A sphere of mass' \(m\) ' moving with velocity ' \(v\) 'collides head-on another sphere of same mass which is at rest. The ratio of final velocity of second sphere to the initial velocity of the first sphere is ( \(e\) is coefficient of restitution and collision is inelastic)

The capacitance of a parallel plate capacitor is \(2.5 \mu \mathrm{F}\). When it is half filled with a dielectric as shown in figure, its capacitance becomes \(5 \mu \mathrm{F}\). The dielectric constant of the dielectric is

In a Young's double slit experiment wavelength of light used is \(6000 Å\). The first order maxima and tenth order maxima fall at 14.50 mm and 16.75 mm from the particular reference point in the interference pattern respectively. If the wavelength is changed to \(5500 Å\) then the position of zero order and tenth order maxima are respectively [The other arrangements remaining same]

I-V characteristics of LED is shown correctly by graph

Two galvanometers ' \(A\) ' and 'B' require currents of \(4 \mathrm{~mA}\) and \(7 \mathrm{~mA}\), respectively to produce the same deflection of 20 divisions. If ' \(\mathrm{S}_{A}{ }^{\prime}\) and \({ }^{\prime} \mathrm{S} \mathrm{B}^{\prime}\) are their sensitivities,
respectively, then

An isotope of the original nucleus can be formed in a radioactive decay, with the emission of following particles.

A thin ring of radius ' \(R\) ' meter has charge ' \(q\) ' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of \(f\) revolution/s. The value of magnetic induction in \(\mathrm{Wb} \mathrm{m}{ }^{-2}\) at the center of the ring is ( \(\mu_0=\) Permeability of free space)

If \(\bar{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}, \quad \bar{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}\), \(\overline{\mathrm{c}}=\mathrm{c}_1 \hat{i}+\mathrm{c}_2 \hat{\mathrm{j}}+\mathrm{c}_3 \hat{\mathrm{k}}\) and \(\left[\begin{array}{lll}3 \overline{\mathrm{a}}+\overline{\mathrm{b}} & 3 \overline{\mathrm{~b}}+\overline{\mathrm{c}} & 3 \overline{\mathrm{c}}+\overline{\mathrm{a}}\end{array}\right]\) \(=\lambda\left|\overline{\mathrm{a}} \cdot \hat{\mathrm{i}} \overline{\mathrm{a}} \cdot \hat{\mathrm{j}} \overline{\mathrm{a}} \cdot \hat{\mathrm{k}} \ \overline{\mathrm{b}} \cdot \hat{\mathrm{i}} \overline{\mathrm{b}} \cdot \hat{\mathrm{j}} \overline{\mathrm{b}} \cdot \hat{\mathrm{k}} \ \overline{\mathrm{c}} \cdot \hat{\mathrm{i}} \overline{\mathrm{c}} \cdot \hat{\mathrm{j}} \overline{\mathrm{c}} \cdot \hat{\mathrm{k}}\right|\) then the value of \(\lambda\) is

If the polar co-ordinates of a point are \(\left(\sqrt{2}, \frac{\pi}{4}\right)\), then its Cartesian co-ordinates are

A parallel plate condenser with oil (dielectric constant 2 ) between the plates has capacitance C. If oil is removed, the capacitance of capacitor becomes

In an electric field due to charge \(Q\), a charge \(q\) moves from point \(A\) to \(B\) as shown in the figure. The work done is ( \(\varepsilon_0=\) permittivity of free space)

Two circular loops P and Q of radii 'r' and 'nr' are made respectively from a uniform wire. Moment of inertia of loop Q about its axis is 4 times that of loop P about its axis. The value of n is

Which among the following statements about \(\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}\) is NOT true?