The velocity \((v)\) and time \((t)\) graph of a body in a straight line motion is shown in the figure. The point \(S\) is at \(4.333\) seconds. The total distance covered by the body in \(6 \;s\) is\(.......m\)

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 \(a=........\)

The initial speed of a bullet fired from a rifle is \(630\, m/s\). The rifle is fired at the centre of a target \(700\, m\) away at the same level as the target. How far above the center of the target (in \(m\)) the rifle must be aimed in order to hit the target? (Take \(g=10 \;m/s^2\))

The \(V-I\) characteristic of a diode is shown in the figure. The ratio of forward to reverse bias resistance is

A circular disc \(D_1\) of mass \(M\) and radius \(R\) has two identical discs \(D_2\) and \(D_3\) of the same mass \(M\) and radius \(R\) attached rigidly as its opposite ends (see figure). The moment of inertia of the system about the axis \(OO\)’, passing through the centre of \(D_1\) as shown in the figure, will

A Zener diode of breakdown voltage \(10 \mathrm{~V}\) is used as a voltage regulator as shown in the figure. The current through the Zener diode is _______.

A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is \(\sqrt{\frac{\mathrm{F}}{\alpha \mathrm{M}}}\) in SI unit. The value of \(\alpha\) is __________.

In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

In a double slit experiment shown in figure, when light of wavelength \(400 \mathrm{~nm}\) is used, dark fringe is observed at \(P\). If \(D=0.2 \mathrm{~m}\). the minimum distance between the slits \(S_1\) and \(S_2\) is ____________ \(mm\).

A radioactive nucleus decays by two different process. The half life of the first process is \(5\) minutes and that of the second process is \(30\,s\). The effective half-life of the nucleus is calculated to be \(\frac{\alpha}{11}\,s\). The value of \(\alpha\) is \(..............\)

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings \(5.50\, mm , 5.55\, mm ,\)\( 5.45\, mm ; 5.65\, mm .\) The average of these four readings is \(5.5375\, mm\) and the standard deviation of the data is \(0.07395\, mm .\) The average diameter of the pencil should therefore be recorded as

The weight of a body on the surface of the earth is \(100\,N\). The gravitational force on it when taken at a height, from the surface of earth, equal to onefourth the radius of the earth is \(..........\,N\)