A series \(L C R\) circuit is connected across a source of alternating emf of changing frequency and resonates at frequency \(f_0\). Keeping capacitance constant, if the inductance \((L)\) is increased by \(\sqrt{3}\) times and resistance is increased \((R)\) by 1.4 times, the resonant frequency now is

A projectile is given an initial velocity of \((\hat{\mathbf{i}}+2 \hat{\mathbf{j}}) \mathrm{ms}^{-1}\). The equation of its path is \(\left(g=10 \mathrm{~ms}^{-2}\right)\)

The threshold frequency for a certain metal is ' \(v_0\) '. When a certain radiation of frequency \(2 v_0\) is incident on this metal surface, maximum velocity of the photo electrons emitted is \(2 \times 10^6 \mathrm{~ms}^{-1}\). If radiation of frequency \(3 v_0\) is incident on the same metal surface, the maximum velocity of the photo electrons emitted is ____

When a hydrogen atom emits a photon during a transition from $n=4$ to $n=2,$ its recoil speed is about

A $TV$ transmitter has a range of $50 \mathrm{km}$. The height of the $TV$ transmitter is _______ $($Radius of the earth $\left.{\mathrm{R}}_{\mathrm{e}}=6.4\times {10}^6 \mathrm{m}\right)$

117.An L-C resonant circuit contains a 400 pF capacitor and an inductor of 400 μH. It is coupled to an antenna. Wavelength of
radiated electromagnetic wave is

Two neutral conducting spheres of diameters \(8 \mathrm{~cm}\) and \(2 \mathrm{~cm}\) separated with a distance of \(15 \mathrm{~cm}\) between their centres are joined by a thin conducting wire. A charge of \(100 \mathrm{nC}\) is given to one of the spheres and the system is allowed to reach electrostatic equilibrium. The electric potential at a point on the line joining the centres of the two spheres where the net electric field becomes zero is ____ V. (Neglect the charge acquired by the wire and \(\frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \mathrm{Nm}^2 \mathrm{C}^{-2}\))

In which of the following pairs, the central atoms have the same number of lone pairs of electrons?

The correct statements about $\mathrm{Z}$from the following are$\left(\mathrm{I}\right)$ It is $\mathrm{o}-$hydroxybenzoic acid.
$\left(\mathrm{II}\right)$It is a non-narcotic analgesic.
$\left(\mathrm{III}\right)$ It acts as an antipyretic.
$\left(\mathrm{IV}\right)$ It acts as an antihistamine.

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

A closed pipe is in resonance with a tuning fork at \(27^{\circ} \mathrm{C}\) when its length is \(20 \mathrm{~cm}\). If the pipe is to be in resonance with the same tuning fork at \(7{ }^{\circ} \mathrm{C}\) then the change in the length of the pipe required is nearly

If the rate of disappearance of \(\mathrm{N}_2 \mathrm{O}_5\) in the following reaction is \(1.2 \times 10^{-5}\) in \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\), the rate of production of \(\mathrm{NO}_2 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\) is
\(2 \mathrm{~N}_2 \mathrm{O}_5(g) \longrightarrow 4 \mathrm{NO}_2(g)+\mathrm{O}_2(g)\)

The general solution of the differential equation \(\left(y^2+x+1\right) d y=(y+1) d x\) is