A metallic ring of radius \(r\) and cross sectional area \(A\) is fitted into a wooden circular disc of radius \(R(R>r)\). If the Young's modulus of the material of the ring is \(Y\), the force with which the metal ring expands is

A cell of emf 1.2 V and internal resistance \(2 \Omega\) is connected in parallel to another cell of emf 1.5 V and internal resistance \(1 \Omega\). If the like poles of the cells are connected together, the emf of the combination of the two cells is

A resistance \(R\) is connected to ' \(n\) ' identical cells. If the current in the resistance is same whether the cells are connected either in series or in parallel, then the internal resistance (r) of each cell is

A steel ball of mass \(200 \mathrm{~g}\) falls freely from a height of 20 \(\mathrm{m}\) and bounces to a height of \(10.8 \mathrm{~m}\) from the ground. If the energy lost in this process is absorbed by the ball, the rise in its temperature is ( \(\mathrm{g}=10 \mathrm{~ms}^{-2}\), specific heat capacity of steel is \(460 \mathrm{Jkg}^{-1} \mathrm{~K}^{-1}\) )

The acceleration of a particle executing SHM is

A particle of mass \(m\) is under an influence of a force \(\mathbf{F}=\left(-k \mathbf{x}+\mathbf{F}_0\right) \mathrm{N}\). The particle when disturbed will oscillate

A point charge \(q\) is placed at origin. Let \(\mathbf{E}_{A^{\prime}} \mathbf{E}_B\) and \(\mathbf{E}_C\) be the electric fields at three points \(A\) \((1,2,3), B(1,1,-1)\) and \(C(2,2,2)\) respectively due to the charge \(q\). Then, the relation between them is
1. \(\mathbf{E}_A \perp \mathbf{E}_B\)
2. \(\mathbf{E}_A \| \mathbf{E}_C\)
3. \(\left|\mathbf{E}_B\right|=4\left|\mathbf{E}_C\right|\)
4. \(\left|\mathbf{E}_B\right|=8\left|\mathbf{E}_C\right|\)

Hot concentrated sulphuric acid on reaction with which one of the following elements, produces two gaseous products?

At 300 K vapour pressure of a pure liquid, 'A' is 70 mm Hg. It forms an ideal solution with another liquid ' B '. The mole fraction of B in the solution is 0.2 and total vapour pressure of solution is 84 mm Hg at same temperature. What is the vapour pressure \((\mathrm{in} \mathrm{mm})\) of pure liquid B at 300 K ?

The ionization potential of hydrogen atom is $13.6 \mathrm{V}$. How much energy need to be supplied to ionize the hydrogen atom in the first excited state.

If the perpendicular distance from the focus of a parabola \(\mathrm{y}^2=4 \mathrm{ax}\) to its directrix is \(\frac{3}{2}\), then the equation of the normal drawn at \((4 a,-4 a)\) is

If \(1, \omega, \omega^2\) denote the cube roots of unity, then the value of \(\left(1-\omega+\omega^2\right)^5+\left(1+\omega-\omega^2\right)^5\) is

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.
\(\begin{array}{llll} \hline & \text { List- I } & & \text { List- II } \\ \hline \text {(A) } & X_L & \text { (i) } & 200 \Omega \\ \hline \text {(B) } & X_C & \text { (ii) } & 300 \Omega \\ \hline \text {(C) } & R & \text { (iii) } & 500 \Omega \\ \hline \text {(D) } & Z & \text { (iv) } & 600 \Omega \\ \hline \end{array}\)