If the uncertainty in velocity and position of a minute particle in space are, \(2.4 \times 10^{-26}\left(\, m\,s ^{-1}\right)\) and \(10^{-7}\,( m )\) respectively. The mass of the particle in \(g\) is \(....\) (Nearest integer) (Given : \(h =6.626 \times 10^{-34} Js\) )

The lanthanoid that does NOT show \(+4\) oxidation state is

Which hydrogen in compound\((E)\) is easily replaceable during bromination reaction in presence of light? \(\mathop {C{H_3} - }\limits_\delta  \mathop {C{H_2} - }\limits_\gamma  \mathop {CH = }\limits_\beta  \mathop {C{H_2}}\limits_\alpha  \)                     \((E)\)

Which one of the following reactions will not form acetaldehyde ?

The noble gas that does Not occur in the atmosphere is

The element with which of the following outer electron configuration may exhibit the largest number of oxidation states in its compounds 

The reaction that occurs in a breath analyser, a device used to determine the alcohol level in a person's blood stream is \(2 \mathrm{~K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}+8 \mathrm{H}_{2} \mathrm{SO}_{4}+3 \mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} \rightarrow 2 \mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}+\) \(3 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}_{2}+2 \mathrm{~K}_{2} \mathrm{SO}_{4}+11 \mathrm{H}_{2} \mathrm{O}\) If the rate of appearance of \(\mathrm{Cr}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is \(2.67 \,\mathrm{~mol}\) \(\min ^{-1}\) at a particular time, the rate of disappearance of \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\) at the same time is ...... \(\mathrm{mol}\, \mathrm{min}^{-1}\) (Nearest integer)

Match List-I with List-II.

List-I	List-II
A. \(\sin^2 \omega t\)	I. Periodic with time period \(T = \dfrac{\pi}{\omega}\) but not simple harmonic motion (SHM)
B. \(\sin^3(2\omega t)\)	II. Periodic with time period \(T = \dfrac{2\pi}{\omega}\) but Not SHM
C. \(\sin(\omega t) + \cos(\pi \omega t)\)	III. Periodic with time period \(T = \dfrac{\pi}{\omega}\) and SHM
D. \(\cos\omega t + \cos 2\omega t\)	IV. Non-periodic

Choose the correct answer from the options given below :

Light is incident normally on a completely absorbing surface with an energy flux of \(25\,W\,cm^{-2}.\) If the surface has an area of \(25\,cm^2,\) the maximum momentum transferred to the surface in \(40\,min\) time duration will be

\(NO_2\) required for a reaction is produced by the decomposition of \(N_2O_5\) in \(CCl_4\) as per the equation  \(2N_2O_5 (g) \to 4NO_2 (g) + O_2 (g)\) The initial concentration of \(N_2O_5\) is \(3.00\, mol\, L^{-1}\) and it is \(2.75\, mol\, L^{-1}\) after \(30\, minutes\). The rate of formation of \(NO_2\) is ............... \(mol\, L^{-1}\, min^{-1}\)

The moles of methane required to produce \(81 \,g\) of water after complete combustion is \(....\,\times 10^{-2}\, mol.\) [nearest integer]

A particle of mass \(m\) moves on a straight line with its velocity increasing with distance according to the equation \(\mathrm{v}=\alpha \sqrt{\mathrm{x}}\), where \(\alpha\) is a constant. The total work done by all the forces applied on the particle during its displacement from \(\mathrm{x}=0\) to \(\mathrm{x}=\mathrm{d}\), will be _______.

If the tangent to the curve \(y=x^{3}-x^{2}+x\) at the point \((a, b)\) is also tangent to the curve \(y=5 x^{2}+\) \(2 x -25\) at the point \((2,-1)\), then \(|2 a +9 b |\) is equal to \(........\)