An object is placed beyond the centre of curvature \({C}\) of the given concave mirror. If the distance of the object is \({d}_{1}\) from \({C}\) and the distance of the image formed is \({d}_{2}\) from \({C}\), the radius of curvature of this mirror is

Electric field in a certain region is given by \(\overrightarrow{ E }=\left(\frac{ A }{ x ^2} \hat{ i }+\frac{ B }{ y ^3} \hat{ j }\right)\). The \(SI\) unit of \(A\) and \(B\) are

A bar magnet has total length \(2 l=20\) units and the field point \(P\) is at a distance \(\mathrm{d}=10\) units from the centre of the magnet. If the relative uncertainty of length measurement is \(1 \%\), then uncertainty of the magnetic field at point P is :

\(A\). The drift velocity of electrons decreases with the increase in the temperature of conductor. \(B\). The drift velocity is inversely proportional to the area of cross-section of given conductor. \(C\). The drift velocity does not depend on the applied potential difference to the conductor. \(D\). The drift velocity of electron is inversely proportional to the length of the conductor. \(E\). The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below:

\(\begin{array}{c|c|c} A & B & Y \\\hline 0 & 0 & 1 \\0 & 1 & 1 \\1 & 0 & 0 \\1 & 1 & 1\end{array}\)
To obtain the given truth table, following logic gate should be placed at G :

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is \(I_{1}\). The same rod is bent into a ring and its moment of inertia about a diameter is \(I _{2}\). If \(\frac{ I _{1}}{ I _{2}}\) is \(\frac{ x \pi^{2}}{3}\), then the value of \(x\) will be ...............

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

A circular coil of radius \(10\, cm\) is placed in a uniform magnetic field of \(3.0 \times 10^{-5}\, T\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\,s.\) The maximum value of \(EMF\) induced (in \(\mu V\) ) in the coil will be close to the integer\(....\mu V\)

The angular frequency of the damped oscillator is given by, \(\omega  = \sqrt {\left( {\frac{k}{m} - \frac{{{r^2}}}{{4{m^2}}}} \right)} \) where \(k\) is the spring constant, \(m\) is the mass of the oscillator and \(r\) is the damping constant. If the ratio \(\frac{{{r^2}}}{{mk}}\) is \(8\%\), the change in time period compared to the undamped oscillator is approximately as follows

Consider the following statements:
A. The junction area of solar cell is made very narrow compared to a photo diode.
B. Solar cells are not connected with any external bias.
C. LED is made of lightly doped p-n junction.
D. Increase of forward current results in continuous increase of LED light intensity.
E. LEDs have to be connected in forward bias for emission of light.
Choose the correct answer from the options given below:

Two nuclei of mass number \(3\) combine with another nucleus of mass number \(4\) to yield a nucleus of mass number \(10\). If the binding energy per nucleon for the mass numbers \(3\), \(4\) and \(10\) are \(5.6\) MeV, \(7.4\) MeV and \(6.1\) MeV, respectively, then in the process, \(\Delta Mc^2 = \) _____ MeV.

If one were to apply Bohr model to a particle of mass \('m'\) and charge \('q'\) moving in a plane under the influence of a magnetic field \('B',\) the energy of the charged particle in the \(n^{th}\) level will be

Experimentally it is found that \(12.8\,eV\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{ x } \times 10^{-10}\,m\). The value of the \(x\) is \(\left(1\,eV =1.6 \times 10^{-19}\,J , \frac{1}{4 \pi \epsilon_0}=9 \times 10^9\,Nm ^2 / C ^2\right.\) and electronic charge \(=1.6 \times 10^{-19}\,J\,C\) )