For a certain radioactive process the graph between \(In\, {R}\) and \({t}\,({sec})\) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately \(....\,{sec}.\)

The heat generated in 1 minute between points A and B in the given circuit, when a battery of 9 V with internal resistance of \(1 \Omega\) is connected across these points is _________ J.

A nucleus \(A\), with a finite de -broglie wavelength \(\lambda_A\), undergoes spontaneous fission into two nuclei \(B\) and \(C\) of equal mass. \(B\) flies in the same direction as that of \(A\), while \(C\) flies in the opposite direction with a velocity equal to half of that of \(B\). The de -Broglie wavelength \(\lambda_B\) and \(\lambda_C\) of \(B\) and \(C\) are respectively

An electric dipole of dipole moment \(6 \times 10^{-6} \mathrm{Cm}\) is placed in uniform electric field of magnitude \(10^6 \mathrm{~V} / \mathrm{m}\). Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

The energy of a system is given as \(\mathrm{E}(\mathrm{t})=\alpha^3 \mathrm{e}^{-\beta t}\), where t is the time and \(\beta=0.3 \mathrm{~s}^{-1}\). The errors in the measurement of \(\alpha\) and \(t\) are \(1.2 \%\) and \(1.6 \%\), respectively. At \(t=5 \mathrm{~s}\), maximum percentage error in the energy is :

Match the LIST-I with LIST-II

LIST-I	LIST-II
(A) Boltzmann constant	I. \(\mathrm{ML}^2 \mathrm{~T}^{-1}\)
(B) Coefficient of viscosity	II. \(\mathrm{MLT}^{-3} \mathrm{~K}^{-1}\)
(C) Planck's constant	III. \(\mathrm{ML}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\)
(D) Thermal conductivity	IV. \(\mathrm{ML}^{-1} \mathrm{~T}^{-1}\)

Choose the correct answer from the options given below :

A glass tumbler having inner depth of \(17.5\, {cm}\) is kept on a table. A student starts pouring water \((\mu=4 / 3)\) into it while looking at the surface of water from the above. When he feels that the tumbler is half filled, he stops pouring water. Up to what height, the tumbler is actually filled ? (In \(cm\))

When unpolarized light is incident at an angle of \(60^{\circ}\) on a transparent medium from air. The reflected ray is completely polarized. The angle of refraction in the medium is _______.

An AC voltage \(\mathrm{V}=20 \sin 200 \pi t\) is applied to a series \(LCR\) circuit which drives a current \(I=10 \sin \left(200 \pi t+\frac{\pi}{3}\right)\). The average power dissipated is _______.

A metal wire of length \(0.5 m\) and cross-sectional area \(10^{-4}\; m ^{2}\) has breaking stress \(5 \times 10^{8}\; Nm ^{-2}\). A block of \(10\; kg\) is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be \(ms ^{-1}\).

In the given potentiometer circuit arrangement, the balancing length \({AC}\) is measured to be \(250\) \({cm}\). When the galvanometer connection is shifted from point \((1)\) to point \((2)\) in the given diagram, the balancing length becomes \(400\, {cm}\). The ratio of the emf of two cells, \(\frac{\varepsilon_{1}}{\varepsilon_{2}}\) is -