A small speaker delivers \(2\, W\) of audio output. At what distance from the speaker will one detect \(120\, dB\) intensity sound ... \(cm\) ? [Given reference intensity of sound as \(10^{-12}\,W/m^2\)]

The maximum height reached by a projectile is \(64 \mathrm{~m}\). If the initial velocity is halved, the new maximum height of the projectile is _______ \(\mathrm{m}\).

If the net electric field at point \(\mathrm{P}\) along \(\mathrm{Y}\) axis is zero, then the ratio of \(\left|\frac{q_2}{q_3}\right|\) is \(\frac{8}{5 \sqrt{x}}\), where \(\mathrm{x}=\) _______.

In the circuit shown in the figure, the ratio of the quality factor and the band width is \(.............\) s.

Two blocks of masses \(3 \,{kg}\) and \(5\, {kg}\) are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is \(\frac{24}{\pi} \times 10^{2}\, {Nm}^{-2}\). What is the minimum radius of the wire? (Take \(\left.g=10\, {ms}^{-2}\right)\) (in \(cm\))

A vehicle travels \(4\,km\) with speed of \(3\,km / h\) and another \(4\,km\) with speed of \(5\,km / h\), then its average speed is \(..........km/h\)

A circular disc has radius \(R_1\) and thickness \(T_1\). Another circular disc made of the same material has radius \(R_2\) and thickness \(T_2\). If the moment of inertia of both discs are same and \(\frac{R_1}{R_2}=2\) then \(\frac{T_1}{T_2}=\frac{1}{\alpha}\).The value of \(\alpha\) is __________ .

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into \(a\) square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:

In the given circuit, the terminal potential difference of the cell is _______.

An ideal gas exists in a state with pressure \(P_0\) volume \(\mathrm{V}_0\).It is isothermally expanded to 4 times of its initial volume \(\left(\mathrm{V}_0\right)\), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is :

A body cools in \(7\) minutes from \(60^{\circ}\,C\) to \(40^{\circ}\,C\). The temperature of the surrounding is \(10^{\circ}\,C\). The temperature of the body after the next \(7\) minutes will be

The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be

A star has \(100 \%\) helium composition. It starts to convert three \({ }^4 \mathrm{He}\) into one \({ }^{12} \mathrm{C}\) via triple alpha process as \({ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\mathrm{Q}\). The mass of the star is \(2.0 \times 10^{32} \mathrm{~kg}\) and it generates energy at the rate of \(5.808 \times 10^{30} \mathrm{~W}\). The rate of converting these \({ }^4 \mathrm{He}\) to \({ }^{12} \mathrm{C}\) is \(\mathrm{n} \times 10^{42} \mathrm{~s}^{-1}\), where \(\mathrm{n}\) is _______. [Take, mass of \({ }^4 \mathrm{He}=4.0026 \mathrm{u}\), mass of \({ }^{12} \mathrm{C}=12 \mathrm{u}\)]