What is the molecular geometry of \(\mathrm{H}_3 \mathrm{O}^{+}\)?

Copper matte contains

\(6 \mathrm{~g}\) of graphite is burnt in a bomb calorimeter at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. The temperature of water increased from \(25^{\circ} \mathrm{C}\) to \(31^{\circ} \mathrm{C}\). If \(\Delta H\) of this reaction is \(-248 \mathrm{~kJ}\) mol, find out \(\mathrm{C}_V\) (in \(\mathrm{kJ} \mathrm{K}^{-1}\) ) of bomb calorimeter.

$\mathrm{Be}$ and $\mathrm{Al}$ show similarities in properties due to the diagonal relationship except in the property $\mathrm{X}$ given below. What is $\mathrm{X}$?

From the following data
\[
\begin{aligned}
& \mathrm{CH}_3 \mathrm{OH}(l)+\frac{3}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{CO}_2(g)+2 \mathrm{H}_2 \mathrm{O}(l) \\
& \Delta_r H^{\circ}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{H}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \longrightarrow \mathrm{H}_2 \mathrm{O}(l) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-286 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
& \mathrm{C}(\text { graphite })+\mathrm{O}_2(\mathrm{~g}) \longrightarrow \mathrm{CO}_2(\mathrm{~g}) \text {; } \\
& \Delta_r \mathrm{H}^{\circ}=-393 \mathrm{~kJ} \mathrm{~mol}^{-1} \\
&
\end{aligned}
\]
The standard enthalpy of formation of \(\mathrm{CH}_3 \mathrm{OH}(l)\) in \(\mathrm{kJ} \mathrm{mol}^{-1}\) is

The energy of second Bohr orbit of hydrogen atom is -3.4 eV. The energy of the fourth Bohr orbit of the \(\mathrm{He}^{+}\)ion will be

If molten $\mathrm{NaCl}$ contains ${\mathrm{SrCl}}_2$ as impurity, crystallization can generate

The equation of the plane passing through \((1,1,1)\) and \((1,-1,-1)\) and perpendicular to \(2 x-y+z+5=0\) is :

If \(\lim _{x \rightarrow 0} \frac{[(a-n) n x-\tan x] \sin n x}{x^2}=0,(n \neq 0)\)
then the minimum possible positive value of \(a\) is

Match the following?

	Column$-\mathrm{I}$		Column$-\mathrm{II}$
(a)	Ratio of change in time period of a simple pendulum with temperature to its original time period	(i)	$\alpha \mathrm{\Delta }T$
(b)	Ratio of the value of a length to its scale reading	(ii)	$T$
(c)	Reciprocal of coefficient of volume expansion for an ideal gas of constant pressure	(iii)	$(1+\alpha \mathrm{\Delta }T)$
(d)	$\frac{F}{YA}=$	(iv)	$\frac{1}{2}\alpha \mathrm{\Delta }T$

If \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-coplanar vectors, then match the items of List-I with those of List-II.


The correct answer is
A \(\quad\) B \(\quad\) B \(\quad\) D

The process which invovles the treatment of the ore with a suitable reagent so as to make it soluble but not impurities is called

\(\mathrm{A}(2,3), \mathrm{B}(3,-5)\) are two vertices of \(\triangle \mathrm{ABC}\). If the centroid of the \(\triangle \mathrm{ABC}\) moves on the line \(2 x+y-2=0\), then the locus of \(\mathrm{C}\) is