A small source of sound vibrating at a frequency \(500 \mathrm{~Hz}\) is rotated along a circle of radius \(\frac{100}{\pi} \mathrm{cm}\) at a constant angular speed of 5 revolutions per second. The minimum and maximum frequency of the sound observed by a listener situation in the plane of the circle is (speed of sound is \(332 \mathrm{~ms}^{-1}\) )

In an LCR series circuit, if the potential differences across inductor, capacitor and resistor are \(60 \mathrm{~V}, 30 \mathrm{~V}\) and 40 V respectively, then the ac voltage applied to the circuit is

Which quantity among the following has neither units nor dimensions?

Names of units of some physical quantities are given in List-I and their dimensions formulae are given in List-Il. Match the correct pairs in the lists
\(\begin{array}{ll|ll}
\hline & \text{ List-I } & \text{ List-II } \\
\hline A. & \mathrm{Pa}-\mathrm{s} & (i) & {\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline B. & \mathrm{NmK}^{-1} & (ii) & {\left[\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\right]} \\
\hline C. & \mathrm{J} \mathrm{kg}^{-1} \mathrm{~K}^{-1} & (iii) & {\left[\mathrm{ML}^{-1} \mathrm{~T}^{-1}\right]} \\
\hline D. & \mathrm{Wm}^{-1} \mathrm{~K}^{-1} & (iv) & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]} \\
\hline
\end{array}\)
\(\begin{array}{llll}A & B & C & D\end{array}\)

A pressure of \(1 \mathrm{~mm}\) of mercury is equivalent to

The magnetic susceptibility of a paramagnetic substance at $-173 °\mathrm{C}$ is $1.5\times {10}^{-2}$. To have the susceptibility $0.5\times {10}^{-2}$, the change in temperature in $°\mathrm{C}$ is

In the equation \(\left(\mathrm{P}+\frac{a}{\mathrm{~V}^2}\right)(\mathrm{V}-b)=\mathrm{RT}\), where P is pressure, V is volume, T is temperature, R is universal gas constant, \(a\) and \(b\) are constants. The dimensions of \(a\) are

The wavenumber of the first line \(\left(n_2=3\right)\) in the Balmer series of hydrogen is \(\overline{\mathrm{v}}_1 \mathrm{~cm}^{-1}\). What is the wavenumber (in \(\mathrm{cm}^{-1}\) ) of the second line ( \(\mathrm{n}_2=4\) ) in the Balmer series of \(\mathrm{He}^{+}\)?

Identify the set of acidic oxides.

Eight drops of mercury, each of same radius and same charge combine to form a bigger drop. The ratio of capacitance of the bigger drop to that of each smaller drop is

Identify the incorrect statement about the group 13 elements

Let $A=\left[\begin{array}{ccc}-2& x& 1\\ x& 1& 1\\ 2& 3& -1\end{array}\right]$. If the roots of the equation $detA=0$ are $l,m$, then $l^3-m^3=$

A radiation of \(3.8 \mathrm{eV}\) falls on a metal surface to produce photo electrons. These electrons are made to enter a magnetic field of \(2 \times 10^{-4} \mathrm{~T}\). If the radius of the largest circular path followed by these electrons is \(30 \mathrm{~mm}\), then work function of the metal is
(Mass of electron \(\mathrm{m}_{\mathrm{e}}=9 \times 10^{-31} \mathrm{~kg}\) )