When \(4 \mathrm{C}, \mathrm{Q} C\) and \(1 \mathrm{C}\) electrical charges are placed along a straight line of length ' \(l\) ' at 0 , \(\frac{l}{2}\) and \(l\) respectively. The respective values of \(\mathrm{Q}\) so that the net force on \(4 \mathrm{C}\) is zero and
\(1 \mathrm{C}\) is zero separately are (in coulomb)

If \(1 \%\) and \(2 \%\) are the errors in the measurement of mass and density of a cube respectively, then the error in the measurement of length is

Light of wavelength \(4000 Å\) is incident on a sodium surface for which the threshold wavelength of photo electrons is \(5420 Å\). The work function of sodium is

When a wire of length 'L' clamped at one end is pulled by a force 'F' from the other end, its length increases by 'L'. If the radius of the wire and the applied force were halved, then the increase in its length is

At any instant ' \(\mathrm{t}\) ' the vertical distance ' \(\mathrm{Y}\) ' and horizontal distance ' \(\mathrm{X}\) ' of a projectile are given by \(2 \mathrm{Y}=6 \mathrm{t}-\mathrm{gt}^2\) and \(X=4 \mathrm{t}\). The initial velocity of projectile is ( \(\mathrm{X}\) and \(\mathrm{Y}\) are in metre and \(\mathrm{t}\) is in second)

An LCR series circuit is connected to an external emf, \(e=200 \sin 100 \pi \mathrm{t} v\). The values of capacitance and resistance in the circuit are \(1 \mu \mathrm{F}\) and \(100 \Omega\) respectively. The amplitude of current in the circuit is maximum when the inductance is (in henry)

A ray of light travels from a medium of refractive index 2 to another medium of refractive index \(\sqrt{2}\). Total internal reflection takes place when the angle of incidence is

\(\mathrm{Cr}(\mathrm{CO})_x\), find the value of \(x\) ?

From the following, identify the reactions which are responsible for depletion of ozone layer.
\(\begin{aligned}
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{NO}_2(g) \rightarrow \mathrm{ClONO}_2(g) \\
& \mathrm{CF}_2 \mathrm{Cl}_2(g) \xrightarrow{\text { uv }} \mathrm{Cl}(g)+\dot{\mathrm{CF}}_2 \mathrm{Cl}(g) \\
& \dot{\mathrm{Cl}}(g)+\mathrm{CH}_4(g) \rightarrow \mathrm{HCl}(g)+\dot{\mathrm{C}} \mathrm{H}_3(g) \\
& \dot{\mathrm{C}} \mathrm{l}(\mathrm{g})+\mathrm{O}_3(g) \rightarrow \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}_2(g) \\
& \mathrm{Cl} \dot{\mathrm{O}}(g)+\mathrm{O}(g) \rightarrow \dot{\mathrm{C}} \mathrm{l}(g)+\mathrm{O}_2(g)
\end{aligned}\)

The heat energy released by water of mass \(2 \mathrm{~kg}\) when it is cooled by \(10^{\circ} \mathrm{C}\) is
(Specific heat capacity of water \(=4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}\) )

If \(b\) and \(c\) are the lengths of the segments of any focal chord of a parabola \(y^2=4 a x\), then the length of the semi-latus rectum is :

\(\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8} \Rightarrow x=\)

Area of the region (in square units) enclosed by the curves \(y^2=8(x+2), y^2=4(1-x)\) and the Y -axis is