A wire of length 1m has a resistance of \(20\ \Omega\) at \(0^\circ\)C. It is uniformly stretched so that its length increases by 21%. Assuming the volume of the wire remains constant, the percentage change in resistance is \(n\%\). Alternatively, if the wire is heated [without stretching] through a temperature of \(27^\circ\) C and if the temperature coefficient of resistance of the material of wire is \(0.004K^{-1}\), the percentage change in resistance is \(m\%\). The values of \(m\) and \(n\) are:

The energy equivalent of \(1 \mathrm{~g}\) of a substance is

A shell of mass \(20 \mathrm{~g}\) is fired by a gun of mass \(100 \mathrm{~kg}\). If the shell leaves the gun with a speed of \(80 \mathrm{~ms}^{-1}\), then the speed of recoil of the gun is

A balloon with mass \(m\) is descending down with an acceleration \(a\) (where, \(a < g\) ). How much mass should be removed from it so that it starts moving up with an acceleration \(a\) ?

Which physical quantity has the unit joule / tesla?

A compound slab is made of two parallel plates of copper and brass of the same thickness and having thermal conductivities in the ratio \(4: 1\). The free face of copper is at \(0^{\circ} \mathrm{C}\). The temperature of the interface is \(20^{\circ} \mathrm{C}\). What is the temperature of the free face of brass?

A metallic rod of \(2 \mathrm{~m}\) length is rotated with a frequency \(100 \mathrm{~Hz}\) about an axis passing through the centre of the circular ring of radius \(2 \mathrm{~m}\). A constant magnetic field \(2 \mathrm{~T}\) is applied parallel to the axis and perpendicular to the length of the rod. The emf developed across the ends of the rod is :

Identify the incorrect statement among the following.

\(\lim _\limits{x \rightarrow 0} \dfrac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}\) equals to

A galvanometer of resistance \(50 \Omega\) is connected to a battery of 4 V along with a resistance of \(3950 \Omega\) in series. A full-scale deflection of 30 divisions is obtained in the galvanometer. In order to reduce this deflection to 10 divisions, the resistance in series should be equal to:

The maximum value of \(x+y\) subject to \(2 x+3 y \leq 6, x \geq 0, y \geq 0\) is

If the equation of pair of lines \(y=m_1 x\) and \(y=m_2 x\) can be written as \(\left(y-m_1 x\right)\) \(\left(y-m_2 x\right)=0\). Then the equation of pair of the angle bisector of the lines \(5 x^2+2 x y+3 y^2=0\) is

Match the reaction in Column I with the major product formed given in Column II.
\(\begin{array}{|l|l|l|} \hline & \text { Column I- Reaction/conditions } & & \text { Column II- Product } \\ \hline A & \mathrm{C}_6 \mathrm{H}_6 \xrightarrow[\substack{\text{(ii) NaOH} \\ \text{(iii) H^+}}]{\text{(i) Oleum}} & P & \text { Pentan-2-ol. } \\ \hline B & \text{Butanal } \xrightarrow[\text{(ii) } \mathrm{H}^+]{\text{(i) } \text{MeMgBr/ dry ether}} & Q & \text { 2-Hydroxybenzoic acid. } \\ \hline C & \text {2-Methylpropene } \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}_2 / \mathrm{NaOH}]{\text { (i) } \mathrm{B}_2 \mathrm{H}_6} & R & \text { Phenol } \\ \hline D & \text{Phenol } \xrightarrow[\text { (ii) } \mathrm{CO}_2, 400 \mathrm{~K}, 7 \mathrm{~atm} .]{\text { (i) } \mathrm{NaOH}} & S & \text { 2-Methylpropan-1-0 I } \\ \hline \end{array}\)