JEE Main 2024 (Online) 27th January Morning Shift

Given below are two statements :
Statement (I) : p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol.
Statement (II) : Ethanol will give immediate turbidity with Lucas reagent.
In the light of the above statements, choose the ...

The ascending order of acidity of \(-\mathrm{OH}\) group in the following compounds is :

Choose the correct answer from the options given below:

Highest enol content will be shown by:

Which of the following is strongest Bronsted base?

Which of the following has highly acidic hydrogen?

Cyclohexene

is ________ type of an organic compound.

IUPAC name of following compound (P) is:

3-Methylhex-2-ene on reaction with \(\mathrm{HBr}\) in presence of peroxide forms an addition product (A). The number of possible stereoisomers for '\(\mathrm{A}\)' is ________.

Among the given organic compounds, the total number of aromatic compounds is

Among the following, total number of meta directing functional groups is (Integer based)
\(-\mathrm{OCH}_3,-\mathrm{NO}_2,-\mathrm{CN},-\mathrm{CH}_3-\mathrm{NHCOCH}_3, -\mathrm{COR},-\mathrm{OH},-\mathrm{COOH},-\mathrm{Cl}\)

Two nucleotides are joined together by a linkage known as :

Choose the polar molecule from the following:

Sum of bond order of CO and NO\(^+\) is ________.

Consider the following data for the given reaction
\(2 \mathrm{HI}_{(\mathrm{g})} \rightarrow \mathrm{H}_{2(\mathrm{~g})}+\mathrm{I}_{2(\mathrm{~g})}\)

The order of the reaction is _________.

Consider the following complex ions
$$\begin{aligned}
& \mathrm{P}=\left[\mathrm{FeF}_6\right]^{3-} \\
& \mathrm{Q}=\left[\mathrm{V}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+} \\
& \mathrm{R}=\left[\mathrm{Fe}\left(\mathrm{H}_2 \math...

Yellow compound of lead chromate gets dissolved on treatment with hot \(\mathrm{NaOH}\) solution. The product of lead formed is a :

Which of the following electronic configuration would be associated with the highest magnetic moment?

\(\mathrm{NaCl}\) reacts with conc. \(\mathrm{H}_2 \mathrm{SO}_4\) and \(\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7\) to give reddish fumes (B), which react with \(\mathrm{NaOH}\) to give yellow solution (C). (B) and (C) respectively are ;

The electronic configuration for Neodymium is:
[Atomic Number for Neodymium 60]

The mass of silver (Molar mass of \(\mathrm{Ag}: 108 \mathrm{~gmol}^{-1}\) ) displaced by a quantity of electricity which displaces \(5600 \mathrm{~mL}\) of \(\mathrm{O}_2\) at S.T.P. will be ______ g.

The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is ;

Given below are two statements :
Statement (I) : Aqueous solution of ammonium carbonate is basic.
Statement (II) : Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on \(K_a\) and \(K_b\) value of acid and th...

Element not showing variable oxidation state is :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : Melting point of Boron (2453 K) is unusually high in group 13 elements.
Reason (R) : Solid Boron has very strong crys...

From the given list, the number of compounds with +4 oxidation state of Sulphur ________.
\(\mathrm{SO}_3, \mathrm{H}_2 \mathrm{SO}_3, \mathrm{SOCl}_2, \mathrm{SF}_4, \mathrm{BaSO}_4, \mathrm{H}_2 \mathrm{S}_2 \mathrm{O}_7\)

Given below are two statements :
Statement (I) : The \(4 \mathrm{f}\) and \(5 \mathrm{f}\) - series of elements are placed separately in the Periodic table to preserve the principle of classification.
Statement (II) : S-block elements can b...

A solution of two miscible liquids showing negative deviation from Raoult's law will have :

Mass of methane required to produce \(22 \mathrm{~g}\) of \(\mathrm{CO}_2\) after complete combustion is _______ g.
(Given Molar mass in g mol-1 \(\mathrm{C}=12.0\), \(\mathrm{H}=1.0\), \(\mathrm{O}=16.0)\)

The number of electrons present in all the completely filled subshells having \(\mathrm{n}=4\) and \(\mathrm{s}=+\frac{1}{2}\) is _______.
(Where \(\mathrm{n}=\) principal quantum number and \(\mathrm{s}=\) spin quantum number)

If three moles of an ideal gas at \(300 \mathrm{~K}\) expand isothermally from \(30 \mathrm{~dm}^3\) to \(45 \mathrm{~dm}^3\) against a constant opposing pressure of \(80 \mathrm{~kPa}\), then the amount of heat transferred is _______ J.

The distance, of the point $(7,-2,11)$ from the line $\frac{x-6}{1}=\frac{y-4}{0}=\frac{z-8}{3}$ along the line $\frac{x-5}{2}=\frac{y-1}{-3}=\frac{z-5}{6}$, is :

If the shortest distance between the lines $\frac{x-4}{1}=\frac{y+1}{2}=\frac{z}{-3}$ and $\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}$ is $\frac{6}{\sqrt{5}}$, then the sum of all possible values of $\lambda$ is :

Let for a differentiable function $f:(0, \infty) \rightarrow \mathbf{R}, f(x)-f(y) \geqslant \log _{\mathrm{e}}\left(\frac{x}{y}\right)+x-y, \forall x, y \in(0, \infty)$. Then $\sum\limits_{n=1}^{20} f^{\prime}\left(\frac{1}{n^2}\right)$ is...

Let the area of the region $\left\{(x, y): x-2 y+4 \geqslant 0, x+2 y^2 \geqslant 0, x+4 y^2 \leq 8, y \geqslant 0\right\}$ be $\frac{\mathrm{m}}{\mathrm{n}}$, where $\mathrm{m}$ and $\mathrm{n}$ are coprime numbers. Then $\mathrm{m}+\mathr...

${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if :

If A denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^{\mathrm{n}}$ and B denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^n$, then :

Four distinct points $(2 k, 3 k),(1,0),(0,1)$ and $(0,0)$ lie on a circle for $k$ equal to :

If $S=\{z \in C:|z-i|=|z+i|=|z-1|\}$, then, $n(S)$ is :

If $\alpha$ satisfies the equation $x^2+x+1=0$ and $(1+\alpha)^7=A+B \alpha+C \alpha^2, A, B, C \geqslant 0$, then $5(3 A-2 B-C)$ is equal to ____________.

If $\int\limits_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} \mathrm{~d} x=\mathrm{a}+\mathrm{b} \sqrt{2}+\mathrm{c} \sqrt{3}$, where $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are rational numbers, then $2 \mathrm{a}+3 \mathrm{~b}-4 \mathrm{c}$ is equal ...

If $(a, b)$ be the orthocentre of the triangle whose vertices are $(1,2),(2,3)$ and $(3,1)$, and $\mathrm{I}_1=\int\limits_{\mathrm{a}}^{\mathrm{b}} x \sin \left(4 x-x^2\right) \mathrm{d} x, \mathrm{I}_2=\int\limits_{\mathrm{a}}^{\mathrm{b}...

Let $x=x(\mathrm{t})$ and $y=y(\mathrm{t})$ be solutions of the differential equations $\frac{\mathrm{d} x}{\mathrm{dt}}+\mathrm{a} x=0$ and $\frac{\mathrm{d} y}{\mathrm{dt}}+\mathrm{by}=0$ respectively, $\mathrm{a}, \mathrm{b} \in \mathbf{...

If the solution of the differential equation $(2 x+3 y-2) \mathrm{d} x+(4 x+6 y-7) \mathrm{d} y=0, y(0)=3$, is
$\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6$, then $\alpha+2 \beta+3 \gamma$ is equal to ____________.

Let $f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in \mathbf{R}$. Then $f^{\prime}(10)$ is equal to ____________.

The length of the chord of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$, whose mid point is $\left(1, \frac{2}{5}\right)$, is equal to :

The function $f: \mathbf{N}-\{1\} \rightarrow \mathbf{N}$; defined by $f(\mathrm{n})=$ the highest prime factor of $\mathrm{n}$, is :

Consider the function.
$$ f(x)=\left\{\begin{array}{cc} \frac{\mathrm{a}\left(7 x-12-x^2\right)}{\mathrm{b}\left|x^2-7 x+12\right|} & , x<3 \\\\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\\\ \mathrm{~b} & , x=3, \end{array}\right. $$
where $[x]...

If $\mathrm{a}=\lim\limits_{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}$ and $\mathrm{b}=\lim\limits _{x \rightarrow 0} \frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}$, then the value of $a b^3$ is :

Consider the matrix $f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$.
Given below are two statements :
Statement I : $ f(-x)$ is the inverse of the matrix $f(x)$.
Statement II : $f(x)...

Let $A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]$, where $B_1, B_2, B_3$ are column matrics, and
$$
\mathrm{AB}_1=\left[\begin{array}{l}
1 \\
0 \\
0
\end{array}\right], \math...