The \(\mathrm{pH}\) of \(0.01 \mathrm{M} \mathrm{BOH}\) solution is 10 . What is its degree of dissociation?
(Given \(\mathrm{K}_{\mathrm{b}}\) of \(\mathrm{BOH}\) is \(1 \times 10^{-6}\) )

Identify the answer in which, the trends corresponding to hydroxides of group 2 element (from \(\mathrm{Mg}(\mathrm{OH})_2\) to \(\mathrm{Ba}(\mathrm{OH})_2\) ) are correctly shown
\begin{array}{lll}
basic character & chemical stability & solubility \\
\end{array}

The number of optical isomers possible for $2-$Bromo-$3-$Chlorobutane are

Which one of the following order is correct for the first ionisation energies of the elements?

\(\mathrm{X}_2\) reacts with water to form \(\mathrm{HX}(\mathrm{aq})\) and \(\mathrm{HOX}(\mathrm{aq}) . \mathrm{Y}_2\) reacts with water to form \(\mathrm{O}_2(\mathrm{~g})\), \(\mathrm{Y}^{-}(\mathrm{aq})\) and \(\mathrm{H}^{+}(\mathrm{aq}) \cdot \mathrm{Z}_2\) does not react with water. \(\mathrm{X}_2, \mathrm{Y}_2, \mathrm{Z}_2\) are respectively

In photoelectric effect, if the energy required to overcome the attractive forces on the electron, (work functions) of \(\mathrm{Li}, \mathrm{Na}\) and \(\mathrm{Rb}\) are \(2.41 \mathrm{eV}\), \(2.30 \mathrm{eV}\) and \(2.09 \mathrm{eV}\) respectively, the work function of ' \(\mathrm{K}\) ' could approximately be in \(\mathrm{eV}\)

Vinegar and butter are the sources for which of the following carboxylic acids respectively?

If \(a>0 .[\cdot]\) denotes greatest integer function and \(\lim _{x \rightarrow a^{-}}\left(\frac{|x|^3}{a}-\left[\frac{x}{a}\right]^3\right)=k, \lim _{x \rightarrow a^{+}}\left(\frac{|x|^3}{a}-\left[\frac{x}{a}\right]^3\right)=l\), then

The \(\mathrm{p} K_a\) values of four carboxylic acids are \(4.76,4.19,0.23\) and 3.41 respectively. The \(\mathrm{p} K_a\) value of strongest carboxylic acid among them is

Match the following List I with List II.
\(\begin{array}{|c|c|c|}
\hline & \text { List I } & \text { List II } \\
\hline \text { (A) } & \text { Transverse wave (i) } & \begin{array}{l}
\text {Vibrations parallel to the } \\
\text {direction of propagation }
\end{array} \\
\hline \text { (B) } & \begin{array}{l}
\text {Longitudinal wave }
\end{array} & \begin{array}{l}
\text {Vibrations perpendicular to } \\
\text {the direction of propagation }
\end{array} \\
\hline \text { (C) } & \text { Beats } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in the opposite directions }
\end{array} \\
\hline \text { (D) } & \text { Stationary waves (iv) } & \begin{array}{l}
\text {Superposition of waves } \\
\text {travelling in same direction }
\end{array} \\
\hline
\end{array}\)
The correct answer is

If the line \(x+2 y=k\) intersects the curve \(x^2-x y+y^2+3 x+3 y-2=0\) at two points \(A\) and \(B\) and if \(O\) is the origin, then the condition for \(\angle \mathrm{AOB}=90^{\circ}\) is

A body of mass \(\mathrm{I} \mathrm{kg}\) is suspended from a spring of negligible mass. Another body of mass \(500 \mathrm{~g}\) moving vertically upwards hits the suspended body with a velocity of \(3 \mathrm{~ms}^{-1}\) and gets embedded in it. If the frequency of oscillation of the system of the two bodies after collision is \(\frac{10}{\pi} \mathrm{Hz}\), the amplitude of the motion and the spring constant are respectively,

The electron gain enthalpy ${\Delta }_{\mathrm{eg}}\mathrm{H}$ of $\mathrm{Cl}\left(\mathrm{g}\right)$ is $-349 \mathrm{kJ} {\mathrm{mol}}^{-1}$. If the ground state energy of $\mathrm{Cl}\left(\mathrm{g}\right)$ is $x \mathrm{kJ} {\mathrm{mol}}^{-1},$the ground state energy $\left(\mathrm{in} \mathrm{kJ} {\mathrm{mol}}^{-1}\right)$ of ${\mathrm{Cl}}^{-}\left(\mathrm{g}\right)$ is