Two radioactive materials \(A\) and \(B\) having decay constant ' \(7 \lambda\) ' and ' \(\lambda\) ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is
Which of the following transitions in hydrogen atom emit photons of highest frequency? ( \(\mathrm{n}=\) principle quantum number)
The total energy of a circularly orbiting satellite is
Water rises up to height ' \(x\) ' in a capillary tube immersed vertically in water. When the whole arrangement is taken to a depth ' \(d\) ' in a mine, the water level rises up to height Y . If R is the radius of the earth then the ratio \(\mathrm{Y}: \mathrm{x}\) is
In Young's double slit experiment, in an interference pattern, a minimum is observed exactly in front of one slit. The distance between the two coherent sources is d and \(\mathrm{D}_{\text { }}\) is the distance between source and screen. The possible wavelengths used are proportional to
The de-Broglie wavelength \((\lambda)\) of a particle
A child stands on a weighing machine inside a lift. When the lift is going down with acceleration \(\mathrm{g} / 3\), the machine shows a reading 20 N . When the lift goes upwards with acceleration \(\mathrm{g} / 3\), the reading would be ( \(\mathrm{g}=\) gravitational acceleration)
The equivalent capacitance between plates ' A ' and ' B ' ( A -area of each plate, d-separation between plates) ( \(\varepsilon_0\) - permittivity of free space) is
In LCR series circuit, R = 18 \(\Omega\) and impedance \(33 \Omega\). An r.m.s. voltage of 220 V is applied across the circuit. The true power consumed in a.c. circuit is
The length of a potentiometer wire is ' \(L\) ' . A cell of e.m.f. \(E\) is balanced at a length \(\frac{L}{5}\) from the positive end of the wire. If the length of the wire is increased by \(\frac{L}{2}\), the same cell will give balance point at distance ' \(x\) '. The value of ' \(x\) ' is
The velocity time graph of a body moving in a straight line is shown in figure. The ratio of displacement to distance travelled by the body in time 0 to 8 s is
Which graph shows correctly the temperature (T). dependence of resistivity \((\rho)\) of a semiconductor?
For an ideal gas, the density of the gas is \(\rho_0\) when temperature and pressure of the gas are \(\mathrm{T}_0\) and \(P_0\) respectively. when the temperature of the gas is \(2 \mathrm{~T}_0\), its pressure becomes \(3 \mathrm{P}_0\). The new density will be
A liquid drop of volume V is placed on the surface of glass plate. Then another glass plate is placed on it such that liquid forms a thin layer of area A between the surfaces of two plates. To separate the plates a force F has to be applied normal to the surfaces. The surface tension of the liquid is
Two uniform wires of same material are vibrating under the same tension. If the \(1^{\text {st }}\) overtone of \(1^{\text {st }}\) wire is equal to the \(2^{\text {nd }}\) overtone of \(2^{\text {nd }}\) wire and radius of \(1^{\text {st }}\) wire is twice the radius of \(2^{\text {nd }}\) wire, the ratio of length of \(1^{\text {st }}\) wire to that \(2^{\text {nd }}\) wire is
A disc of mass 25 kg and radius 0.2 m is rotating at 240 r.p.m. A retarding torque brings it to rest in 20 second. If the torque is due to a force applied tangentially on the rim of the disc then the magnitude of the force is
Which of the following logic gates is called as Universal gate?
Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is \(\pi / 2\) at point P and \(\pi\) at point Q on the screen. The difference between the resultant intensities at points P and Q is \(\left(\cos 90^{\circ}=0, \cos \pi=-1\right)\)
Two identical long parallel wires carry currents ' \(\mathrm{I}_1\) ' and ' \(\mathrm{I}_2\) ' such that \(\mathrm{I}_1>\mathrm{I}_2\). When the currents are in the same direction, the magnetic field at a point midway between the wires is \(8 \times 10^{-6} \mathrm{~T}\). If the direction of \(\mathrm{I}_2\) is reversed, the field becomes \(3.2 \times 10^{-5} \mathrm{~T}\). The ratio of \(\mathrm{I}_2\) to \(\mathrm{I}_1\) is
In series LCR resonant circuit, R \(=800 \Omega\), \(\mathrm{C}=2 \mu \mathrm{~F}\) and voltage across resistance is 200 V . The angular frequency is \(250 \mathrm{rad} / \mathrm{s}\). At resonance, the voltage across the inductance is
The three vector \(\vec{A}=3 \hat{i}-2 \hat{j}+\hat{k}, \vec{B}=\hat{i}-3 \hat{j}+5 k\) and \(\vec{C}=2 \hat{i}-\hat{j}+4 \hat{k}\) will form
Two coils \(P\) and \(Q\) are kept near each other. When no current flows through coil \(P\) and current increases in coil Q at the rate of \(10 \mathrm{~A} / \mathrm{S}\), the e.m.f. in coil P is 15 mV . When coil Q carries no current and current of 1.8 A flows through coil \(P\), the magnetic flux linked with coil Q is
A mass \(m\) is suspended from a spring of negligible mass. The spring is pulled a little and then released, so that mass executes S.H.M. of time period \(T\). If the mass is increased by \(m_0\), the periodic time becomes \(\frac{5 \mathrm{~T}}{4}\). The ratio \(\frac{\mathrm{m}_0}{\mathrm{M}}\)
When a diatomic gas (rigid) undergoes adiabatic change, its pressure \((\mathrm{P})\) and temperature \((\mathrm{T})\) are related as \(P \propto T^c\). The value of \(c\) is
