The relation between time ' \(t\) ' and distance ' \(x\) ' is \(t=\) \(\alpha x^2+\beta x\), where \(\alpha\) and \(\beta\) are constants. The relation between acceleration \((a)\) and velocity \((v)\) is _______.

A series combination of resistor of resistance \(100\,\Omega\), inductor of inductance \(1\,H\) and capacitor of capacitance \(6.25\,\mu F\) is connected to an ac source. The quality factor of the circuit will be \(.............\).

\(T\) is the time period of simple pendulum on the earth's surface. Its time period becomes \(x T\) when taken to a height \(R\) (equal to earth's radius) above the earth's surface. Then, the value of \(x\) will be:

A body of mass 2 kg moving with velocity of \(\overrightarrow{\mathrm{v}}_{\mathrm{in}}=3 \hat{\mathrm{i}}+4 \hat{\mathrm{j}} \mathrm{ms}^{-1}\) enters into a constant force field of 6 N directed along positive z -axis. If the body remains in the field for a period of \(\frac{5}{3}\) seconds, then velocity of the body when it emerges from force field is

In an unbiased \(n-p\) junction electrons diffuse from \(n-\) region to \(p-\) region because

The three charges \(q / 2, q\) and \(q / 2\) are placed at the corners \(A , B\) and \(C\) of a square of side ' \(a\) ' as shown in figure. The magnitude of electric field \((E)\) at the comer \(D\) of the square, is

A closely wounded circular coil of radius \(5\,cm\) produces a magnetic field of \(37.68 \times 10^{-4}\,T\) at its center. The current through the coil is \(......A\). [Given, number of turns in the coil is \(100\) and \(\pi=3.14]\)

A person has been using spectacles of power- \(1.0\) diopter for distant vision and a separate reading glass of power \(2.0\) diopters. What is the least distance of distinct vision for this person \(.......cm\)

The current voltage relation of a diode is given by \(I=(e^{1000V/T} -1)mA\) where the applied voltage \(V\) is in volts and the temperature \(T\) is in degree kelvin. If a student makes an error measuring \(±0.01\ V\) while measuring the current of \(5\ mA\) at \(300\ K\), what will be the error in the value of current in \(mA?\)

A block of mass ' \(m\) ' (as shown in figure) moving with kinetic energy \(E\) compresses a spring through a distance \(25\,cm\) when, its speed is halved. The value of spring constant of used spring will be \(nE\; Nm ^{-1}\) for \(n=\)