As per given figure \(A , B\) and \(C\) are the first, second and third excited energy level of hydrogen atom respectively. If the ratio of the two wavelengths \(\left(\right.\) i.e. \(\left.\frac{\lambda_1}{\lambda_2}\right)\) is \(\frac{7}{4 n}\), then the value of \(n\) will be

In a scries \(LCR\) resonance circuit, if we change the resistance only, from a lower to higher value

The position vector of the centre of mass \(\vec r\, cm\) of an asymmetric uniform bar of negligible area of cross-section as shown in figure is

Small water droplets of radius \(0.01 \mathrm{~mm}\) are formed in the upper atmosphere and falling with a terminal velocity of \(10 \mathrm{~cm} / \mathrm{s}\). Due to condensation, if \(8 \mathrm{such}\) droplets are coalesced and formed a larger drop, the new terminal velocity will be _______ \(\mathrm{cm} / \mathrm{s}\).

At room temperature \(\left(27^{\circ} \mathrm{C}\right)\), the resistance of a heating element is \(50 \Omega\). The temperature coefficient of the material is \(2.4 \times 10^{-4}{ }^{\circ} \mathrm{C}^1\). The temperature of the element, when its resistance is \(62 \Omega\) is _______ \({ }^{\circ} \mathrm{C}\).

A wire of length \(L\) and radius \(r\) is clamped rigidly at one end. When the other end of the wire is pulled by a force \(f\), its length increases by \(l\). Another wire of same material of length \(2 L\) and radius \(2 r\) is pulled by a force \(2 f\). Then the increase in its length will be

In an experiment to measure the focal length ( \(f\) ) of a convex lens, the magnitude of object distance \((x)\) and the image distance \((y)\) are measured with reference to the focal point of the lens. The \(y-x\) plot is shown in figure. The focal length of the lens is _______ \(\mathrm{cm}\).

A hole is drilled in a metal sheet. At \(27^{\circ} C\), the diameter of hole is 5 cm . When the sheet is heated to \(177^{\circ} C\), the change in the diameter of hole is \(d \times 10^{-3} cm\). The value of \(d\) will be ________ , if coefficient of linear expansion of the metal is \(1.6 \times 10^{-5} /{ }^{\circ} C\)

Two masses \(m\) and \(\frac{m}{2}\) are connected at the two ends of a massless rigid rod of length \(l\). The rod is suspended by a thin wire of torsional constant \(k\) at the centre of mass of the rodmass system (see figure). Because of torsional constant \(k\), the restoring torque is \(\tau  = k\,\theta \) for angular displacement \(\theta \). If the rod is rotated by \(\theta _0\) and released, the tension in it when it passes through its mean position will be

The current flowing through \(R _2\) is:

The helium and argon are put in the flask at the same room temperature ( 300 K). The ratio of average kinetic energies (per molecule) of helium and argon is :
(Give : Molar mass of helium \(=4 \mathrm{~g} / \mathrm{mol}\), Molar mass of argon \(=40 \mathrm{~g} / \mathrm{mol}\))

Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is

A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is \(\frac{4}{3}\),  and the diver's eyes are \(15\, cm\) below the surface of water. Then the radius of the circle is