Chemistry

Observe the following stoichiometric equation
$$ \mathrm{P}_4+3 \mathrm{OH}^{-}+3 \mathrm{H}_2 \mathrm{O} \rightarrow \mathrm{PH}_3+3 x^{-} $$
What is the conjugate acid of $x^{-}$?
Given below are two statements :
Statement I For isothermal irreversible change of an ideal gas, $q=-w=p_{\text {ext }}\left(V_{\text {final }}-V_{\text {initial }}\right)$
Statement II For adiabatic change, $\Delta U=w_{\text {adiabatic }}$
The correct answer is :

$K_{\mathrm{c}}$ for the following reaction is 99.0
$$ A_2(g) \stackrel{T(K)}{\rightleftharpoons} B_2(g) $$
In a one litre flask, 2 moles of $A_2$ was heated to $T(\mathrm{~K})$ and the above equilibrium is reached. The concentration at equilibrium of $A_2$ and $B_2$ are $C_1\left(A_2\right)$ and $C_2\left(B_2\right)$ respectively. Now, one mole of $A_2$ was added to flask and heated to $T(\mathrm{~K})$ to established the equilibrium again. The concentration of $A_2$ and $B_2$ are $C_3\left(A_2\right)$ and $C_4\left(B_2\right)$ respectively. what is the value of $C_3\left(A_2\right)$ in $\mathrm{mol} \mathrm{L}^{-1}$ ?
The correct statements among the following are
(i) saline hydrides produce $\mathrm{H}_2$ gas when reacted with water
(ii) presently $\sim 77 \%$ of the industrial dihydrogen is produced from coal
(iii) commercially marketed $\mathrm{H}_2 \mathrm{O}_2$ contains $3 \% \mathrm{H}_2 \mathrm{O}_2$
Identify the correct statements
i. Oxidation of $\mathrm{NaBH}_4$ with $\mathrm{I}_2$ gives $\mathrm{B}_2 \mathrm{H}_6$
ii. $\mathrm{B}_2 \mathrm{H}_6$ burns in oxygen and releases an enormous amount of energy
iii. $\mathrm{B}_2 \mathrm{H}_6$ on hydrolysis gives a tribasic acid
Two statements are given below :
I. In dry cleaning, the solvent $\mathrm{Cl}_2 \mathrm{C}=\mathrm{CCl}_2$ was earlier used and now it is replaced by liquefied $\mathrm{CO}_2$
II. In bleaching of paper, $\mathrm{H}_2 \mathrm{O}_2$ was used earlier and now it is replaced by chlorine gas. Correct anwer is
What are $X$ and $Y$ respectively in the following reaction sequence?
$$ \text { Isopentane } \xrightarrow{\mathrm{KMnO}_4} X \xrightarrow{\text { Dehydration }} Y \text { Major } $$
Some substances are given below
$$ \begin{aligned} & \mathrm{Ag}, \mathrm{CO}_2(s), \mathrm{SiO}_2, \mathrm{ZnS} \\ & \mathrm{SO}_2(s), \mathrm{AlN}, \mathrm{HCl}(\mathrm{~s}), \mathrm{H}_2 \mathrm{O}(\mathrm{~s}) \end{aligned} $$
The number of molecular solids and network solids in the above list is respectively.





Mathematics
Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$
Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$
Which one of the following is correct?
The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$
If $f(x)=\left\{\begin{array}{ll}3 a x-2 b, & x>1 \\ a x+b+1, & x<1\end{array}\right.$ and
$\lim \limits_{x \rightarrow 1} f(x)$ exists, then the relation between $a$ and $b$ is
If $f(x)=\left\{\begin{array}{cl}x^\alpha \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$
which of the following is true?
Physics





