This question has Statement \(-1\) and Statement \(-2\). Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement \(1\) : Very large size telescopes are reflecting telescopes instead of refracting telescopes. Statement \(2\) : It is easier to provide mechanical support to large size mirrors than large size lenses.

A thin rod of mass \(0.9\, kg\) and length \(1 \,m\) is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move \(0.1\, kg\) moving in a straight line with velocity \(80\,m / s\) hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in \(rad/s\)) of the rod immediately after the collision will be

A light wave is propagating with plane wave fronts of the type \(x+y+z=\) constant. The angle made by the direction of wave propagation with the \(x\)-axis is:

In a screw gauge, there are \(100\) divisions on the circular scale and the main scale moves by \(0.5\,mm\) on a complete rotation of the circular scale. The zero of circular scale lies \(6\) divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, \(4\) linear scale divisions are clearly visible while \(46^{\text {th }}\) division the circular scale coincide with the reference line. The diameter of the wire is \(...........\times 10^{-2}\,mm\)

The number density of molecules of a gas depends on their distance \(r\) from the origin as, \(n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}\). Then the total number of molecules is proportional to

An ideal monoatomic gas is confined in a cylinder by a spring loaded piston of cross section \(8.0\times10^{-3}\, m^2\) . Initially the gas is at \(300\, K\) and occupies a volume of \(2.4\times10^{-3}\, m^3\) and the spring is in its relaxed state as shown in figure. The gas is heated by a small heater until the piston moves out slowly by \(0.1\, m\). The force constant of the spring is \(8000\, N/m\) and the atmospheric pressure is \(1.0\times10^5\, N/m^2\) . The cylinder and the piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and the cylinder. The final temperature of the gas will be: (Neglect the heat loss through the lead wires of the heater . The heat capacity of the heater coil is also negligible)

A body of mass \(1000 \mathrm{~kg}\) is moving horizontally with a velocity \(6 \mathrm{~m} / \mathrm{s}\). If \(200 \mathrm{~kg}\) extra mass is added, the final velocity (in \(\mathrm{m} / \mathrm{s}\) ) is:

A plane electromagnetic wave of frequency \(100\, MHz\) is travelling in vacuum along the \(x -\) direction. At a particular point in space and time, \(\overrightarrow{ B }=2.0 \times 10^{-8} \hat{ k } T\). (where, \(\hat{ k }\) is unit vector along \(z-\)direction) What is \(\overrightarrow{ E }\) at this point ?

On celcius scale the temperature of body increases by \(40^{\circ} \mathrm{C}\). The increase in temperature on Fahrenheit scale is _______.

Following statements are given : \((1)\) The average kinetic energy of a gas molecule decreases when the temperature is reduced. \((2)\) The average kinetic energy of a gas molecule increases with increase in pressure at constant temperature. \((3)\) The average kinetic energy of a gas molecule decreases with increases in volume. \((4)\) Pressure of a gas increases with increase in temperature at constant pressure. \((5)\) The volume of gas decreases with increase in temperature. Choose the correct answer from the options given below:

A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

The torque of a force \(5 \hat{i}+3 \hat{j}-7 \hat{k}\) about the origin is \(\tau\). If the force acts on a particle whose position vector is \(2 \hat{i}+2 \hat{j}+\hat{k}\), then the value of \(\tau\) will be.