If the equilibrium constant for \(A \rightleftharpoons B+C\) is \(K _{ eq }^{(1)}\) and that of \(B + C \rightleftharpoons P \quad\) is \(K _{ eq }^{(2)},\) the equilibrium constant for \(A \rightleftharpoons P\) is :-

Chromatographic techniques based on the principle of differential adsorption is _______. \(A\). Column chromatography \(B\). Thin layer chromatography \(C\). Paper chromatography Choose the most appropriate answer from the options given below:

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

The pair of lanthanides in which both elements have high third-ionization energy is:

Which of the following xenon-oxo compounds may not be obtained by hydrolysis of xenon fluorides?

The order of stability of the following carbocations is : \((I)\,\,C{H_2} = CH - \mathop C\limits^ \oplus  {H_2}\) \((II)\,\,C{H_3} - CH_2 - \mathop C\limits^ \oplus  {H_2}\)

Given below are two statements. Statement \(I :\) Phenols are weakly acidic. Statement \(II :\) Therefore they are freely soluble in \(NaOH\) solution and are weaker acids than alcohols and water. Choose the most appropriate option

The explosive in a Hydrogen bomb is a mixture of \({ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3\) and \({ }_3 \mathrm{Li}^6\) in some condensed form. The chain reaction is given by \( { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \) \( { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1\) During the explosion the energy released is approximately [Given : \(\mathrm{M}(\mathrm{Li})=6.01690\  \mathrm{amu} . \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \  amu.\) \(\mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388\  \mathrm{amu}\),\( and\ \)\(1 \ \mathrm{amu}=931.5\) \(\mathrm{MeV}]\)

If \(\sin\left(\dfrac{\pi}{18}\right) \sin\left(\dfrac{5\pi}{18}\right) \sin\left(\dfrac{7\pi}{18}\right) = K\), then the value of \(\sin\left(\dfrac{10K\pi}{3}\right)\) is :

At some location on earth the horizontal component of earth’s magnetic field is \(18\times10^{-6}\,T\). At this location, magnetic needle of length \(0.12\, m\) and pole strength \(1.8\, A\,m\) is suspended from its mid-point using a thread, it makes \(45^o\) angle with horizontal in equilibrium. To keep this needle horizontal, the vertical force that should be applied at one of its ends is

A wire \(A\), bent in the shape of an arc of a circle, carrying a current of \(2\, A\) and having radius \(2\, cm\) and another wire \(B ,\) also bent in the shape of arc of a circle, carrying a current of \(3\, A\) and having radius of \(4\, cm ,\) are placed as shown in the figure. The ratio of the magnetic fields due to the wires \(A\) and \(B\) at the common centre \(O\) is

The value of \(\lim _{n \rightarrow \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{(2 j-1)+8 n}{(2 j-1)+4 n}\) is equal to:

Given below are two statements : one is labelled as Assertion \((A)\) and the other is labelled as Reason \((R)\). Assertion \((A)\) : \(\alpha\)-halocarboxylic acid on reaction with dil. \(NH _3\) gives good yield of \(\alpha\)-amino carboxylic acid whereas the yield of amines is very low when prepared from alkyl halides. Reason \((R):\) Amino acids exist in zwitter ion form in aqueous medium. In the light of the above statements, choose the correct answer from the options given below :