JEE Main 2025 (Online) 7th April Morning Shift

Given below are two statements :
Statement I : Dimethyl ether is completely soluble in water. However, diethyl ether is soluble in water to a very small extent.
Statement II : Sodium metal can be used to dry diethyl ether and not ethyl alco...

Which of the following is the correct IUPAC name of given organic compound (X)?

Given below are two statements:
Statement I: D-(+)-glucose + D-(+) fructose $\xrightarrow{-\mathrm{H}_2 \mathrm{O}}$ Sucrose
$$\text { sucrose } \xrightarrow{\text { hydrolysis }} \mathrm{D}-(+) \text { glucose }+\mathrm{D}-(+) \text { fruc...

Match the List I with List II.

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A person's wound was exposed to some bacteria and then bacterial growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay(r) was found to be proportional with t...

Reaction $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. It was started with pure A

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Which of the following amine (s) show (s) positive carbylamine test?

B. $\left(\mathrm{CH}_3\right)_2 \mathrm{NH}$
C. $\mathrm{CH}_3 \mathrm{NH}_2$
D. $\left(\mathrm{CH}_3\right)_3 \mathrm{~N}$

Choose the correct answer from the options g...

An octahedral complex having molecular composition $\mathrm{Co} \cdot 5 \mathrm{NH}_3 \cdot \mathrm{Cl}^2 . \mathrm{SO}_4$ has two isomers A and B. The solution of A gives a white precipitate with $\mathrm{AgNO}_3$ solution and the solution...

The number of paramagnetic complexes among $\left[\mathrm{FeF}_6\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$, $\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-},...

The first transition series metal ' $M$ ' has the highest enthalpy of atomisation in its series. One of its aquated ion $\left(\mathrm{M}^{\mathrm{n}+}\right)$ exists in green colour. The nature of the oxide formed by the above $\mathrm{M}^...

1 Faraday electricity was passed through $\mathrm{Cu}^{2+}(1.5 \mathrm{M}, 1 \mathrm{~L}) / \mathrm{Cu}$ and 0.1 Faraday was passed through $\mathrm{Ag}^{+}(0.2 \mathrm{M}, 1 \mathrm{~L}) / \mathrm{Ag}$ electrolytic cells. After this the tw...

At the sea level, the dry air mass percentage composition is given as nitrogen gas: 70.0 , oxygen gas: 27.0 and argon gas: 3.0 . If total pressure is 1.15 atm , then calculate the ratio of following respectively:
(i) partial pressure of nit...

The reactions which cannot be applied to prepare an alkene by elimination, are

Choose the correct answer from the options given below:

Given below are two statements:
Statement I : Ozonolysis followed by treatment with $\mathrm{Zn}, \mathrm{H}_2 \mathrm{O}$ of cis-2-butene gives ethanal.
Statement II : The product obtained by ozonolysis followed by treatment with $\mathrm{...

An aqueous solution of HCl with pH 1.0 is diluted by adding equal volume of water (ignoring dissociation of water). The pH of HCl solution would
$($ Given $\log 2=0.30)$

The percentage dissociation of a salt $\left(\mathrm{MX}_3\right)$ solution at given temperature (van't Hoff factor $\mathrm{i}=2$ ) is ___________ %(Nearest integer)

The number of valence electrons present in the metal among $\mathrm{Cr}, \mathrm{Co}, \mathrm{Fe}$ and Ni which has the lowest enthalpy of atomisation is :

The group 14 elements $A$ and $B$ have the first ionisation enthalpy values of 708 and $715 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The above values are lowest among their group members. The nature of their ions $\mathrm{A}^{2+}$ and...

Which of the following compounds is least likely to give effervescence of $\mathrm{CO}_2$ in presence of aq. $\mathrm{NaHCO}_3 ?$

Given below are two statements :
Statement I : Mohr's salt is composed of only three types of ions-ferrous, ammonium and sulfate.
Statement II : If the molar conductance at infinite dilution for ferrous, ammonium and sulfate ions are $x_1, ...

When a salt is treated with sodium hydroxide solution it gives gas X . On passing gas X through reagent Y a brown coloured precipitate is formed. X and Y respectively, are

An organic compound weighing 500 mg , produced 220 mg of $\mathrm{CO}_2$, on complete combustion. The percentage composition of carbon in the compound is _________ $\%$. (nearest integer)
(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1}$ ...

Thyroxine, the hormone has given below structure

The percentage of iodine in thyroxine is __________ %. (nearest integer)
(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{C}: 12, \mathrm{H}: 1, \mathrm{O}: 16, \mathrm{~N}: 14, \m...

Which of the following statements are correct, if the threshold frequency of caesium is $5.16 \times$ $10^{14} \mathrm{~Hz}$ ?
A. When Cs is placed inside a vacuum chamber with an ammeter connected to it and yellow light is focused on Cs ,...

Total enthalpy change for freezing of 1 mol of water at $10^{\circ} \mathrm{C}$ to ice at $-10^{\circ} \mathrm{C}$ is ________
(Given: $\Delta_{\text {fus }} \mathrm{H}=x \mathrm{~kJ} / \mathrm{mol}$
$$\begin{aligned}
& \mathrm{C}_{\mathrm{...

Let the line L pass through $(1,1,1)$ and intersect the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z}{1}$. Then, which of the following points lies on the line $L$ ?

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

Let $x=-1$ and $x=2$ be the critical points of the function $f(x)=x^3+a x^2+b \log _{\mathrm{e}}|x|+1, x \neq 0$.
Let $m$ and M respectively be the absolute minimum and the absolute maximum values of $f$ in the interval $\left[-2,-\frac{1}{...

If the area of the region bounded by the curves $y=4-\frac{x^2}{4}$ and $y=\frac{x-4}{2}$ is equal to $\alpha$, then $6 \alpha$. equals

The remainder when $\left((64)^{(64)}\right)^{(64)}$ is divided by 7 is equal to

Let $C_1$ be the circle in the third quadrant of radius 3 , that touches both coordinate axes. Let $C_2$ be the circle with centre $(1,3)$ that touches $\mathrm{C}_1$ externally at the point $(\alpha, \beta)$. If $(\beta-\alpha)^2=\frac{m}{...

Among the statements
(S1) : The set $\left\{z \in \mathbb{C}-\{-i\}:|z|=1\right.$ and $\frac{z-i}{z+i}$ is purely real $\}$ contains exactly two elements, and
(S2) : The set $\left\{z \in \mathbb{C}-\{-1\}:|z|=1\right.$ and $\frac{z-1}{z+1}...

The integral $\int_0^\pi \frac{(x+3) \sin x}{1+3 \cos ^2 x} d x$ is equal to

Let $y=y(x)$ be the solution curve of the differential equation
$x\left(x^2+e^x\right) d y+\left(\mathrm{e}^x(x-2) y-x^3\right) \mathrm{d} x=0, x>0$, passing through the point $(1,0)$. Then $y(2)$ is equal to :

Consider the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ having one of its focus at $\mathrm{P}(-3,0)$. If the latus ractum through its other focus subtends a right angle at P and $a^2 b^2=\alpha \sqrt{2}-\beta, \alpha, \beta \in \mathbb{...

$\lim _\limits{x \rightarrow 0^{+}} \frac{\tan \left(5(x)^{\frac{1}{3}}\right) \log _e\left(1+3 x^2\right)}{\left(\tan ^{-1} 3 \sqrt{x}\right)^2\left(e^{5(x)^{\frac{4}{3}}}-1\right)}$ is equal to

The number of points of discontinuity of the function $f(x)=\left[\frac{x^2}{2}\right]-[\sqrt{x}], x \in[0,4]$, where $[\cdot]$ denotes the greatest integer function, is ________.

Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} \mathrm{A}))|=81$. If $S=\left\{n \in \mathbb{Z}:(|\operatorname{adj}(\operatorname{adj} A)|)^{\frac{(n-1)^2}{2}}=|A|^{\left(3 n^2-5 n-4\r...

Let the system of equations :

$$ \begin{aligned} & 2 x+3 y+5 z=9 \\ & 7 x+3 y-2 z=8 \\ & 12 x+3 y-(4+\lambda) z=16-\mu \end{aligned}$$
have infinitely many solutions. Then the radius of the circle centred at $(\lambda, \mu)$ and touching t...

The number of singular matrices of order 2 , whose elements are from the set $\{2,3,6,9\}$, is __________.

Let P be the parabola, whose focus is $(-2,1)$ and directrix is $2 x+y+2=0$. Then the sum of the ordinates of the points on P, whose abscissa is $-$2, is

From a group of 7 batsmen and 6 bowlers, 10 players are to be chosen for a team, which should include atleast 4 batsmen and atleast 4 bowlers. One batsmen and one bowler who are captain and vice-captain respectively of the team should be in...

Let the set of all values of $p \in \mathbb{R}$, for which both the roots of the equation $x^2-(p+2) x+(2 p+9)=0$ are negative real numbers, be the interval $(\alpha, \beta]$. Then $\beta-2 \alpha$ is equal to

Let $x_1, x_2, x_3, x_4$ be in a geometric progression. If $2,7,9,5$ are subtracted respectively from $x_1, x_2, x_3, x_4$, then the resulting numbers are in an arithmetic progression. Then the value of $\frac{1}{24}\left(x_1 x_2 x_3 x_4\ri...

The number of relations on the set $A=\{1,2,3\}$, containing at most 6 elements including $(1,2)$, which are reflexive and transitive but not symmetric, is __________.

For $n \geq 2$, let $S_n$ denote the set of all subsets of $\{1,2, \ldots, n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in S_6$, but $\{1,2,4\} \notin S_6$. Then $n\left(S_5\right)$ is equal to ________

The mean and standard deviation of 100 observations are 40 and 5.1 , respectively. By mistake one observation is taken as 50 instead of 40 . If the correct mean and the correct standard deviation are $\mu$ and $\sigma$ respectively, then $1...

Let ABC be the triangle such that the equations of lines AB and AC be $3 y-x=2$ and $x+y=2$, respectively, and the points B and C lie on $x$-axis. If P is the orthocentre of the triangle ABC , then the area of the triangle PBC is equal to

If for $\theta \in\left[-\frac{\pi}{3}, 0\right]$, the points $(x, y)=\left(3 \tan \left(\theta+\frac{\pi}{3}\right), 2 \tan \left(\theta+\frac{\pi}{6}\right)\right)$ lie on $x y+\alpha x+\beta y+\gamma=0$, then $\alpha^2+\beta^2+\gamma^2$ ...

Let the angle $\theta, 0<\theta<\frac{\pi}{2}$ between two unit vectors $\hat{a}$ and $\hat{b}$ be $\sin ^{-1}\left(\frac{\sqrt{65}}{9}\right)$. If the vector $\vec{c}=3 \hat{a}+6 \hat{b}+9(\hat{a} \times \hat{b})$, then the value of $9(\ve...