JEE Main 2025 (Online) 23rd January Morning Shift

What amount of bromine will be required to convert 2 g of phenol into 2,4,6-tribromophenol? (Given molar mass in $\mathrm{g} \mathrm{mol}^{-1}$ of $\mathrm{C}, \mathrm{H}, \mathrm{O}, \mathrm{Br}$ are $12,1,16,80$ respectively )

The major product of the following reaction is :
$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}=\mathrm{O} \xrightarrow[\text { reflux }]{\substack{\text { excess } \mathrm{HCHO} \\ \text { alkali }}}$ ?

The correct stability order of the following species/molecules is :

Given below are two statements:
Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent
Statement II: In the presence of base, fructose undergoes rearrangement to give glucose.
In the light of the above ...

Match the List - I with List - II

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For the thermal decomposition of $\mathrm{N}_2 \mathrm{O}_5(\mathrm{~g})$ at constant volume, the following table can be formed, for the reaction mentioned below.
$$2 \mathrm{~N}_2 \mathrm{O}_5(\mathrm{~g}) \rightarrow 2 \mathrm{~N}_2 \math...

Consider the following sequence of reactions to produce major product (A)

$\begin{aligned} & \text { Molar mass of product }(\mathrm{A}) \text { is } \mathrm{g} \mathrm{~mol}^{-1} \text {. } \\ & \text { (Given molar mass in } \mathrm{g} \...

Which among the following react with Hinsberg's reagent?
A.
B.
$\text { C. } \mathrm{CH}_3-\mathrm{NH}_2$
D. $\mathrm{N}\left(\mathrm{CH}_3\right)_3$
E.
Choose the correct answer from the options given below :

$\mathrm{CrCl}_3 \cdot \mathrm{xNH}_3$ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of $0.558^{\circ} \mathrm{C}$. Assuming $100 \%$ ionisation of this complex and coordination numb...

The complex that shows Facial - Meridional isomerism is :

The d-electronic configuration of an octahedral Co (II) complex having magnetic moment of 3.95 BM is:

The correct set of ions (aqueous solution) with same colour from the following is:

\(\mathrm{FeO}_4^{2-} \xrightarrow{+2.0 \mathrm{~V}} \mathrm{Fe}^{3+} \xrightarrow{0.8 \mathrm{~V}} \mathrm{Fe}^{2+} \xrightarrow{-0.5 \mathrm{~V}} \mathrm{Fe}^0\)


In the above diagram, the standard electrode potentials are given in vol...

Propane molecule on chlorination under photochemical condition gives two di-chloro products, " $x$ " and " $y$ ". Amongst " $x$ " and " $y$ ", " $x$ " is an optically active molecule. How many tri-chloro products (consider only structural i...

Match the List - I with List - II

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If 1 mM solution of ethylamine produces $\mathrm{pH}=9$, then the ionization constant $\left(\mathrm{K}_{\mathrm{b}}\right)$ of ethylamine is $10^{-x}$. The value of $x$ is _________ (nearest integer).
[The degree of ionization of ethylamin...

Which of the following happens when $\mathrm{NH}_4 \mathrm{OH}$ is added gradually to the solution containing 1 M $\mathrm{A}^{2+}$ and $1 \mathrm{M} \mathrm{B}^{3+}$ ions?
Given : $\mathrm{K}_{\text {sp }}\left[\mathrm{A}(\mathrm{OH})_2\ri...

The incorrect statement among the following is

The element that does not belong to the same period of the remaining elements (modern periodic table) is:

Given below are two statements:
Statement I: In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds.
Statement II: The sodium fusion extract of an organic compound having N and S gives prussian blue colour ...

$2.8 \times 10^{-3} \mathrm{~mol}$ of $\mathrm{CO}_2$ is left after removing $10^{21}$ molecules from its ' $x$ ' mg sample. The mass of $\mathrm{CO}_2$ taken initially is
Given: $\mathrm{N}_{\mathrm{A}}=6.02 \times 10^{23} \mathrm{~mol}^{-...

During " S " estimation, 160 mg of an organic compound gives 466 mg of barium sulphate. The percentage of Sulphur in the given compound is _________ %.
(Given molar mass in $\mathrm{g} \mathrm{~mol}^{-1}$ of $\mathrm{Ba}: 137, \mathrm{~S}: ...

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm . Which spectral line of H atom is suitable for this?
Given : Rydberg constant $\left.\mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10...

Ice at $-5^{\circ} \mathrm{C}$ is heated to become vapor with temperature of $110^{\circ} \mathrm{C}$ at atmospheric pressure. The entropy change associated with this process can be obtained from

The standard enthalpy and standard entropy of decomposition of $\mathrm{N}_2 \mathrm{O}_4$ to $\mathrm{NO}_2$ are $55.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $175.0 \mathrm{~J} / \mathrm{K} / \mathrm{mol}$ respectively. The standard free ene...

Let P be the foot of the perpendicular from the point $\mathrm{Q}(10,-3,-1)$ on the line $\frac{x-3}{7}=\frac{y-2}{-1}=\frac{z+1}{-2}$. Then the area of the right angled triangle $P Q R$, where $R$ is the point $(3,-2,1)$, is

If the set of all values of $a$, for which the equation $5 x^3-15 x-a=0$ has three distinct real roots, is the interval $(\alpha, \beta)$, then $\beta-2 \alpha$ is equal to _________.

If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $\mathrm{y}=|\mathrm{x}-1|$ is $\frac{1}{4}(\mathrm{~b} \pi+\mathrm{c}), \mathrm{b}, \mathrm{c} \in N$, then $\mathrm{b}+\mathrm{c}$ is equal to _________

The sum of all rational terms in the expansion of $\left(1+2^{1 / 3}+3^{1 / 2}\right)^6$ is equal to _________.

Let the circle $C$ touch the line $x-y+1=0$, have the centre on the positive $x$-axis, and cut off a chord of length $\frac{4}{\sqrt{13}}$ along the line $-3 x+2 y=1$. Let H be the hyperbola $\frac{x^2}{\alpha^2}-\frac{y^2}{\beta^2}=1$, who...

Let $\left|\frac{\bar{z}-i}{2 \bar{z}+i}\right|=\frac{1}{3}, z \in C$, be the equation of a circle with center at $C$. If the area of the triangle, whose vertices are at the points $(0,0), C$ and $(\alpha, 0)$ is 11 square units, then $\alp...

The value of $\int_{e^2}^{e^4} \frac{1}{x}\left(\frac{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}}{e^{\left(\left(\log _e x\right)^2+1\right)^{-1}}+e^{\left(\left(6-\log _e x\right)^2+1\right)^{-1}}}\right) d x$ is

Let a curve $y=f(x)$ pass through the points $(0,5)$ and $\left(\log _e 2, k\right)$. If the curve satisfies the differential equation $2(3+y) e^{2 x} d x-\left(7+e^{2 x}\right) d y=0$, then $k$ is equal to

Let $f(x)=\log _{\mathrm{e}} x$ and $g(x)=\frac{x^4-2 x^3+3 x^2-2 x+2}{2 x^2-2 x+1}$. Then the domain of $f \circ g$ is

Let $\mathrm{I}(x)=\int \frac{d x}{(x-11)^{\frac{11}{13}}(x+15)^{\frac{15}{13}}}$. If $\mathrm{I}(37)-\mathrm{I}(24)=\frac{1}{4}\left(\frac{1}{\mathrm{~b}^{\frac{1}{13}}}-\frac{1}{\mathrm{c}^{\frac{1}{13}}}\right), \mathrm{b}, \mathrm{c} \i...

If $\frac{\pi}{2} \leq x \leq \frac{3 \pi}{4}$, then $\cos ^{-1}\left(\frac{12}{13} \cos x+\frac{5}{13} \sin x\right)$ is equal to

If the function

$$
f(x)=\left\{\begin{array}{l}
\frac{2}{x}\left\{\sin \left(k_1+1\right) x+\sin \left(k_2-1\right) x\right\}, \quad x<0 \\
4, \quad x=0 \\
\frac{2}{x} \log _e\left(\frac{2+k_1 x}{2+k_2 x}\right), \quad x>0
\end{array}\righ...

 If the system of equations

$$ \begin{aligned} & (\lambda-1) x+(\lambda-4) y+\lambda z=5 \\ & \lambda x+(\lambda-1) y+(\lambda-4) z=7 \\ & (\lambda+1) x+(\lambda+2) y-(\lambda+2) z=9 \end{aligned}$$
has infinitely many solutions, then $\la...

If $\mathrm{A}, \mathrm{B}, \operatorname{and}\left(\operatorname{adj}\left(\mathrm{A}^{-1}\right)+\operatorname{adj}\left(\mathrm{B}^{-1}\right)\right)$ are non-singular matrices of same order, then the inverse of $A\left(\operatorname{adj...

If the line $3 x-2 y+12=0$ intersects the parabola $4 y=3 x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment AB subtends an angle equal to

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is :

One die has two faces marked 1 , two faces marked 2 , one face marked 3 and one face marked 4 . Another die has one face marked 1 , two faces marked 2 , two faces marked 3 and one face marked 4. The probability of getting the sum of numbers...

Let the area of a $\triangle P Q R$ with vertices $P(5,4), Q(-2,4)$ and $R(a, b)$ be 35 square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to

If the equation $\mathrm{a}(\mathrm{b}-\mathrm{c}) \mathrm{x}^2+\mathrm{b}(\mathrm{c}-\mathrm{a}) \mathrm{x}+\mathrm{c}(\mathrm{a}-\mathrm{b})=0$ has equal roots, where $\mathrm{a}+\mathrm{c}=15$ and $\mathrm{b}=\frac{36}{5}$, then $a^2+c^2...

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

Let $\mathrm{R}=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in R so that R becomes an equivalence relation, is:

Marks obtains by all the students of class 12 are presented in a freqency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of s...

The value of $\left(\sin 70^{\circ}\right)\left(\cot 10^{\circ} \cot 70^{\circ}-1\right)$ is

Let the arc $A C$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $A C$, divides the arc $A C$ such that $\frac{\text { length of } \operatorname{arc} A B}{\text { length of } \operatorname{arc} B C}=\frac{1...

Let the position vectors of the vertices $\mathrm{A}, \mathrm{B}$ and C of a tetrahedron ABCD be $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathrm{k}}, \hat{\mathrm{i}}+3 \hat{\mathrm{j}}-2 \hat{k}$ and $2 \hat{i}+\hat{j}-\hat{k}$ respectiv...