The energy band gap of semiconducting material to produce violet (wavelength \(=4000 \,A^{\circ}\) ) LED is \(.......eV\). (Round off to the nearest integer).

An object with mass 500 g moves along x -axis with speed \(v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}\). The force acting on the object is :

An alternating \(emf\) \(E =440 \sin 100 \pi t\) is applited to a circuit containing an inductance of \(\frac{\sqrt{2}}{\pi} H\). If an a.c. ammeter is connected in the circuit, its reading will be \(.......A\)

In the circuit shown here, the voltage across \(L\) and \(C\) are respectively \(300\, V\) and \(400\, V\). The voltage \(E\) of the ac source is......\(Volt\)

In a hydrogen spectrum, \(\lambda\) be the wavelength of first transition line of Lyman series. The wavelength difference will be "a \(\lambda^{\prime}\) between the wavelength of \(3^{\text {rd }}\) transition line of Paschen series and that of \(2^{\text {nd }}\) transition line of Balmer Series where \(a=........\)

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)

In a scries \(LR\) circuit, power of \(400\, W\) is dissipated from a source of \(250\, V , 50\, Hz\). The power factor of the circuit is \(0.8 .\) In order to bring the power factor to unity, a capacitor of value \(C\) is added in series to the \(L\) and \(R\). Taking the value of \(C\) as \(\left(\frac{ n }{3 \pi}\right) \mu F ,\) then value of \(n\) is\(......\)

The magnetic intensity at the centre of a long current carrying solenoid is found to be \(1.6 \times 10^3 Am ^{-1}\). If the number of turns is 8 per cm, then the current flowing through the solenoid is \(................\,A\)

A refrigerator consumes an average \(35\, {W}\) power to operate between temperature \(-10^{\circ} {C}\) to \(25^{\circ} {C}\). If there is no loss of energy then how much average heat per second does it transfer? (in \({J} / {s}\))

The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point , \(P\), located as shown, would be (nearly)

The root mean square velocity of molecules of gas is

A body of mass \(M\) thrown horizontally with velocity \(v\) from the top of the tower of height \(\mathrm{H}\) touches the ground at a distance of \(100 \mathrm{~m}\) from the foot of the tower. A body of mass \(2 \mathrm{M}\) thrown at a velocity \(\frac{v}{2}\) from the top of the tower of height \(4 \mathrm{H}\) will touch the ground at a distance of _______.