JEE Main 2023 (Online) 30th January Evening Shift

The correct order of $\mathrm{pK}_{\mathrm{a}}$ values for the following compounds is:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: can be easily reduced using $\mathrm{Zn}-\mathrm{Hg} / \mathrm{HCl}$ to
Reason $\mathrm{R}: \mathrm{Zn}-\mathrm{Hg} / \math...

Number of compounds from the following which will not dissolve in cold $\mathrm{NaHCO}_{3}$ and $\mathrm{NaOH}$ solutions but will dissolve in hot $\mathrm{NaOH}$ solution is ________.

Match List I with List II:

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A short peptide on complete hydrolysis produces 3 moles of glycine (G), two moles of leucine (L) and two moles of valine (V) per mole of peptide. The number of peptide linkages in it are ________.

Consider the following equation:

$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g), \Delta H=-190 \mathrm{~kJ}$

The number of factors which will increase the yield of $\mathrm{SO}_{3}$ at equilibrium from th...

An organic compound undergoes first-order decomposition. If the time taken for the $60 \%$ decomposition is $540 \mathrm{~s}$, then the time required for $90 \%$ decomposition will be ________ s. (Nearest integer).

Given: $\ln 10=2.3 ; \lo...

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $\mathbf{R}$.

Assertion A: Antihistamines do not affect the secretion of acid in stomach.

Reason $\mathbf{R}$ : Antiallergic and antacid dr...

The most stable carbocation for the following is:

In the above conversion of compound $(\mathrm{X})$ to product $(\mathrm{Y})$, the sequence of reagents to be used will be:

Match List I with List II:

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The $\mathrm{Cl}-\mathrm{Co}-\mathrm{Cl}$ bond angle values in a fac- $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{3} \mathrm{Cl}_{3}\right]$ complex is/are :

Formulae for Nessler's reagent is :

$\mathrm{KMnO}_4$ oxidises $\mathrm{I}^{-}$ in acidic and neutral/faintly alkaline solutions, respectively, to :

The electrode potential of the following half cell at $298 \mathrm{~K}$

$\mathrm{X}\left|\mathrm{X}^{2+}(0.001 \mathrm{M}) \| \mathrm{Y}^{2+}(0.01 \mathrm{M})\right| \mathrm{Y}$ is _______ $\times 10^{-2} \mathrm{~V}$ (Nearest integer)

Gi...

The water quality of a pond was analyzed and its BOD was found to be 4. The pond has :

Decreasing order towards SN 1 reaction for the following compounds is:

Given below are two statements:

Statement I: During Electrolytic refining, the pure metal is made to act as anode and its impure metallic form is used as cathode.

Statement II: During the Hall-Heroult electrolysis process, purified $\math...

Boric acid is solid, whereas $\mathrm{BF}_3$ is gas at room temperature because of :

Bond dissociation energy of "E-H" bond of the "$\mathrm{H}_{2} \mathrm{E}$ " hydrides of group 16 elements (given below), follows order.
A. $\mathrm{O}$
B. $\mathrm{S}$
C. Se
D. $\mathrm{Te}$

Choose the correct from the options given below...

Chlorides of which metal are soluble in organic solvents :

Which of the following reaction is correct?

Iron oxide FeO, crystallises in a cubic lattice with a unit cell edge length of 5.0 Å. If density of the $\mathrm{FeO}$ in the crystal is $4.0 \mathrm{~g} \mathrm{~cm}^{-3}$, then the number of $\mathrm{FeO}$ units present per unit cell is ...

Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Ne...

$1 \mathrm{~L}, 0.02 \mathrm{M}$ solution of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm{SO}_{4}\right]$ Br is mixed with $1 \mathrm{~L}, 0.02 \mathrm{M}$ solution of $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{5} \mathrm...

The strength of 50 volume solution of hydrogen peroxide is ______ $\mathrm{g} / \mathrm{L}$ (Nearest integer).

Given:

Molar mass of $\mathrm{H}_{2} \mathrm{O}_{2}$ is $34 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar volume of gas at $\mathrm{ST...

Maximum number of electrons that can be accommodated in shell with $n=4$ are:

The wave function $(\Psi)$ of $2 \mathrm{~s}$ is given by
\(\Psi_{2 \mathrm{~s}}=\frac{1}{2 \sqrt{2 \pi}}\left(\frac{1}{a_0}\right)^{1 / 2}\left(2-\frac{r}{a_0}\right) e^{-r / 2 a_0}\)
At $r=r_0$, radial node is formed. Thus, $r_0$ in ter...

The graph of $\log \frac{x}{m}$ vs $\log \mathrm{p}$ for an adsorption process is a straight line inclined at an angle of $45^{\circ}$ with intercept equal to $0.6020$. The mass of gas adsorbed per unit mass of adsorbent at the pressure of ...

1 mole of ideal gas is allowed to expand reversibly and adiabatically from a temperature of $27^{\circ} \mathrm{C}$. The work done is $3 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The final temperature of the gas is ________ $\mathrm{K}$ (Nearest in...

A vector $\vec{v}$ in the first octant is inclined to the $x$-axis at $60^{\circ}$, to the $y$-axis at 45 and to the $z$-axis at an acute angle. If a plane passing through the points $(\sqrt{2},-1,1)$ and $(a, b, c)$, is normal to $\vec{v}$...

If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is :

Let a line $L$ pass through the point $P(2,3,1)$ and be parallel to the line $x+3 y-2 z-2=0=x-y+2 z$. If the distance of $L$ from the point $(5,3,8)$ is $\alpha$, then $3 \alpha^2$ is equal to :

If the functions $f(x)=\frac{x^3}{3}+2 b x+\frac{a x^2}{2}$
and $g(x)=\frac{x^3}{3}+a x+b x^2, a \neq 2 b$ have a common extreme point, then $a+2 b+7$ is equal to :

Let $q$ be the maximum integral value of $p$ in $[0,10]$ for which the roots of the equation $x^2-p x+\frac{5}{4} p=0$ are rational. Then the area of the region $\left\{(x, y): 0 \leq y \leq(x-q)^2, 0 \leq x \leq q\right\}$ is :

Let $A$ be the area of the region
$\left\{(x, y): y \geq x^2, y \geq(1-x)^2, y \leq 2 x(1-x)\right\}$.
Then $540 \mathrm{~A}$ is equal to :

Let $x=(8 \sqrt{3}+13)^{13}$ and $y=(7 \sqrt{2}+9)^9$. If $[t]$ denotes the greatest integer $\leq t$, then :

$50^{\text {th }}$ root of a number $x$ is 12 and $50^{\text {th }}$ root of another number $y$ is 18 . Then the remainder obtained on dividing $(x+y)$ by 25 is ____________.

Let $P\left(a_1, b_1\right)$ and $Q\left(a_2, b_2\right)$ be two distinct points on a circle with center $C(\sqrt{2}, \sqrt{3})$. Let $\mathrm{O}$ be the origin and $\mathrm{OC}$ be perpendicular to both $\mathrm{CP}$ and $\mathrm{CQ}$. If ...

$\lim\limits_{n \rightarrow \infty} \frac{3}{n}\left\{4+\left(2+\frac{1}{n}\right)^2+\left(2+\frac{2}{n}\right)^2+\ldots+\left(3-\frac{1}{n}\right)^2\right\}$ is equal to :

The solution of the differential equation
$\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is :

The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is :

Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f: A \rightarrow A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to ___________.

If $\int \sqrt{\sec 2 x-1} d x=\alpha \log _e\left|\cos 2 x+\beta+\sqrt{\cos 2 x\left(1+\cos \frac{1}{\beta} x\right)}\right|+$ constant, then $\beta-\alpha$ is equal to ____________.

Let $a_{1}=1, a_{2}, a_{3}, a_{4}, \ldots .$. be consecutive natural numbers.

Then $\tan ^{-1}\left(\frac{1}{1+a_{1} a_{2}}\right)+\tan ^{-1}\left(\frac{1}{1+a_{2} a_{3}}\right)+\ldots . .+\tan ^{-1}\left(\frac{1}{1+a_{2021} a_{2022}}\righ...

Let $f, g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as
$f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.$
$g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-...

Consider the following statements:
P : I have fever
Q: I will not take medicine
$\mathrm{R}$ : I will take rest.
The statement "If I have fever, then I will take medicine and I will take rest" is equivalent to :

For $\alpha, \beta \in \mathbb{R}$, suppose the system of linear equations
$$ \begin{aligned} & x-y+z=5 \\ & 2 x+2 y+\alpha z=8 \\ & 3 x-y+4 z=\beta \end{aligned} $$
has infinitely many solutions. Then $\alpha$ and $\beta$ are the roots of ...

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>1$, then :

Let $A$ be a point on the $x$-axis. Common tangents are drawn from $A$ to the curves $x^2+y^2=8$ and $y^2=16 x$. If one of these tangents touches the two curves at $Q$ and $R$, then $(Q R)^2$ is equal to :