Two cars \({X}\) and \({Y}\) are approaching each other with velocities \(36\; {km} / {h}\) and \(72\; {km} / {h}\) respectively. The frequency of a whistle sound as emitted by a passenger in car \({X}\), heard by the passenger in car \({Y}\) is \(1320 \;{Hz}\). If the velocity of sound in air is \(340\; {m} / {s}\), the actual frequency of the whistle sound produced is ........ \(Hz.\)

Unpolarized light of intensity \(I\) is incident on a system of two polarizers, \(A\) followed by \(B.\)  The intensity of emergent light is \(I/2.\)  If a third polarizer \(C\)  is placed between \(A\) and \(B,\)  the intensity of emergent light is reduced to \(I/3 .\)  The angle between the polarizers \(A\) and \(C\) is \(\theta \) . Then

The resistances of the platinum wire of a platinum resistance thermometer at the ice point and steam point are \(8 \Omega\) and \(10 \Omega\) respectively. After inserting in a hot bath of temperature \(400^{\circ} \mathrm{C}\), the resistance of platinum wire is _______.

One mole of a diatomic ideal gas undergoes a cyclic process \(ABC\) as shown in figure. The process \(BC\) is adiabatic. The temperatures at \(A, B\) and \(C\) are \(400\ K, 800\ K \) and \(600\ K\) respectively. Choose the correct statement

A body of \(\mathrm{m} \mathrm{kg}\) slides from rest along the curve of vertical circle from point \(A\) to \(B\) in friction less path. The velocity of the body at \(B\) is _______. (given, \(\mathrm{R}=14 \mathrm{~m}, \mathrm{~g}=10 \mathrm{~m} / \mathrm{s}^2\) and \(\sqrt{2}=1.4\) )

Mass numbers of two nuclei are in the ratio of \(4: 3\). Their nuclear densities will be in the ratio of

When both jaws of vernier callipers touch each other, zero mark of the vernier scale is right to zero mark of main scale, \(4^{\text {th}}\) mark on vernier scale coincides with certain mark on the main scale. While measuring the length of a cylinder, observer observes 15 divisions on main scale and \(5^{\text {th}}\) division of vernier scale coincides with a main scale division. Measured length of cylinder is ___________ mm. (Least count of Vernier calliper \(= 0.1\ mm\))

A hoop of radius \(r\) and mass \(m\) rotating with an angular velocity \(\omega_0\) is placed on a rough horizontal surface. The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

A source of sound \(A\) emitting waves of frequency \(1800\,Hz\) is falling towards ground with a terminal speed \(v.\) The observer \(B\) on the ground directly beneath the source receives waves of frequency \(2150\,Hz.\) The source \(A\) receives waves, reflected from ground of frequency nearly ..... \(Hz\) (Speed of sound \(= 343\,m/s\) )

The de Broglie wavelength associated with an electron accelerated through a potential difference V is \(\lambda_e\) and the de Broglie wavelength associated with a proton accelerated through the same potential difference is \(\lambda_p\). If their corresponding masses are \(m_e\) and \(m_p\), respectively, then the ratio of their de Broglie wavelengths \(\left(\dfrac{\lambda_e}{\lambda_p}\right)\) is ______.

A square shaped hole of side \(l=\frac{a}{2}\) is carved out at a distance \(d =\frac{ a }{2}\) from the centre \('O'\) of a uniform circular disk of radius \(a\). If the distance of the centre of mass of the remaining portion from \(O\) is \(-\frac{a}{X},\) value of \(X\) (to the nearest integer) is.......