An \(NPN\) transistor is used in common emitter configuration as an amplifier with \(1\,k\Omega \) load resistance. Signal voltage of \(10\,mV\) is applied across the base emitter. This produces a \(3\,mA\) change in the collector current and \(15\,\mu A\) change in the base current of the amplifier. The input resistance and voltage gain are

A car is standing \(200\, m\) behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration \(2\,m/s^2\) and the car has acceleration \(4\, m/s^2\) . The car will catch up with the bus after a time of

A steel wire of length \(3.2 m \left( Y _{ S }=2.0 \times 10^{11}\,Nm ^{-2}\right)\) and a copper wire of length \(4.4\,M\) \(\left( Y _{ C }=1.1 \times 10^{11}\,Nm ^{-2}\right)\), both of radius \(1.4\,mm\) are connected end to end. When stretched by a load, the net elongation is found to be \(1.4\,mm\). The load applied, in Newton, will be. (Given \(\pi=\frac{22}{7}\))

The sum of two forces \(\overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) is \(\overrightarrow{\mathrm{R}}\) such that \(|\overrightarrow{\mathrm{R}}|=|\overrightarrow{\mathrm{P}}| .\) The angle \(\theta\) (in degrees) that the resultant of \(2 \overrightarrow{\mathrm{P}}\) and \(\overrightarrow{\mathrm{Q}}\) will make with \(\overrightarrow{\mathrm{Q}}\) is

A parallel beam of light of wavelength \(900\,nm\) and intensity \(100\,Wm ^{-2}\) is incident on a surface perpendicular to the beam. Tire number of photons crossing \(1\,cm ^{2}\) area perpendicular to the beam in one second is :

A sonometer wire oflength \(1.5\ m\) is made of steel. The tension in it produces an elastic strain of \(1 \%\). What is the fundamental frequency of steel if density and elasticity of steel are \(7.7 \times 10^3 \) \(kg/m^3\) and \(2.2 \times 10^{11}\) \(N/m^2\) respectively?

A solid sphere of mass \(M\) and radius \(R\) is divided into two unequal parts. The smaller part having mass \(M/8\) is converted into a sphere of radius \(r\) and the larger part is converted into a circular disc of thickness \(t\) and radius \(2R\). If \(I_1\) is moment of inertia of a sphere having radius \(r\) about an axis through its centre and \(I_2\) is the moment of inertia of a disc about its diameter, the ratio of their moment of inertia \(I_2/I_1 = \) _____.

Two short bar magnets oflength \(1\ cm\) each have magnetic moments \(1.20\ Am^2\) and \(1.00\ Am^2\) respectively. They are placed on a horizontal table parallel to each other with their \(N\) poles pointing towards the South. They have a common magnetic equator and are separated by a distance of \(20.0\ cm\). The value of the resultand horizontal magnetic induction at the mid-point \(O\) of the line joining their centres is close to  (Horizontal component of earth.s magnetic induction is \(3.6 \times  10^{-5}\) \(Wbm^{-2}\)  )

A magnetic needle of magnetic moment \(6.7 \times 10^{-2} \) \(Am^2\) and moment of inertia \(7.5 \times  10^{-6}\) \( kgm^2\) is performing simple harmonic oscillations in a magnetic field of \(0.01\ T\). Time taken for \(10\) complete oscillations is.....\(s\)

For the given logic circuit, which of the following inputs combination will make both LED\(-1\) and LED\(-2\) to glow?

When \(M_1\) gram of ice at \(-10\,^oC\) (specific heat \(= 0.5\, cal\, g^{-1}\,^oC^{-1}\)) is added to \(M_2\) gram of water at \(50\,^oC\), finally no ice is left and the water is at \(0\,^oC\). The value of latent heat of ice, in \(cal\, g^{-1}\) is

Half lives of two radioactive nuclei \(A\) and \(B\) are \(10\, minutes\) and \(20\, minutes\), respectively. If, initially a sample has equal number of nuclei, then after \(60\) \(minutes\) , the ratio of decayed numbers of nuclei \(A\) and \(B\) will be