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The Gibbs energy for the decomposition of $Al_{2}O_{3}$ at $500_{∘}C$ is as follows: $32 Al_{2}O_{3}→34 Al+O_{2},Δ_{r}G=+966kJ mol_{−1}$ The potential difference needed for electrolytic reduction of $Al_{2}O_{3}$ at $500_{∘}C$ is at least

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The $pK_{a}$ of a weak acid, HA, is 4.80. The $pK_{b}$ of a weak base, BOH, is 4.78. The pH of an aqueous solution of the corresponding salt, BA, will be

The sum of the series $2!1 −3!1 +4!1 −…$ upto infinity is

The statement $pqp $is equivalent to

The dimension of magnetic field in M, L, T and C (Coulomb) is given as

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If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then. Which of the following does not change with time ?

The projections of a vector on the three coordinate axis are $6,3,2$ respectively. The direction cosines of the vector are(A) $6,−3,2$ (B) $56 ,5−3 ,52 $ (C) $76 ,7−3 ,72 $ (D) $7−6 ,7−3 ,72 $

The bond dissociation energy of $B−FinBF_{3}is646kJmol_{−1}$ whereas that of $C−FinCF_{4}is515kJmol_{−1}$. The correct reason for higher B-F bond dissociation energy as compared to that of $C−F$ is