ^{6} x\right)^{1 / \lambda}+c\) where \(c\) is a constant of integration, then \(\lambda f\left(\frac{\pi}{3}\right)\) is equal to