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In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

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The largest interval lying in $(−2π ,2π )$for which the function \displaystyle{\left[{f{{\left({x}\right)}}}={4}^{{-{{x}}}}^{2}+{{\cos}^{{-{1}}}{\left(\frac{{x}}{{2}}-{1}\right)}}+{\log{{\left({\cos{{x}}}\right)}}}\right]} is defined, is

Larger number of oxidation states are exhibited by the actinoids than those by the lanthanoids, the main reason being

The area enclosed between the curves $y_{2}=xandy=∣x∣$is

A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the $4_{th}$ bright fringe of the unknown light. From this data, the wavelength of the unknown light is

Phenol, when it first react with concentrated sulphuric acid and then with concentrated nitric acid, gives

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yzplane at the point $(0,217 ,2−13 )$.Then

One kg of a diatomic gas is at a pressure of $8×10_{4}N/m_{2}$. The density of the gas is $4kg/m_{3}$. What is the energy of the gas due to its thermal motion ?

Among the following substituted silanes the one which will give rise to cross linked silicone polymer on hydrolysis is