If $I_n = \int \sin^n x \, dx$,then $n I_n - (n-1) I_{n-2}$ equals

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines represented by $5x^2 - 8xy + 3y^2 = 0$,then $m_1 : m_2$ equals

If $f: R \rightarrow R$ is defined by $f(x) = [\frac{x}{5}]$ for $x \in R$,where $[y]$ denotes the greatest integer not exceeding $y$,then $\{f(x) : |x| < 71\}$ is equal to

The ratio of the ionization energy of a Bohr hydrogen atom to that of a Bohr hydrogen-like lithium atom is:

The compound$(s)$ with $P - H$ bond$(s)$ is$(are)$
$(A) \ H _3 PO _4$ $(B) \ H _3 PO _3$ $(C) \ H _4 P _2 O _7$ $(D) \ H _3 PO _2$

$1.00 \ g$ of a non-electrolyte solute (molar mass $250 \ g \ mol^{-1}$) is dissolved in $51.2 \ g$ of benzene. If the freezing point depression constant of benzene is $5.12 \ K \ kg \ mol^{-1}$,then the freezing point of benzene decreases by ...... $K$.