A particle is executing simple harmonic motion with an amplitude \(A\) and time period \(T\). The displacement of the particles after \(2 T\) period from its initial position is

If a slit of width ' \(x\) ' was illuminated by red light having wavelength \(6500 Å\), the first minima was obtained at \(\theta=30^{\circ}\). Then the value of ' \(x\) ' is

Two charges \(2 \mathrm{C}\) and \(6 \mathrm{C}\) are separated by a finite distance. If a charge of \(-4 \mathrm{C}\) is added to each of them, the initial force of \(12 \times 10^3 \mathrm{~N}\) will change to

A wire of length 0.5 m and area of cross-section \(4 \times 10^{-6} \mathrm{~m}^2\) at a temperature of \(100^{\circ} \mathrm{C}\) is suspended vertically by fixing its upper end to the ceiling. The wire is then cooled to \(0^{\circ} \mathrm{C}\), but is prevented from contracting, by attaching a mass at the lower end. If the mass of the wire is negligible, then the value of the mass attached to the wire is
[Young's modulus of material of the wire \(=10^{11} \mathrm{~N} \mathrm{~m}^{-2}\); coefficient of linear expansion of the material of the wire \(=10^{-5} \mathrm{~K}^{-1}\) and acceleration due to gravity \(\left.=10 \mathrm{~m} \mathrm{~s}^{-2}\right]\)

If equal masses of 10 liquids of specific heats \(\mathrm{s}, 2 \mathrm{~s}, 3 \mathrm{~s}, \ldots \ldots \ldots 10 \mathrm{~s}\) at temperatures \(10^{\circ} \mathrm{C}, 20^{\circ} \mathrm{C}, 30^{\circ} \mathrm{C}, \ldots \ldots 100^{\circ} \mathrm{C}\) respectively are mixed, the resultant temperature of the mixture is _________ .

The reactance of an inductor at \(50 \mathrm{~Hz}\) is \(10 \Omega\). The reactance of it at \(200 \mathrm{~Hz}\) is

As shown in the figure, two infinitely long straight parallel wires \(P\) and \(Q\) carrying equal currents in opposite directions are arranged parallel to \(\mathrm{Y}\)-axis. If the magnetic field due to wire \(\mathrm{P}\) at the origin ' \(\mathrm{O}\) ' of the co-ordinate system is B, then match the resultant magnetic fields at various points given in column \(A\) with the points given in column \(B\).
\(\begin{array}{ll}
\text{Column A} & \text{Column B} \\
\text{A)} \frac{B}{4} & \text{i)} (0,0) \\
\text{B)} \frac{B}{2} & \text{ii)} (a, 0) \\
\text{C)} \frac{2 \mathrm{~B}}{3} & \text{iii)} (2a, 0) \\
\text{D)} 2 \mathrm{~B} & \text{iv)} (3 \mathrm{a}, 0) \\
\end{array}\)


The correct answer is

The mean deviation from the median for the following data is

\(x_i\)	\(9\)	\(3\)	\(7\)	\(2\)	\(5\)
\(f_i\)	\(1\)	\(6\)	\(2\)	\(8\)	\(4\)

\(\frac{1}{4}-\frac{5}{4 \cdot 8}+\frac{5 \cdot 7}{4 \cdot 8 \cdot 12}-\ldots=\)

The horizontal and vertical displacements of a projectile at time \(t\) are \(x=36 t\) and \(y=48 t-4.9 t^2\), respectively. Initial velocity of the projectile in \(\mathrm{m} / \mathrm{s}\) is

If the coefficients of variation of two distributions are 60 and 70 and their standard deviations are 21 and 16 respectively, then their arithmetic means are respectively

Two particles having position vectors \(\mathbf{r}_1=(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}})\) metres and \(\mathbf{r}_2=(-5 \hat{\mathbf{i}}-3 \hat{\mathbf{j}})\) metres are moving with velocities \(\mathbf{v}_1=(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}\) and \(\mathbf{v}_2=(a \hat{\mathbf{i}}+7 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}\). If they collide after \(2 \mathrm{~s}\), then the value of \(a\) is :

The most probable speed \(\left(\mathrm{u}_{\mathrm{mp}}\right)\) of 8 g of \(\mathrm{H}_2\) is \(2 \times 10^2 \mathrm{~ms}^{-1}\). The kinetic energy (in J) of same amount of \(\mathrm{H}_2\) gas is