A light ray is incident, at an incident angle \(\theta_{1}\), on the system of two plane mirrors \(M_{1}\) and \(M_{2}\) having an inclination angle \(75^{\circ}\) between them (as shown in figure). After reflecting from mirror \(M_{1}\) it gets reflected back by the mirror \(M _{2}\) with an angle of reflection \(30^{\circ}\). The total deviation of the ray will be \(\dots\) degree.

Two iron solid discs of negligible thickness have radius \(R_1\) and \(R_2\) and moment of intertia \(I_1\) and \(I_2\), respectively. For \(R_2=2 R_1\), the ratio of \(I_1\) and \(I_2\) would be \(1 / x\), where \(\mathrm{x}=\) ________ -

Two balls \(A\) and \(B\) are placed at the top of \(180 \,m\) tall tower. Ball \(A\) is released from the top at \(t =0 \,s\). Ball \(B\) is thrown vertically down with an initial velocity \(u\)' at \(t=2\, s\). After a certain time, both balls meet \(100 \,m\) above the ground. Find the value of \(u\) in ............... \(ms ^{-1}\). [use \(g =10 \,ms ^{-2}\) ]

An electron of mass m with an initial velocity \(\overrightarrow{ V }= V_0 \hat i \,(V_0 > 0)\) enters an electric field \(\vec E = -\vec E_0 \hat i \,(E_0 =\) constant \(> 0)\) at \(t = 0.\) If \(\lambda_0\) is its de-Broglie wavelength initially,then its de-Broglie wavelenght at time \(t\) is

A mixture of hydrogen and oxygen has volume \(2000 \; cm ^{3}\), temperature \(300 \; K\), pressure \(100 \; kPa\) and mass \(0.76 \; g\) The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be

In a building there are \(15\) bulbs of \(45\; \mathrm{W}, 15\) bulbs of \(100\; \mathrm{W}, 15\) small fans of \(10 \;\mathrm{W}\) and \(2\) heaters of \(1 \;\mathrm{kW}\). The voltage of electric main is \(220\; \mathrm{V}\). The minimum fuse capacity (rated value) of the building will be: .......... \(A\)

As shown in the figure, a potentiometer wire of resistance \(20\,\Omega\) and length \(300\,cm\) is connected with resistance box (R.B.) and a standard cell of emf \(4\,V\). For a resistance ' \(R\) ' of resistance box introduced into the circuit, the null point for a cell of \(20\,mV\) is found to be \(60\,cm\). The value of ' \(R\) ' is \(.....\Omega\)

A dipole with two electric charges of \(2 \mu \mathrm{C}\) magnitude each, with separation distance \(0.5 \mu \mathrm{~m}\), is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by \(30^{\circ}\) from the axis, it tends to realign in the direction due to a torque. The value of torque is :

A flexible chain of mass \(m\) hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is \(30^{\circ}\). Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is _________ .

The reading of pressure metre attached with a closed pipe is \(4.5 \times 10^4 \mathrm{~N} / \mathrm{m}^2\). On opening the valve, water starts flowing and the reading of pressure metre falls to \(2.0 \times 10^4 \mathrm{~N} / \mathrm{m}^2\). The velocity of water is found to be \(\sqrt{\mathrm{V}} \mathrm{m} / \mathrm{s}\). The value of \(\mathrm{V}\) is__________