JEE Main 2025 (Online) 7th April Evening Shift

" P " is an optically active compound with molecular formula $\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}$. When ' P ' is treated with 2, 4-dinitrophenylhydrazine, it gives a positive test. However, in presence of Tollens reagent, " P " gives a...

Identify the structure of the final product (D) in the following sequence of the reactions :

Total number of $\mathrm{sp}^2$ hybridised carbon atoms in product D is ____________.

The descending order of basicity of the following amines is :



(D) $ \mathrm{CH}_3 \mathrm{NH}_2$
(E) $\left(\mathrm{CH}_3\right)_2 \mathrm{NH}$
Choose the correct answer from the options given below :

The number of optically active products obtained from the complete ozonolysis of the given compound is :

Given below are two statements :Statement (I) : On hydrolysis, oligo peptides give rise to fewer number of α-amino acids while proteins give rise to a large number of β-amino acids.Statement (II) : Natural proteins are denatured by acids wh...

In SO2, NO2$-$ and N3$-$, the hybridizations at the central atom are respectively :

Given below are two statements :Statement (I) : is more polar than Statement (II) : Boiling point of is lower than but it is more polar than .In the light of the above statements, choose the most appropriate answer from the options given...

A(g) → B(g) + C(g) is a first order reaction.




Time
t
∞




Psystem
Pt
P∞




The reaction was started with reactant A only. Which of the following expressions is correct for ra...

Match List - I with List - II.

List - I (Conversion)
List - II (Reagents, Conditions used)



(I) Warm H2O



(II) (a) NaOH, 368K; (b) H3O+



(III) (a) NaOH, 443K; (b) H3O+



(IV)...

Match List - I with List - II.

List - I (Complex)
List - II (Primary valency and Secondary valency)


(A) [Co(en)2Cl2]Cl
(I) 3,    6


(B) [Pt(NH3)2Cl(NO2)]
(II) 3,    4


(C) Hg [Co(SCN)4]
(II...

The number of unpaired electrons responsible for the paramagnetic nature of the following complex species are respectively : [Fe(CN)6]3−, [FeF6]3−, [CoF6]3−, [Mn(CN)6]3−

'X' is the number of acidic oxides among VO2, V2O3, CrO3, V2O5 and Mn2O7. The primary valency of cobalt in [Co(H2NCH2CH2NH2)3]2(SO4)3 is Y. The value of X + Y is _________.

The number of paramagnetic metal complex species among $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+},\left[\mathrm{Co}\left(\mathrm{C}_2 \mathrm{O}_4\right)_3\right]^{3-}$, $\left[\mathrm{MnCl}_6\right]^{3-},\left[\mathrm{Mn}(\...

Given below are two statements : 1 M aqueous solutions of each of Cu(NO3)2, AgNO3, Hg2(NO3)2, Mg(NO3)2 are electrolysed using inert electrodes. Given: E0Ag+/Ag = 0.80 V, E0Hg22+/Hg = 0.79 V, E0Cu2+/Cu = 0.24 V and E0Mg2+/Mg = -2.37 V.Statem...

One litre buffer solution was prepared by adding 0.10 mol each of $\mathrm{NH}_3$ and $\mathrm{NH}_4 \mathrm{Cl}$ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is ______________ $\times 10^{-2}$.
...

The correct statements from the following are :(A) Tl3+ is a powerful oxidising agent(B) Al3+ does not get reduced easily(C) Both Al3+ and Tl3+ are very stable in solution(D) Tl1+ is more stable than Tl3+(E) Al3+ and Tl1+ are highly stableC...

Choose the incorrect trend in the atomic radii (r) of the elements.

A mixture of 1 g each of chlorobenzene, aniline, and benzoic acid is dissolved in 50 mL ethyl acetate and placed in a separating funnel. 5 M NaOH (30 mL) was added in the same funnel. The funnel was shaken vigorously and then kept aside. Th...

In Dumas' method 292 mg of an organic compound released 50 mL of nitrogen gas $\left(\mathrm{N}_2\right)$ at 300 K temperature and 715 mm Hg pressure. The percentage composition of ' N ' in the organic compound is _____________ % (Nearest i...

Liquid A and B form an ideal solution. The vapour pressures of pure liquids A and B are 350 and 750 mm Hg respectively at the same temperature. If $x_A$ and $x_B$ are the mole fraction of A and B in solution while $y_A$ and $y_B$ are the mo...

Match List - I with List - II.


List - I
List - II


(A) Solution of chloroform and acetone
(I) Minimum boiling azeotrope


(B) Solution of ethanol and water
(II) Dimerizes


(C) Solution of benzen...

Butane reacts with oxygen to produce carbon dioxide and water following the equation given below.
$$ \mathrm{C}_4 \mathrm{H}_{10}(\mathrm{~g})+\frac{13}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow 4 \mathrm{CO}_2(\mathrm{~g})+5 \mathrm{H}_2 \m...

The extra stability of half-filled subshell is due to :
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
...

The hydration energies of $K^+$ and $Cl^-$ are $-x$ and $-y$ kJ/mol respectively. If the lattice energy of KCl is $-z$ kJ/mol, then the heat of solution of KCl is :

The correct statement amongst the following is :

If the equation of the line passing through the point $ \left( 0, -\frac{1}{2}, 0 \right) $ and perpendicular to the lines $ \vec{r} = \lambda \left( \hat{i} + a\hat{j} + b\hat{k} \right) $ and $ \vec{r} = \left( \hat{i} - \hat{j} - 6\hat{k...

Consider the lines L1: x - 1 = y - 2 = z and L2: x - 2 = y = z - 1. Let the feet of the perpendiculars from the point P(5, 1, -3) on the lines L1 and L2 be Q and R respectively. If the area of the triangle PQR is A, then 4A2 is equal to :

Let f : ℝ \(\to\) ℝ be a polynomial function of degree four having extreme values at x = 4 and x = 5. If $ \lim\limits_{x \to 0} \frac{f(x)}{x^2} = 5 $, then f(2) is equal to :

If the area of the region $ \{(x, y) : 1 + x^2 \leq y \leq \min \{x+7, 11-3x\}\} $ is $ A $, then $ 3A $ is equal to :

The sum of the series $2 \times 1 \times{ }^{20} \mathrm{C}_4-3 \times 2 \times{ }^{20} \mathrm{C}_5+4 \times 3 \times{ }^{20} \mathrm{C}_6-5 \times 4 \times{ }^{20} \mathrm{C}_7+\cdots \cdots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}$, i...

If the locus of z ∈ ℂ, such that Re$ \left( \frac{z - 1}{2z + i} \right) + \text{Re} \left( \frac{\overline{z} - 1}{2\overline{z} - i} \right) = 2 $, is a circle of radius r and center $(a, b)$, then $ \frac{15ab}{r^2} $ is equal to :

Let y = y(x) be the solution of the differential equation $(x^2 + 1)y' - 2xy = (x^4 + 2x^2 + 1)\cos x$,
$y(0) = 1$. Then $ \int\limits_{-3}^{3} y(x) \, dx $ is :

Let the length of a latus rectum of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ be 10. If its eccentricity is the minimum value of the function $f(t) = t^2 + t + \frac{11}{12}$, $t \in \mathbb{R}$, then $a^2 + b^2$ is equal to :

Let p be the number of all triangles that can be formed by joining the vertices of a regular polygon P of n sides and q be the number of all quadrilaterals that can be formed by joining the vertices of P. If p + q = 126, then the eccentrici...

If the range of the function $ f(x) = \frac{5-x}{x^2 - 3x + 2} , \ x \neq 1, 2, $ is $ (-\infty , \alpha] \cup [\beta, \infty) $, then $ \alpha^2 + \beta^2 $ is equal to :

Let e1 and e2 be the eccentricities of the ellipse $\frac{x^2}{b^2} + \frac{y^2}{25} = 1$ and the hyperbola $\frac{x^2}{16} - \frac{y^2}{b^2} = 1$, respectively. If b < 5 and e1e2 = 1, then the eccentricity of the ellipse having its axes al...

Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be $2 a$ and $2 b$, respectively, and one focus and the corresponding directrix of this hyperbola be $(-5,0)$ and $5 x+9=0$, respectively. If the product o...

If $\int\left(\frac{1}{x}+\frac{1}{x^3}\right)\left(\sqrt[23]{3 x^{-24}+x^{-26}}\right) \mathrm{d} x=-\frac{\alpha}{3(\alpha+1)}\left(3 x^\beta+x^\gamma\right)^{\frac{\alpha+1}{\alpha}}+C, x>0,(\alpha, \beta, \gamma \in \mathbf{Z})$, where ...

If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $x=0$, then $f(0)$ is equal to ____________.

For $\mathrm{t}>-1$, let $\alpha_{\mathrm{t}}$ and $\beta_{\mathrm{t}}$ be the roots of the equation
$$ \left((\mathrm{t}+2)^{1 / 7}-1\right) x^2+\left((\mathrm{t}+2)^{1 / 6}-1\right) x+\left((\mathrm{t}+2)^{1 / 21}-1\right)=0 \text {. If }...

Let the system of equations
x + 5y - z = 1
4x + 3y - 3z = 7
24x + y + λz = μ
λ, μ ∈ ℝ, have infinitely many solutions. Then the number of the solutions of this system, if x, y, z are integers and satisfy 7 ≤ x + y + z ≤ 77, is :

A bag contains 19 unbiased coins and one coin with head on both sides. One coin drawn at random is tossed and head turns up. If the probability that the drawn coin was unbiased, is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $n^2 - m^2$ is equal ...

Let a random variable X take values 0, 1, 2, 3 with P(X=0)=P(X=1)=p, P(X=2)=P(X=3) and E(X2)=2E(X). Then the value of 8p−1 is :

The number of real roots of the equation $x |x - 2| + 3|x - 3| + 1 = 0$ is :

Let $a_n$ be the $n^{th}$ term of an A.P. If $S_n = a_1 + a_2 + a_3 + \ldots + a_n = 700$, $a_6 = 7$ and $S_7 = 7$, then $a_n$ is equal to :

If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309, then the sum of its first nine terms is :

Let A = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : |$\alpha$ - 1| $\leq 4$ and |$\beta$ - 5| $\leq 6$ } and B = { ($\alpha, \beta$) $\in \mathbb{R} \times \mathbb{R}$ : 16($\alpha$ - $2)^2 $+ 9($\beta$ - $6)^2$ $\leq 144$ }. T...

If the orthocenter of the triangle formed by the lines y = x + 1, y = 4x - 8 and y = mx + c is at (3, -1), then m - c is :

The number of solutions of the equation
$ \cos 2\theta \cos \frac{\theta}{2} + \cos \frac{5\theta}{2} = 2\cos^3 \frac{5\theta}{2} $ in $ \left[ -\frac{\pi}{2}, \frac{\pi}{2} \right] $ is :

Let $ \vec{a} $ and $ \vec{b} $ be the vectors of the same magnitude such that
$ \frac{|\vec{a} + \vec{b}| + |\vec{a} - \vec{b}|}{|\vec{a} + \vec{b}| - |\vec{a} - \vec{b}|} = \sqrt{2} + 1. $ Then $ \frac{|\vec{a} + \vec{b}|^2}{|\vec{a}|^2} ...