A spring of spring constant \(200 \mathrm{Nm}^{-1}\) is initially stretched by 10 cm from the unstretched position. The work to be done to stretch the spring further by another 10 cm is

Assertion (A) : It is more difficult to push a magnet into a coil with more number of turns.

Reason (R) : The emf induced in a coil opposes the motion of a magnet when it is moved towards the coil.

A carrier wave of peak voltage \(60 \mathrm{~V}\) is used to transmit a message signal. Then the peak voltage of the modulating signal in order to have a modulation index of \(90 \%\) is

One mole of a gas having \(\gamma=\frac{7}{5}\) is mixed with one mole of a gas having \(\gamma=\frac{4}{3}\) The value of \(\gamma\) for the mixture is ( \(\gamma\) is the ratio of the specific heats of the gas)

At a given instant of time two particles are having the position vectors \(4 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}+57 \hat{\mathbf{k}}\) metres and \(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) respectively. If the velocity of the first particle be \(0.4 \hat{\mathbf{i}} \mathrm{ms}^{-1}\), the velocity of second particle in metre per second if they collide after \(10 \mathrm{sec}\) is

The ratio of radii of two wires is \(1: 2\) and the density of their materials are in the ratio \(1: 4\). If same tension is applied to both the wires then the ratio of the speed of transverse waves produced in them is

\(\mathrm{AU}^{235}\) nuclear reactor generates energy at a rate of \(3.70 \times 10^7 \mathrm{~J} / \mathrm{s}\). Each fission liberates \(185 \mathrm{MeV}\) useful energy. If the reactor has to operate for \(144 \times 10^4 \mathrm{~s}\), then, the mass of the fuel needed is (Assume Avogadro's number \(\left.=6 \times 10^{23} \mathrm{~mol}^{-1}, 1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}\right)\)

A mass of $1 \mathrm{kg}$ falls from a height of $1 \mathrm{m}$ and lands on a mass less platform supported by a spring having spring constant $15 \mathrm{N} {\mathrm{m}}^{-1}$ as shown in the figure. The maximum compression of the spring is.
(acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

From the following data at \(25^{\circ} \mathrm{C}\), calculate the \(\Delta_{\mathrm{r}} \mathrm{H}^0\) for \(\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow 2 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g})\)
reaction: \(\Delta_{\mathrm{r}} \mathrm{H}^0\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)\)
\[
\begin{array}{ll}
\frac{1}{2} \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{OH}(\mathrm{g}) & 42.09 \\
\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g}) & -242 \\
\mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g}) & 436 \\
\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{O}(\mathrm{g}) & 496
\end{array}
\]

\((1+\sqrt{3} i)^6-(\sqrt{3}+i)^6=\)

\(A B C D\) is a square with side 16 units and \(A\) is the origin. If the equation of the circle circumscribing the square \(A B C D\) is \(x^2+y^2=4 k(x+y)\), then \(k=\)

\(\int \frac{3 e^x-7 e^{-x}}{7 e^x+3 e^{-x}} d x=K x+L \log \left(e^{-2 x}+\frac{7}{3}\right)+C\)
then \(K+L=\)

The number of significant figures in the simplification of \(\frac{0.501}{0.05}(0.312-0.03)\) is