JEE Main 2025 (Online) 29th January Morning Shift

0.1 mole of compound ‘S’ will weigh ___________ g.(Given molar mass in g mol−1 C : 12, H : 1, O : 16)

The product (P) formed in the following reaction is :

Match List - I with List - II.

List - I (Structure)
List - II (IUPAC Name)


(A)
(I) 4-Methylpent-1-ene


(B) (CH3)2C(C3H7)2
(II) 3-Ethyl-5-methylheptane


(C)
(III) 4,4-Dimethylheptane

...

Total number of nucleophiles from the following is :

Match List - I with List - II.



List - I (Carbohydrate)
List - II (Linkage Source)




(A) Amylose
(I) $\beta$ - $C_1 - C_4$, plant


(B) Cellulose
(II) $\alpha$ - $C_1 - C_4$, animal


(C) Glycogen
(III) $\alpha$ - $C_1 - C_4$, $\alpha$ ...

At temperature T, compound $AB_{2(g)}$ dissociates as $AB_{2(g)} \rightleftharpoons AB_{(g)} + \frac{1}{2} B_{2(g)}$ having degree of dissociation $ x $ (small compared to unity). The correct expression for $ x $ in terms of $ K_p $ and $ p...

The reaction $A_2 + B_2 \rightarrow 2AB$ follows the mechanism:$A_2 \overset{k_1}{\underset{k_{-1}}{\rightleftharpoons}} A + A$ (fast)$A + B_2 \xrightarrow{k_2} AB + B$ (slow)$A + B \rightarrow AB$ (fast)The overall order of the reaction is...

In the following substitution reaction :

Product 'P' formed is :

The steam volatile compounds among the following are :

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

Given below are some nitrogen containing compounds :Each of them is treated with HCl separately. 1.0 g of the most basic compound will consume _______ mg of HCl.(Given molar mass in g mol−1 C : 12, H : 1, O : 16, Cl : 35.5)

The correct increasing order of stability of the complexes based on $\Delta_0$ value is :

I. $[\text{Mn}(\text{CN})_6]^{3-}$
II. $[\text{Co}(\text{CN})_6]^{4-}$
III. $[\text{Fe}(\text{CN})_6]^{4-}$
IV. $[\text{Fe}(\text{CN})_6]^{3-}$

Match List - I with List - II.


List - I (Complex)
List - II (Hybridisation & Magnetic characters)


(A) [MnBr4]2-
(I) d2sp3 & diamagnetic


(B) [FeF6]3-
(II) sp3d2 & paramagnetic


(C) [Co(C2O4)3]...

The correct option with order of melting points of the pairs (Mn, Fe), (Tc, Ru) and (Re, Os) is :

The molar mass of the water insoluble product formed from the fusion of chromite ore (FeCr₂O₄) with Na₂CO₃ in presence of O₂ is ___________ g mol⁻¹.

For a Mg | Mg2+ (aq) || Ag+ (aq) | Ag the correct Nernst Equation is :

The molar conductivity of a weak electrolyte when plotted against the square root of its concentration, which of the following is expected to be observed?

The standard reduction potential values of some of the p-block ions are given below. Predict the one with the strongest oxidising capacity.

The sum of sigma (σ) and pi (π) bonds in Hex-1,3-dien-5-yne is ________.

An element ‘E’ has the ionisation enthalpy value of 374 kJ mol⁻¹. ‘E’ reacts with elements A, B, C and D with electron gain enthalpy values of −328, −349, −325 and −295 kJ mol⁻¹, respectively. The correct order of the products EA, EB, EC an...

Given below are two statements :Statement (I) : The radii of isoelectronic species increases in the order.
Mg2+ < Na+ < F$-$ < O2-Statement (II) : The magnitude of electron gain enthalpy of halogen decreases in the order.
Cl > F > Br > IIn ...

1.24 g of AX2 (molar mass 124 g mol−1) is dissolved in 1 kg of water to form a solution with boiling point of 100.015°C, while 25.4 g of AY2 (molar mass 250 g mol−1) in 2 kg of water constitutes a solution with a boiling point of 100.0260°C...

If A2B is 30% ionised in an aqueous solution, then the value of van't Hoff factor (i) is _______ × 10−1.

Choose the correct statements.(A) Weight of a substance is the amount of matter present in it.(B) Mass is the force exerted by gravity on an object.(C) Volume is the amount of space occupied by a substance.(D) Temperatures below 0°C are pos...

If $a$0 is denoted as the Bohr radius of hydrogen atom, then what is the de-Broglie wavelength (λ) of the electron present in the second orbit of hydrogen atom? [n : any integer]

500 J of energy is transferred as heat to 0.5 mol of Argon gas at 298 K and 1.00 atm. The final temperature and the change in internal energy respectively are: Given: R = 8.3 J K-1 mol-1

Let $\mathrm{L}_1: \frac{x-1}{1}=\frac{y-2}{-1}=\frac{z-1}{2}$ and $\mathrm{L}_2: \frac{x+1}{-1}=\frac{y-2}{2}=\frac{z}{1}$ be two lines.
Let $L_3$ be a line passing through the point $(\alpha, \beta, \gamma)$ and be perpendicular to both $...

Let the area of the region $ (x, y) : 2y \leq x^2 + 3,\ y + |x| \leq 3, \ y \geq |x - 1| $ be $ A $. Then $ 6A $ is equal to :

The least value of n for which the number of integral terms in the Binomial expansion of $(\sqrt[3]{7}+\sqrt[12]{11})^n$ is 183, is :

Let the line x+y=1 meet the circle $x^2+y^2=4$ at the points A and B. If the line perpendicular to AB and passing through the mid-point of the chord AB intersects the circle at C and D, then the area of the quadrilateral ABCD is equal to :

Let $ |z_1 − 8−2i| \leq 1 $ and $ |z_2−2+6i| \leq 2 $, $ z_1, z_2 \in \mathbb{C} $. Then the minimum value of $ |z_1 − z_2| $ is :

The integral $80 \int\limits_0^{\frac{\pi}{4}}\left(\frac{\sin \theta+\cos \theta}{9+16 \sin 2 \theta}\right) d \theta$ is equal to :

Let $f:(0, \infty) \rightarrow \mathbf{R}$ be a twice differentiable function. If for some $a\ne 0, \int\limits_0^1 f(\lambda x) \mathrm{d} \mathrm{\lambda}=a f(x), f(1)=1$ and $f(16)=\frac{1}{8}$, then $16-f^{\prime}\left(\frac{1}{16}\righ...

Let y = y(x) be the solution of the differential equation :
$\cos x\left(\log _e(\cos x)\right)^2 d y+\left(\sin x-3 y \sin x \log _e(\cos x)\right) d x=0$, x ∈ (0, $\frac{\pi}{2}$ ). If $ y(\frac{\pi}{4}) $ = $-\frac{1}{\log_{e}2}$, then $...

Let the ellipse $E_1: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, $a > b$ and $E_2: \frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$, $A < B$ have same eccentricity $\frac{1}{\sqrt{3}}$. Let the product of their lengths of latus rectums be $\frac{32}{\sq...

Let S = $ \left\{ x : \cos^{-1} x = \pi + \sin^{-1} x + \sin^{-1} [2x + 1] \right\} $. Then $ \sum\limits_{x \in S} (2x - 1)^2 $ is equal to _______.

The value of $\lim \limits_{n \rightarrow \infty}\left(\sum\limits_{k=1}^n \frac{k^3+6 k^2+11 k+5}{(k+3)!}\right)$ is :

Let [t] be the greatest integer less than or equal to t. Then the least value of p ∈ N for which
$ \lim\limits_{x \to 0^+} \left( x (\left[ \frac{1}{x} \right] + \left[ \frac{2}{x} \right] + \ldots + \left[ \frac{p}{x} \right] \right) - x^2...

Let $ A = \begin{bmatrix} a_{ij} \end{bmatrix} = \begin{bmatrix} \log_5 128 & \log_4 5 \\ \log_5 8 & \log_4 25 \end{bmatrix} $. If $ A_{ij} $ is the cofactor of $ a_{ij} $, $ C_{ij} = \sum\limits_{k=1}^{2} a_{ik} A_{jk} , 1 \leq i, j \leq 2...

Let M and m respectively be the maximum and the minimum values of
$f(x)=\left|\begin{array}{ccc}1+\sin ^2 x & \cos ^2 x & 4 \sin 4 x \\ \sin ^2 x & 1+\cos ^2 x & 4 \sin 4 x \\ \sin ^2 x & \cos ^2 x & 1+4 \sin 4 x\end{array}\right|, x \in R$...

Let $S=\left\{m \in \mathbf{Z}: A^{m^2}+A^m=3 I-A^{-6}\right\}$, where $A=\left[\begin{array}{cc}2 & -1 \\ 1 & 0\end{array}\right]$. Then $n(S)$ is equal to __________.

Two parabolas have the same focus (4, 3) and their directrices are the x-axis and the y-axis, respectively. If these parabolas intersect at the points A and B, then (AB)2 is equal to :

Let $ P $ be the set of seven digit numbers with sum of their digits equal to 11. If the numbers in $ P $ are formed by using the digits 1, 2 and 3 only, then the number of elements in the set $ P $ is :

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is _________.

The number of solutions of the equation $ \left( \frac{9}{x} - \frac{9}{\sqrt{x}} + 2 \right) \left( \frac{2}{x} - \frac{7}{\sqrt{x}} + 3 \right) = 0 $ is :

Consider an A. P. of positive integers, whose sum of the first three terms is 54 and the sum of the first twenty terms lies between 1600 and 1800. Then its 11th term is :

Define a relation R on the interval $ \left[0, \frac{\pi}{2}\right) $ by $ x $ R $ y $ if and only if $ \sec^2x - \tan^2y = 1 $. Then R is :

Let $x_1, x_2, ..., x_{10}$ be ten observations such that $\sum\limits_{i=1}^{10} (x_i - 2) = 30$, $\sum\limits_{i=1}^{10} (x_i - \beta)^2 = 98$, $\beta > 2$, and their variance is $\frac{4}{5}$. If $\mu$ and $\sigma^2$ are respectively the...

Let ΔABC be a triangle formed by the lines 7x – 6y + 3 = 0, x + 2y – 31 = 0 and 9x – 2y – 19 = 0. Let the point (h, k) be the image of the centroid of ΔABC in the line 3x + 6y – 53 = 0. Then h2 + k2 + hk is equal to :

Let $\vec{a}=\hat{i}+2 \hat{j}+\hat{k}$ and $\vec{b}=2 \hat{i}+7 \hat{j}+3 \hat{k}$. Let $\mathrm{L}_1 : \overrightarrow{\mathrm{r}}=(-\hat{i}+2 \hat{j}+\hat{k})+\lambda \vec{a}, \mathrm{\lambda} \in \mathbf{R}$ and $\mathrm{L}_2: \overrigh...

Let $ \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k}, \ \vec{b} = 3\hat{i} - 5\hat{j} + \hat{k} $ and $ \vec{c} $ be a vector such that $ \vec{a} \times \vec{c} = \vec{a} \times \vec{b} = \vec{c} \times \vec{b} $ and $ (\vec{a} + \vec{c}) \cdot (\...