JEE Main 2024 (Online) 1st February Morning Shift

Identify $A$ and $B$ in the following sequence of reaction

Match List - I with List - II.

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Ionic reactions with organic compounds proceed through :
(A) homolytic bond cleavage
(B) heterolytic bond cleavage
(C) free radical formation
(D) primary free radical
(E) secondary free radical

Choose the correct answer from the options gi...

Which of the following compound will most easily be attacked by an electrophile?

Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is _______ .

Number of optical isomers possible for 2-chlorobutane ________.

If one strand of a DNA has the sequence ATGCTTCA, sequence of the bases in complementary strand is :

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): $\mathrm{PH}_3$ has lower boiling point than $\mathrm{NH}_3$.
Reason (R) : In liquid state $\mathrm{NH}_3$ molecules ar...

Arrange the bonds in order of increasing ionic character in the molecules. $\mathrm{LiF}$, $\mathrm{K}_2 \mathrm{O}, \mathrm{N}_2, \mathrm{SO}_2$ and $\mathrm{ClF}_3$ :

The number of molecules/ion/s having trigonal bipyramidal shape is _______.
$\mathrm{PF}_5, \mathrm{BrF}_5, \mathrm{PCl}_5,\left[\mathrm{Pt} \mathrm{Cl}_4\right]^{2-}, \mathrm{BF}_3, \mathrm{Fe}(\mathrm{CO})_5$

The lowest oxidation number of an atom in a compound $\mathrm{A}_2 \mathrm{B}$ is -2 . The number of electrons in its valence shell is _______.

The ratio of $\frac{{ }^{14} \mathrm{C}}{{ }^{12} \mathrm{C}}$ in a piece of wood is $\frac{1}{8}$ part that of atmosphere. If half life of ${ }^{14} \mathrm{C}$ is 5730 years, the age of wood sample is ________ years.

Given below are two statements :
Statement (I) : The $\mathrm{NH}_2$ group in Aniline is ortho and para directing and a powerful activating group.

Statement (II) : Aniline does not undergo Friedel-Craft's reaction (alkylation and acylation...

Given below are two statements :
Statement (I) : Aminobenzene and aniline are same organic compounds.
Statement (II) : Aminobenzene and aniline are different organic compounds.
In the light of the above statements, choose the most appropria...

Which of the following complex is homoleptic?

Given below are two statements :
Statement (I) : A solution of $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ is green in colour.
Statement (II) : A solution of $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ is colour...

The potential for the given half cell at $298 \mathrm{~K}$ is (-) __________ $\times 10^{-2} \mathrm{~V}$
$$
\begin{aligned}
& 2 \mathrm{H}_{(\mathrm{aq})}^{+}+2 \mathrm{e}^{-} \longrightarrow \mathrm{H}_2(\mathrm{~g}) \\\\
& {\left[\mathrm...

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Haloalkanes react with KCN to form alkyl cyanides as a main product while with $\mathrm{AgCN}$ form isocyanide as the...

$\mathrm{K}_{\mathrm{a}}$ for $\mathrm{CH}_3 \mathrm{COOH}$ is $1.8 \times 10^{-5}$ and $\mathrm{K}_{\mathrm{b}}$ for $\mathrm{NH}_4 \mathrm{OH}$ is $1.8 \times 10^{-5}$. The $\mathrm{pH}$ of ammonium acetate solution will be _________.

Among the following oxides of p-block elements, number of oxides having amphoteric nature is ________.$\mathrm{Cl}_2 \mathrm{O}_7, \mathrm{CO}, \mathrm{PbO}_2, \mathrm{~N}_2 \mathrm{O}, \mathrm{NO}, \mathrm{Al}_2 \mathrm{O}_3, \mathrm{SiO}_...

In Kjeldahl's method for estimation of nitrogen, $\mathrm{CuSO}_4$ acts as :

Given below are two statements :
Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution.

Statement (II) : In this titration phenolphthalein can be used as indicator.
In the light...

Which of the following reactions are disproportionation reactions?
(A) $\mathrm{Cu}^{+} \rightarrow \mathrm{Cu}^{2+}+\mathrm{Cu}$
(B) $3 \mathrm{MnO}_4^{2-}+4 \mathrm{H}^{+} \longrightarrow 2 \mathrm{MnO}_4^{-}+\mathrm{MnO}_2+2 \mathrm{H}_2...

In acidic medium, $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ shows oxidising action as represented in the half reaction:
$$
\mathrm{Cr}_2 \mathrm{O}_7{ }^{2-}+\mathrm{XH}^{+}+\mathrm{Ye}^{\ominus} \rightarrow 2 \mathrm{~A}+\mathrm{ZH}_2 \mat...

The number of white coloured salts, among the following is
(a) $\mathrm{SrSO}_4$
(b) $\mathrm{Mg}\left(\mathrm{NH}_4\right) \mathrm{PO}_4$
(c) $\mathrm{BaCrO}_4$
(d) $\mathrm{Mn}(\mathrm{OH})_2$
(e) $\mathrm{PbSO}_4$
(f) $\mathrm{PbCrO}_4$
...

We have three aqueous solutions of $\mathrm{NaCl}$ labelled as ' $\mathrm{A}$ ', ' $\mathrm{B}$ ' and ' $\mathrm{C}$ ' with concentration $0.1 \mathrm{M}$, $0.01 \mathrm{M}$ and $0.001 \mathrm{M}$, respectively. The value of van 't Hoff fac...

Consider the following reaction :
\(3 \mathrm{PbCl}_2+2\left(\mathrm{NH}_4\right)_3 \mathrm{PO}_4 \rightarrow \mathrm{Pb}_3\left(\mathrm{PO}_4\right)_2+6 \mathrm{NH}_4 \mathrm{Cl}\)

If $72 ~\mathrm{mmol}$ of $\mathrm{PbCl}_2$ is mixed wi...

In case of isoelectronic species the size of $\mathrm{F}^{-}, \mathrm{Ne}$ and $\mathrm{Na}^{+}$is affected by :

According to the wave-particle duality of matter by de-Broglie, which of the following graph plot presents most appropriate relationship between wavelength of electron $(\lambda)$ and momentum of electron $(p)$?

Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :

If the shortest distance between the lines $\frac{x-\lambda}{-2}=\frac{y-2}{1}=\frac{z-1}{1}$ and $\frac{x-\sqrt{3}}{1}=\frac{y-1}{-2}=\frac{z-2}{1}$ is 1 , then the sum of all possible values of $\lambda$ is :

Let the line of the shortest distance between the lines
$$
\begin{aligned}
& \mathrm{L}_1: \overrightarrow{\mathrm{r}}=(\hat{i}+2 \hat{j}+3 \hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k}) \text { and } \\\\
& \mathrm{L}_2: \overrightarrow{\mathrm...

If $5 f(x)+4 f\left(\frac{1}{x}\right)=x^2-2, \forall x \neq 0$ and $y=9 x^2 f(x)$, then $y$ is strictly increasing in :

The area enclosed by the curves $x y+4 y=16$ and $x+y=6$ is equal to :

If the Coefficient of $x^{30}$ in the expansion of $\left(1+\frac{1}{x}\right)^6\left(1+x^2\right)^7\left(1-x^3\right)^8 ; x \neq 0$ is $\alpha$, then $|\alpha|$ equals ___________.

Let $C: x^2+y^2=4$ and $C^{\prime}: x^2+y^2-4 \lambda x+9=0$ be two circles. If the set of all values of $\lambda$ so that the circles $\mathrm{C}$ and $\mathrm{C}$ intersect at two distinct points, is $\mathrm{R}-[\mathrm{a}, \mathrm{b}]$,...

Let $\mathrm{S}=|\mathrm{z} \in \mathrm{C}:| z-1 \mid=1$ and $(\sqrt{2}-1)(z+\bar{z})-i(z-\bar{z})=2 \sqrt{2} \mid$. Let $z_1, z_2 \in \mathrm{S}$ be such that $\left|z_1\right|=\max\limits_{z \in s}|z|$ and $\left|z_2\right|=\min\limits _{...

Let $\mathrm{P}=\{\mathrm{z} \in \mathbb{C}:|z+2-3 i| \leq 1\}$ and $\mathrm{Q}=\{\mathrm{z} \in \mathbb{C}: z(1+i)+\bar{z}(1-i) \leq-8\}$. Let in $\mathrm{P} \cap \mathrm{Q}$, $|z-3+2 i|$ be maximum and minimum at $z_1$ and $z_2$ respectiv...

The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$ equals :

If $\int\limits_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x \mathrm{~d} x}{\left(1+\mathrm{e}^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _{\mathrm{e}}(3+2 \sqrt{2})$, where $\alpha, \beta$ are integers, then $\alpha^2+\...

Let $y=y(x)$ be the solution of the differential equation
$\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x(x+y)^3-x(x+y)-1, y(0)=1$.
Then, $\left(\frac{1}{\sqrt{2}}+y\left(\frac{1}{\sqrt{2}}\right)\right)^2$ equals :

If $x=x(t)$ is the solution of the differential equation $(t+1) \mathrm{d} x=\left(2 x+(t+1)^4\right) \mathrm{dt}, x(0)=2$, then, $x(1)$ equals _________.

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, \mathrm{a}>\mathrm{b}$ be an ellipse, whose eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latusrectum is $\sqrt{14}$. Then the square of the eccentricity of $\frac{x^2}{a^2}-\frac{y^2}{b^...

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ and $g: \mathbf{R} \rightarrow \mathbf{R}$ be defined as
$f(x)=\left\{\begin{array}{ll}\log _{\mathrm{e}} x, & x>0 \\ \mathrm{e}^{-x}, & x \leq 0\end{array}\right.$ and
$g(x)=\left\{\begin{array}...

For $0<\theta<\pi / 2$, if the eccentricity of the hyperbola
$x^2-y^2 \operatorname{cosec}^2 \theta=5$ is $\sqrt{7}$ times eccentricity of the ellipse $x^2 \operatorname{cosec}^2 \theta+y^2=5$, then the value of $\theta$ is :

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be defined as :
$$ f(x)= \begin{cases}\frac{a-b \cos 2 x}{x^2} ; & x<0 \\\\ x^2+c x+2 ; & 0 \leq x \leq 1 \\\\ 2 x+1 ; & x>1\end{cases} $$

If $f$ is continuous everywhere in $\mathbf{R}$ and $m$ i...

Let $\{x\}$ denote the fractional part of $x$ and $f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0$. If $\mathrm{L}$ and $\mathrm{R}$ respectively denotes the left hand limit and the right hand limi...

If $\mathrm{A}=\left[\begin{array}{cc}\sqrt{2} & 1 \\ -1 & \sqrt{2}\end{array}\right], \mathrm{B}=\left[\begin{array}{ll}1 & 0 \\ 1 & 1\end{array}\right], \mathrm{C}=\mathrm{ABA}^{\mathrm{T}}$ and $\mathrm{X}=\mathrm{A}^{\mathrm{T}} \mathrm...

If the system of equations
$$ \begin{aligned} & 2 x+3 y-z=5 \\\\ & x+\alpha y+3 z=-4 \\\\ & 3 x-y+\beta z=7 \end{aligned} $$
has infinitely many solutions, then $13 \alpha \beta$ is equal to :

Let the line $\mathrm{L}: \sqrt{2} x+y=\alpha$ pass through the point of the intersection $\mathrm{P}$ (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola $x^2=2 y$. Let the line $\mathrm{L}$ touch two circles $\mathrm{C}_1$ ...