The electric potential at the surface of an atomic nucleus \((Z=50)\) of radius \(9 \times 10^{-15} \mathrm{~m}\) is

A tension of \(22 \mathrm{~N}\) is applied to a copper wire of cross-sectional area \(0.02 \mathrm{~cm}^2\) Young's modulus of copper is \(1.1 \times 10^{11} \mathrm{~N} / \mathrm{m}^2\) and Poisson's ratio 0.32 . The decrease in cross-sectional area will be

The first law of thermodynamics confirms the law of _____

Two cells \(A\) and. \(B\) are connected in the secondary circuit of a potentiometer one at a time and the balancing length are respectively \(400 \mathrm{~cm}\) and \(440 \mathrm{~cm}\). The emf of the cell \(A\) is 1.08 volt. The emf of the second cell \(B\) in volts is

A block of mass \(50 \mathrm{~kg}\) is pulled with a constant speed of \(4 \mathrm{~ms}^{-1}\) across a horizontal floor by an applied force of \(500 \mathrm{~N}\) directed \(30^{\circ}\) above the horizontal. The rate at which the force does work on the block in watt is

If the voltage and current in an ac circuit are respectively \(50 \sin (50 t) V\) and \(50 \sin \left(50 \mathrm{t}+\frac{\pi}{4}\right) \mathrm{mA}\), then the power dissipated in the circuit is nearly

When an inductor of inductance \(\frac{6}{\pi} \mathrm{H}\), a capacitor of capacitance \(\frac{50}{\pi} \mu \mathrm{F}\) and resistor of resistance \(R\) are connected in series with an AC supply of rms voltage \(220 \mathrm{~V}\) and frequency \(50 \mathrm{~Hz}\), the rms current through the circuit is \(440 \mathrm{~mA}\). Match the inductive reactance, \(X_L\) the capacitive reactance, \(X_C\) the resistance \(R\) and the impedance \(Z\) of the circuit given in List-I with the corresponding values given in List-II.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)

Which acid among the following has the highest \(\mathrm{p} K_a\) value?

If the straight line $x\cos \alpha +y\sin \alpha =p$ touches the curve ${\left(\frac{x}{a}\right)}^n+{\left(\frac{y}{b}\right)}^n=2$ at the point $\left(a,b\right)$ on it and $\frac{1}{a^2}+\frac{1}{b^2}=\frac{k}{p^2}$ then $k=$

In which of the following pairs the polymer is correctly matched with the forces possessed by them.
A. Neoprene --- Weak intermolecular forces
B. Terylene --- Hydrogen bonding
C. Polystyrene ---- Very weak intermolecular forces
D. Polythene --- Hydrogen bonding

Arrange the following in increasing order of acidic charater.

Which among the following species acts as a self-indicator?

Two balls each of mass 250 g moving in opposite directions each with a speed \(16 \mathrm{~m} \mathrm{~s}^{-1}\) collide and rebound with the same speeds. The impulse imparted to one ball due to the other is