JEE Main 2025 (Online) 22nd January Morning Shift

The compounds which give positive Fehling's test are :

Choose the correct answer from the options given below :

In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl . The percentage composition of chlorine in the compound is _________ %. (Given : molar mass in $\mathrm{g} \mathrm{~mol}^{-1}$ of $\mathrm...

The incorrect statements regarding geometrical isomerism are :
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than tr...

How many different stereoisomers are possible for the given molecule?

The IUPAC name of the following compound is :

Which of the following acids is a vitamin ?

The number of molecules/ions that show linear geometry among the following is __________.
$\mathrm{SO}_2, \mathrm{BeCl}_2, \mathrm{CO}_2, \mathrm{~N}_3^{-}, \mathrm{NO}_2, \mathrm{~F}_2 \mathrm{O}, \mathrm{XeF}_2, \mathrm{NO}_2^{+}, \mathrm...

A vessel at 1000 K contains $\mathrm{CO}_2$ with a pressure of 0.5 atm . Some of $\mathrm{CO}_2$ is converted into CO on addition of graphite. If total pressure at equilibrium is 0.8 atm , then Kp is :

$\mathrm{A \rightarrow B}$
The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 \m...

Which of the following statement is not true for radioactive decay?

The products formed in the following reaction sequence are :

Consider the following sequence of reactions :

Molar mass of the product formed $(\mathrm{A})$ is __________ $\mathrm{g} \mathrm{~mol}^{-1}$.

 In which of the following complexes the CFSE, $\Delta_o$ will be equal to zero?

From the magnetic behaviour of $\left[\mathrm{NiCl}_4\right]^{2-}$ (paramagnetic) and $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ (diamagnetic), choose the correct geometry and oxidation state.

Lanthanoid ions with $4 \mathrm{f}^7$ configuration are :
(A) $\mathrm{Eu}^{2+}$
(B) $\mathrm{Gd}^{3+}$
(C) $\mathrm{Eu}^{3+}$
(D) $\mathrm{Tb}^{3+}$
(E) $ \mathrm{Sm}^{2+}$
Choose the correct answer from the options given below :

Which of the following electrolyte can be used to obtain $\mathrm{H}_2 \mathrm{~S}_2 \mathrm{O}_8$ by the process of electrolysis ?

A solution of aluminium chloride is electrolysed for 30 minutes using a current of 2 A . The amount of the aluminium deposited at the cathode is __________ .
[Given : molar mass of aluminium and chlorine are $27 \mathrm{~g} \mathrm{~mol}^{-...

Given below are two statements :
Statement I : $\quad \mathrm{CH}_3-\mathrm{O}-\mathrm{CH}_2-\mathrm{Cl}$ will undergo $\mathrm{S}_{\mathrm{N}} 1$ reaction though it is a primary halide.
Statement II : will not undergo $\mathrm{S}_{\mathrm...

Given below are two statements :
Statement I : One mole of propyne reacts with excess of sodium to liberate half a mole of $\mathrm{H}_2$ gas.
Statement II : Four g of propyne reacts with $\mathrm{NaNH}_2$ to liberate $\mathrm{NH}_3$ gas wh...

Which of the following electronegativity order is incorrect?

Match List-I with List-II.

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Some $\mathrm{CO}_2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of $\mathrm{CO}_2$ gas was later passed through an aqueous solution of $\mathrm{Ca}(\mathrm{OH})_2$. The excess unreacted $\mat...

Arrange the following solutions in order of their increasing boiling points.
(i) $10^{-4} \mathrm{M} \mathrm{NaCl}$
(ii) $10^{-4} \mathrm{M}$ Urea
(iii) $10^{-3} \mathrm{M} \mathrm{NaCl}$
(iv) $10^{-2} \mathrm{M} \mathrm{NaCl}$

Radius of the first excited state of Helium ion is given as : $\mathrm{a}_0 \rightarrow$ radius of first stationary state of hydrogen atom.

A liquid when kept inside a thermally insulated closed vessel at $25^{\circ} \mathrm{C}$ was mechanically stirred from outside. What will be the correct option for the following thermodynamic parameters ?

Let $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and $\mathrm{L}_2: \frac{x-2}{2}=\frac{y}{0}=\frac{z+4}{\alpha}, \alpha \in \mathbf{R}$, be two lines, which intersect at the point $B$. If $P$ is the foot of perpendicular from...

Let $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ and $\mathrm{L}_2: \frac{x-2}{3}=\frac{y-4}{4}=\frac{z-5}{5}$ be two lines. Then which of the following points lies on the line of the shortest distance between $\mathrm{L}_1$ an...

The area of the region, inside the circle $(x-2 \sqrt{3})^2+y^2=12$ and outside the parabola $y^2=2 \sqrt{3} x$ is :

If $\sum_\limits{r=0}^5 \frac{{ }^{11} C_{2 r+1}}{2 r+2}=\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}-\mathrm{n}$ is equal to __________.

A circle C of radius 2 lies in the second quadrant and touches both the coordinate axes. Let r be the radius of a circle that has centre at the point $(2,5)$ and intersects the circle $C$ at exactly two points. If the set of all possible va...

Let $z_1, z_2$ and $z_3$ be three complex numbers on the circle $|z|=1$ with $\arg \left(z_1\right)=\frac{-\pi}{4}, \arg \left(z_2\right)=0$ and $\arg \left(z_3\right)=\frac{\pi}{4}$. If $\left|z_1 \bar{z}_2+z_2 \bar{z}_3+z_3 \bar{z}_1\righ...

Let for $f(x)=7 \tan ^8 x+7 \tan ^6 x-3 \tan ^4 x-3 \tan ^2 x, \quad \mathrm{I}_1=\int_0^{\pi / 4} f(x) \mathrm{d} x$ and $\mathrm{I}_2=\int_0^{\pi / 4} x f(x) \mathrm{d} x$. Then $7 \mathrm{I}_1+12 \mathrm{I}_2$ is equal to :

Let $f: \mathbf{R} \rightarrow \mathbf{R}$ be a twice differentiable function such that $f(x+y)=f(x) f(y)$ for all $x, y \in \mathbf{R}$. If $f^{\prime}(0)=4 \mathrm{a}$ and $f$ satisfies $f^{\prime \prime}(x)-3 \mathrm{a} f^{\prime}(x)-f(x...

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

Let $f(x)$ be a real differentiable function such that $f(0)=1$ and $f(x+y)=f(x) f^{\prime}(y)+f^{\prime}(x) f(y)$ for all $x, y \in \mathbf{R}$. Then $\sum_\limits{n=1}^{100} \log _e f(n)$ is equal to :

Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :

Using the principal values of the inverse trigonometric functions, the sum of the maximum and the minimum values of $16\left(\left(\sec ^{-1} x\right)^2+\left(\operatorname{cosec}^{-1} x\right)^2\right)$ is :

Let the function,
$$f(x)= \begin{cases}-3 \mathrm{ax}^2-2, & x<1 \\ \mathrm{a}^2+\mathrm{b} x, & x \geqslant 1\end{cases}$$
be differentiable for all $x \in \mathbf{R}$, where $\mathrm{a}>1, \mathrm{~b} \in \mathbf{R}$. If the area of the r...

If $\sum_\limits{r=1}^n T_r=\frac{(2 n-1)(2 n+1)(2 n+3)(2 n+5)}{64}$, then $\lim _\limits{n \rightarrow \infty} \sum_\limits{r=1}^n\left(\frac{1}{T_r}\right)$ is equal to :

The product of all solutions of the equation $\mathrm{e}^{5\left(\log _{\mathrm{e}} x\right)^2+3}=x^8, x>0$, is :

Let $A$ be a square matrix of order 3 such that $\operatorname{det}(A)=-2$ and $\operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=2^{m+n} \cdot 3^{m n}, m>n$. Then $4 m+2 n$ is equal to __________.

Let the parabola $y=x^2+\mathrm{p} x-3$, meet the coordinate axes at the points $\mathrm{P}, \mathrm{Q}$ and R . If the circle C with centre at $(-1,-1)$ passes through the points $P, Q$ and $R$, then the area of $\triangle P Q R$ is :

From all the English alphabets, five letters are chosen and are arranged in alphabetical order. The total number of ways, in which the middle letter is ' M ', is :

A coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of $X$, then the value of $64\left(\mu+\sigma^2\right)$ is:

Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{m}{n}$, ...

Let $a_1, a_2, a_3, \ldots$ be a G.P. of increasing positive terms. If $a_1 a_5=28$ and $a_2+a_4=29$, then $a_6$ is equal to:

Let $A=\{1,2,3, \ldots, 10\}$ and $B=\left\{\frac{m}{n}: m, n \in A, m< n\right.$ and $\left.\operatorname{gcd}(m, n)=1\right\}$. Then $n(B)$ is equal to :

The number of non-empty equivalence relations on the set $\{1,2,3\}$ is :

Let the triangle PQR be the image of the triangle with vertices $(1,3),(3,1)$ and $(2,4)$ in the line $x+2 y=2$. If the centroid of $\triangle \mathrm{PQR}$ is the point $(\alpha, \beta)$, then $15(\alpha-\beta)$ is equal to :

Let $\vec{c}$ be the projection vector of $\vec{b}=\lambda \hat{i}+4 \hat{k}, \lambda>0$, on the vector $\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by the vectors $\vec{b}$ and ...