JEE Main 2025 (Online) 3rd April Morning Shift

Number of molecules from below which cannot give iodoform reaction is :
Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol.

\(\text {Identify the correct statements from the following. }\)

\(\text {Choose the correct answer from the options given below: }\)

\(\text { The least acidic compound, among the following is: }\)

\(\text { Which of the following is the correct structure of L-Fructose? }\)

In the following system, $\mathrm{PCl}_5(\mathrm{~g}) \leftrightharpoons \mathrm{PCl}_3(\mathrm{~g})+\mathrm{Cl}_2(\mathrm{~g})$ at equilibrium, upon addition of xenon gas at constant T & p , the concentration of

Given below are two statements :
Statement I : A catalyst cannot alter the equilibrium constant $\left(\mathrm{K}_{\mathrm{c}}\right)$ of the reaction, temperature remaining constant.
Statement II : A homogenous catalyst can change the equi...

In a reaction $A+B \rightarrow C$, initial concentrations of $A$ and $B$ are related as $[A]_0=8[B]_0$. The half lives of $A$ and $B$ are 10 min and 40 min , respectively. If they start to disappear at the same time, both following first or...

\(\text {Identify }[\mathrm{A}],[\mathrm{B}] \text { and }[\mathrm{C}] \text {, respectively in the following reaction sequence : }\)

\(\text { In the following reactions, which one is NOT correct? }\)

The correct order of the complexes $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5\left(\mathrm{H}_2 \mathrm{O}\right)\right]^{3+}(\mathrm{A}),\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}(\mathrm{B}),\left[\mathrm{Co}(\mathrm{CN...

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


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The number of optical isomers exhibited by the iron complex $(\mathrm{A})$ obtained from the following reaction is___________.
\(\mathrm{FeCl}_3+\mathrm{KOH}+\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \rightarrow \mathrm{~A}\)

The metal ions that have the calculated spin-only magnetic moment value of 4.9 B.M. are :
A. $\mathrm{Cr}^{2+}$
B. $\mathrm{Fe}^{2+}$
C. $\mathrm{Fe}^{3+}$
D. $\mathrm{Co}^{2+}$
E. $\mathrm{Mn}^{3+}$
Choose the correct answer from the optio...

Consider the following reactions
$$ \begin{aligned} & \mathrm{A}+\underset{\substack{ \text { Little } \\ \text { amount }}}{\mathrm{NaCl}}+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{CrO}_2 \mathrm{Cl}_2+\text { Side Products } \\ & \ma...

Correct order of limiting molar conductivity for cations in water at 298 K is :

\(\text { Which compound would give 3-methyl-6-oxoheptanal upon ozonolysis? }\)

Given below are two statements :
Statement I : The N - N single bond is weaker and longer than that of P - P single bond.
Statement II : Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions.
In ...

Which of the following statements are correct?
A. The process of adding an electron to a neutral gaseous atom is always exothermic.
B. The process of removing an electron from an isolated gaseous atom is always endothermic.
C. The $1^{\text...

2 moles each of ethylene glycol and glucose are dissolved in 500 g of water. The boiling point of the resulting solution is:
(Given : Ebullioscopic constant of water $=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )

Which of the following properties will change when system containing solution 1 will become solution 2 ?

Among $10^{-9} \mathrm{~g}$ (each) of the following elements, which one will have the highest number of atoms?
Element: $\mathrm{Pb}, \mathrm{Po}, \mathrm{Pr}$ and Pt

\(\text {During estimation of nitrogen by Dumas' method of compound } \mathrm{X}(0.42 \mathrm{~g})\)
_________mL of $\mathrm{N}_2$ gas will be liberated at STP. (nearest integer) (Given molar mass in $\mathrm{g}~ \mathrm{mol}^{-1}: \mathr...

0.5 g of an organic compound on combustion gave 1.46 g of $\mathrm{CO}_2$ and 0.9 g of $\mathrm{H}_2 \mathrm{O}$. The percentage of carbon in the compound is _______________. (Nearest integer)
[Given : Molar mass (in $\left.\mathrm{g} \math...

Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom?

Given :
$$ \begin{aligned} & \left.\Delta \mathrm{H}^{\ominus}{ }_{\text {sub }}[\mathrm{C} \text { (graphite })\right]=710 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \Delta_{\mathrm{C}-\mathrm{H}} \mathrm{H}^{\ominus}=414 \mathrm{~kJ} \mathrm{~m...

Let a line passing through the point $(4,1,0)$ intersect the line $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{4}$ at the point $A(\alpha, \beta, \gamma)$ and the line $\mathrm{L}_2: x-6=y=-z+4$ at the point $B(a, b, c)$. Then $\le...

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to $z$-axis. Line $L_2$ passes through the point $(\lambda, 5,6)$ and is parallel to $y$-axis. Let for $\lambda=\lambda_1, \lambda_2, \lambda_2<\lambda_1$, the shortest distance ...

The area of the region bounded by the curve $y=\max \{|x|, x|x-2|\}$, the $x$-axis and the lines $x=-2$ and $x=4$ is equal to__________

The sum of all rational terms in the expansion of $(2+\sqrt{3})^8$ is :

If $\sum\limits_{r=1}^9\left(\frac{r+3}{2^r}\right) \cdot{ }^9 C_r=\alpha\left(\frac{3}{2}\right)^9-\beta, \alpha, \beta \in \mathbb{N}$, then $(\alpha+\beta)^2$ is equal to

Let $z \in C$ be such that $\frac{z^2+3 i}{z-2+i}=2+3 i$. Then the sum of all possible values of $z^2$ is :

Let the domain of the function $f(x)=\log _2 \log _4 \log _6\left(3+4 x-x^2\right)$ be $(a, b)$. If $\int_0^{b-a}\left[x^2\right] d x=p-\sqrt{q}-\sqrt{r}, p, q, r \in \mathbb{N}, \operatorname{gcd}(p, q, r)=1$, where $[\cdot]$ is the greate...

Let $g$ be a differentiable function such that $\int_0^x g(t) d t=x-\int_0^x \operatorname{tg}(t) d t, x \geq 0$ and let $y=y(x)$ satisfy the differential equation $\frac{d y}{d x}-y \tan x=2(x+1) \sec x g(x), x \in\left[0, \frac{\pi}{2}\ri...

$$ \text { If } y(x)=\left|\begin{array}{ccc} \sin x & \cos x & \sin x+\cos x+1 \\ 27 & 28 & 27 \\ 1 & 1 & 1 \end{array}\right|, x \in \mathbb{R} \text {, then } \frac{d^2 y}{d x^2}+y \text { is equal to } $$

A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse $\frac{x^2}{36}+\frac{y^2}{25}=1$ at $A$ and $B$ such that $(P A) \cdot(P B)$ is maximum. Then $5\left(P A^2+P B^2\right)$ is equal to :

\(\text { If the domain of the function } f(x)=\log _e\left(\frac{2 x-3}{5+4 x}\right)+\sin ^{-1}\left(\frac{4+3 x}{2-x}\right) \text { is }[\alpha, \beta) \text {, then } \alpha^2+4 \beta \text { is equal to }\)

Let the product of the focal distances of the point $\mathbf{P}(4,2 \sqrt{3})$ on the hyperbola $\mathrm{H}: \frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ be 32 . Let the length of the conjugate axis of H be $p$ and the length of its latus rectum be $...

\(\text { Let } f(x)=\int x^3 \sqrt{3-x^2} d x \text {. If } 5 f(\sqrt{2})=-4 \text {, then } f(1) \text { is equal to }\)

Let $\quad f(x)= \begin{cases}(1+a x)^{1 / x} & , x<0 \\ 1+b, & x=0 \\ \frac{(x+4)^{1 / 2}-2}{(x+c)^{1 / 3}-2}, & x>0\end{cases}$ be continuous at $x=0$. Then $e^a b c$ is equal to:

Let $A$ be a matrix of order $3 \times 3$ and $|A|=5$. If $|2 \operatorname{adj}(3 A \operatorname{adj}(2 A))|=2^\alpha \cdot 3^\beta \cdot 5^\gamma, \alpha, \beta, \gamma \in N$, then $\alpha+\beta+\gamma$ is equal to

The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $\mathrm{W}_{\mathrm{n}}$. Let the probability $\mathrm{P}\left...

If the number of seven-digit numbers, such that the sum of their digits is even, is $m \cdot n \cdot 10^n ; m, n \in\{1,2,3, \ldots, 9\}$, then $m+n$ is equal to__________

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt{3} x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3 x-1=0$. If $P_n=$ $\alpha^n+\beta^n$ and $Q_n=\gamma^n+\hat{o}^n$, then $\frac{P_{25}+\sqrt{3} P_{24}}{2 P_{23}}+\frac{Q_{25}-Q...

Let $a_1, a_2, a_3, \ldots$. be a G.P. of increasing positive numbers. If $a_3 a_5=729$ and $a_2+a_4=\frac{111}{4}$, then $24\left(a_1+a_2+a_3\right)$ is equal to

The sum $1+3+11+25+45+71+\ldots$ upto 20 terms, is equal to

Let $\mathrm{A}=\{-3,-2,-1,0,1,2,3\}$. Let R be a relation on A defined by $x \mathrm{R} y$ if and only if $0 \leq x^2+2 y \leq 4$. Let $l$ be the number of elements in R and $m$ be the minimum number of elements required to be added in R t...

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $\mathrm{L}_1: 2 x+y+6=0$ and $\mathrm{L}_2: 4 x+2 y-p=0, p>0$, at the points A and B , respectively. If $A B=\frac{9}{\sqrt{...

\(\text { The number of solutions of the equation } 2 x+3 \tan x=\pi, x \in[-2 \pi, 2 \pi]-\left\{ \pm \frac{\pi}{2}, \pm \frac{3 \pi}{2}\right\} \text { is: }\)

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=3 \hat{i}+2 \hat{j}-\hat{k}, \vec{c}=\lambda \hat{j}+\mu \hat{k}$ and $\hat{d}$ be a unit vector such that $\vec{a} \times \hat{d}=\vec{b} \times \hat{d}$ and $\vec{c} \cdot \hat{d}=1$. If $\vec...