JEE Main 2025 (Online) 3rd April Evening Shift

\(\text {The major product }(\mathrm{P}) \text { in the following reaction is : }\)

\(\text { What is the correct IUPAC name of }\)
?

The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula $\mathrm{C}_9 \mathrm{H}_{12}$ is________.

Given below are two statements :
Statement I : Hyperconjugation is not a permanent effect.
Statement II : In general, greater the number of alkyl groups attached to a positively charged Cation, greater is the hyperconjugation interaction an...

Fat soluble vitamins are:
A. Vitamin $\mathrm{B}_1$
B. Vitamin C
C. Vitamin E
D. Vitamin B 12
E. Vitamin K
Choose the correct answer from the options given below:

Given below are two statements:
Statement I : Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes.
Statement II : Intermolecular hydrogen bonding with wat...

Consider the following statements related to temperature dependence of rate constants.
Identify the correct statements.
A. The Arrhenius equation holds true only for an elementary homogenous reaction.
B. The unit of $A$ is same as that of $...

The sequence from the following that would result in giving predominantly $3,4,5-$ Tribromoaniline is :

Identify the diamagnetic octahedral complex ions from below ;
A. $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$
B. $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$
C. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{4-}$
D. $\left[\math...

Among, $\mathrm{Sc}, \mathrm{Mn}, \mathrm{Co}$ and Cu , identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is__________BM (in nearest integer).

Given below are two statements:
Statement I : $\mathrm{CrO}_3$ is a stronger oxidizing agent than $\mathrm{MoO}_3$
Statement II : $\mathrm{Cr}(\mathrm{VI})$ is more stable than $\mathrm{Mo}(\mathrm{VI})$
In the light of the above statements...

The standard cell potential $\left(\mathrm{E}_{\text {cell }}^{\ominus}\right)$ of a fuel cell based on the oxidation of methanol in air that has been used to power television relay station is measured as 1.21 V . The standard half cell red...

\(\text {In the following series of reactions identify the major products } \mathrm{A} \& \mathrm{~B} \text { respectively }\)

40 mL of a mixture of $\mathrm{CH}_3 \mathrm{COOH}$ and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometrically. Which of the following statement is correct?

The correct orders among the following are
Atomic radius : $\mathrm{B}<\mathrm{Al}<\mathrm{Ga}<\mathrm{In}<\mathrm{Tl}$
Electronegativity : $\mathrm{Al}<\mathrm{Ga}<\mathrm{In}<\mathrm{Tl}<\mathrm{B}$
Density : $\mathrm{Tl}<\mathrm{In}<\mat...

\(\text { Match the LIST-I with LIST-II }\)


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Compounds that should not be used as primary standards in titrimetric analysis are :
A. $\mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7$
B. Oxalic acid
C. NaOH
D. $\mathrm{FeSO}_4 \cdot 6 \mathrm{H}_2 \mathrm{O}$
E. Sodium tetraborate
Choose the ...

X g of nitrobenzene on nitration gave 4.2 g of m -dinitrobenzene. X = __________g. (nearest integer)
[Given : molar mass (in $\left.\left.\mathrm{g} \mathrm{mol}^{-1}\right) \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16, \mathrm{~N}: 14\rig...

In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is
(Given : Aqueous tension at $30...

10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 moles of HCl and made the volume upto the mark with distilled water. The ...

Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is
Given: Molar mass of Mg is $24 \mathrm{~g} \mathrm{~mol}^{-1}$.

For electrons in ' 2 s ' and ' 2 p ' orbitals, the orbital angular momentum values, respectively are:

A perfect gas ( 0.1 mol ) having $\overline{\mathrm{C}}_v=1.50 \mathrm{R}$ (independent of temperature) undergoes the above transformation from point 1 to point 4. If each step is reversible, the total work done (w) while going from point 1...

A sample of n -octane $(1.14 \mathrm{~g})$ was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is $5 \mathrm{~kJ} \mathrm{~K}^{-1}$. As a result of combustion reaction, the temperature of the calorimeter is i...

Given below are two statements:
Statement I : When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted.
Sta...

The distance of the point $(7,10,11)$ from the line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

Each of the angles $\beta$ and $\gamma$ that a given line makes with the positive $y$ - and $z$-axes, respectively, is half of the angle that this line makes with the positive $x$-axes. Then the sum of all possible values of the angle $\bet...

Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function defined by $f(x)=||x+2|-2| x \|$. If $m$ is the number of points of local minima and $n$ is the number of points of local maxima of $f$, then $m+n$ is

The shortest distance between the curves $y^2=8 x$ and $x^2+y^2+12 y+35=0$ is:

The area of the region $\{(x, y):|x-y| \leq y \leq 4 \sqrt{x}\}$ is

Let $\left(1+x+x^2\right)^{10}=a_0+a_1 x+a_2 x^2+\ldots+a_{20} x^{20}$. If $\left(a_1+a_3+a_5+\ldots+a_{19}\right)-11 a_2=121 k$, then $k$ is equal to_________ .

If the four distinct points $(4,6),(-1,5),(0,0)$ and $(k, 3 k)$ lie on a circle of radius $r$, then $10 k+r^2$ is equal to

\(If\,\,{z_1},{z_2},{z_3} \in \,\,are\,\,the\,\,vertices\,\,of\,\,an\,\,equilateral\,\,triangle,\,\,whose\,\,centroid\,\,is\,\,{z_0},\,\,then\,\,\sum\limits_{k = 1}^3 {{{\left( {{z_k} - {z_0}} \right)}^2}\,is\,\,equal\,\,to}\)

The integral $\int_0^\pi \frac{8 x d x}{4 \cos ^2 x+\sin ^2 x}$ is equal to

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x, y(0)=\frac{1}{3}+e^3$. Then $y\left(\frac{\pi}{4}\right)$ is equal to :

Let $C$ be the circle of minimum area enclosing the ellipse $E: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with eccentricity $\frac{1}{2}$ and foci $( \pm 2,0)$. Let $P Q R$ be a variable triangle, whose vertex $P$ is on the circle $C$ and the side...

Let $f$ be a function such that $f(x)+3 f\left(\frac{24}{x}\right)=4 x, x \neq 0$. Then $f(3)+f(8)$ is equal to

If the domain of the function $f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right)$ is $(\alpha, \beta) \cup(\gamma, o)$, then $\alpha+\beta+\gamma+\hat{o}$ is equal to

If the equation of the hyperbola with foci $(4,2)$ and $(8,2)$ is $3 x^2-y^2-\alpha x+\beta y+\gamma=0$, then $\alpha+\beta+\gamma$ is equal to__________.

\(If\,\,\mathop {\lim }\limits_{x \to 0} \left(\frac{\tan x}{x}\right)^{\frac{1}{x^2}}=p \text {, then } 96 \log _{\mathrm{e}} p \text { is equal to____________ }\)

Let $I$ be the identity matrix of order $3 \times 3$ and for the matrix $A=\left[\begin{array}{ccc}\lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & -1 & 2\end{array}\right],|A|=-1$. Let $B$ be the inverse of the matrix $\operatorname{adj}\left(\operator...

Line $L_1$ of slope 2 and line $L_2$ of slope $\frac{1}{2}$ intersect at the origin O . In the first quadrant, $\mathrm{P}_1$, $P_2, \ldots, P_{12}$ are 12 points on line $L_1$ and $Q_1, Q_2, \ldots, Q_9$ are 9 points on line $L_2$. Then th...

If the probability that the random variable $X$ takes the value $x$ is given by
$P(X=x)=k(x+1) 3^{-x}, x=0,1,2,3 \ldots$, where $k$ is a constant, then $P(X \geq 3)$ is equal to

Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $\left(k, \frac{k}{2}\right)$ from the line $3 x+4 y+5=0$ is

The sum $1+\frac{1+3}{2!}+\frac{1+3+5}{3!}+\frac{1+3+5+7}{4!}+\ldots$ upto $\infty$ terms, is equal to

Let $A=\{-2,-1,0,1,2,3\}$. Let R be a relation on $A$ defined by $x \mathrm{R} y$ if and only if $y=\max \{x, 1\}$. Let $l$ be the number of elements in R . Let $m$ and $n$ be the minimum number of elements required to be added in R to make...

Let the Mean and Variance of five observations $x_1=1, x_2=3, x_3=a, x_4=7$ and $x_5=\mathrm{b}, a>\mathrm{b}$, be 5 and 10 respectively. Then the Variance of the observations $n+x_n, n=1,2, \ldots, 5$ is

Consider the lines $x(3 \lambda+1)+y(7 \lambda+2)=17 \lambda+5, \lambda$ being a parameter, all passing through a point P. One of these lines (say $L$ ) is farthest from the origin. If the distance of $L$ from the point $(3,6)$ is $d$, then...

The number of solutions of the equation
$(4-\sqrt{3}) \sin x-2 \sqrt{3} \cos ^2 x=-\frac{4}{1+\sqrt{3}}, x \in\left[-2 \pi, \frac{5 \pi}{2}\right]$ is

Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}, \vec{b}=3 \hat{i}-3 \hat{j}+3 \hat{k}, \vec{c}=2 \hat{i}-\hat{j}+2 \hat{k}$ and $\vec{d}$ be a vector such that $\vec{b} \times \vec{d}=\vec{c} \times \vec{d}$ and $\vec{a} \cdot \vec{d}=4$. Then $|(\...