JEE Main 2026 (Online) 24th January Morning Shift
JEE Main / 75 questions
2026Sat, Jan 24, 2026 3:30 AM75 PYQs
1Alcohols Phenols And Ethers
A hydroxy compound $(\mathrm{X})$ with molar mass $122 \mathrm{~g} \mathrm{~mol}^{-1}$ is acetylated with acetic anhydride, using a large excess of the reagent ensuring complete acetylation of all hydroxyl groups. The product obtained has a...
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2Aldehydes Ketones And Carboxylic Acids
A student is given one compound among the following compounds that gives positive test with Tollen's reagent.
The compound is :
The compound is :
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3Aldehydes Ketones And Carboxylic Acids
\(\text { Consider the following two reactions } \mathrm{A} \text { and } \mathrm{B} \text {. }\)
Numerical value of [molar mass of $x+$ molar mass of $y$ ] is $\_\_\_\_$
Numerical value of [molar mass of $x+$ molar mass of $y$ ] is $\_\_\_\_$
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4Basics Of Organic Chemistry
\(\text { Arrange the following carbanions in the decreasing order of stability. }\)
Choose the correct answer from the options given below :
Choose the correct answer from the options given below :
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5Chemical Bonding And Molecular Structure
Given below are statements about some molecules/ions.
Identify the CORRECT statements.
A. The dipole moment value of $\mathrm{NF}_3$ is higher than that of $\mathrm{NH}_3$.
B. The dipole moment value of $\mathrm{BeH}_2$ is zero.
C. The bond...
Identify the CORRECT statements.
A. The dipole moment value of $\mathrm{NF}_3$ is higher than that of $\mathrm{NH}_3$.
B. The dipole moment value of $\mathrm{BeH}_2$ is zero.
C. The bond...
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6Chemical Bonding And Molecular Structure
Among the following, the CORRECT combinations are
A. $\mathrm{IF}_3 \rightarrow \mathrm{~T}$-shaped ( $\mathrm{sp}^3 \mathrm{~d}$ )
B. $\mathrm{IF}_5 \rightarrow$ Square pyramidal $\left(\mathrm{sp}^3 \mathrm{~d}^2\right)$
C. $\mathrm{IF}_7...
A. $\mathrm{IF}_3 \rightarrow \mathrm{~T}$-shaped ( $\mathrm{sp}^3 \mathrm{~d}$ )
B. $\mathrm{IF}_5 \rightarrow$ Square pyramidal $\left(\mathrm{sp}^3 \mathrm{~d}^2\right)$
C. $\mathrm{IF}_7...
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7Chemical Kinetics And Nuclear Chemistry
$\mathrm{A} \rightarrow \mathrm{D}$ is an endothermic reaction occurring in three steps (elementary).
(i) $\mathrm{A} \rightarrow \mathrm{B} \Delta \mathrm{H}_i=+\mathrm{ve}$
(ii) $\mathrm{B} \rightarrow \mathrm{C} \Delta \mathrm{H}_{i i}=-...
(i) $\mathrm{A} \rightarrow \mathrm{B} \Delta \mathrm{H}_i=+\mathrm{ve}$
(ii) $\mathrm{B} \rightarrow \mathrm{C} \Delta \mathrm{H}_{i i}=-...
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8Chemical Kinetics And Nuclear Chemistry
At $27^{\circ} \mathrm{C}$ in presence of a catalyst, activation energy of a reaction is lowered by $10 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The logarithm of ratio of $\frac{\mathrm{k} \text { (catalysed) }}{\mathrm{k} \text { (uncatalysed) }}...
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9Compounds Containing Nitrogen
\(\text { The correct stability order of the following diazonium salts is }\)
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10Coordination Compounds
Given below are two statements :
Statement I : Hybridisation, shape and spin only magnetic moment of $\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{CO}_3\right)_3\right]$ is $\mathrm{sp}^3 \mathrm{~d}^2$, octahedral and 4.9 BM respectively.
St...
Statement I : Hybridisation, shape and spin only magnetic moment of $\mathrm{K}_3\left[\mathrm{Co}\left(\mathrm{CO}_3\right)_3\right]$ is $\mathrm{sp}^3 \mathrm{~d}^2$, octahedral and 4.9 BM respectively.
St...
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11Coordination Compounds
Consider a mixture ' X ' which is made by dissolving 0.4 mol of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{SO}_4\right] \mathrm{Br}$ and 0.4 mol of $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_5 \mathrm{Br}\right] \mathrm{SO}_4$...
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12Coordination Compounds
Given below are two statements:
Statement I : The number of paramagnetic species among $\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{TiF}_6\right]^{3-}$, $\mathrm{V}_2 \mathrm{O}_5$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ is 3 ...
Statement I : The number of paramagnetic species among $\left[\mathrm{CoF}_6\right]^{3-},\left[\mathrm{TiF}_6\right]^{3-}$, $\mathrm{V}_2 \mathrm{O}_5$ and $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$ is 3 ...
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13Electrochemistry
Electricity is passed through an acidic solution of $\mathrm{Cu}^{2+}$ till all the $\mathrm{Cu}^{2+}$ was exhausted, leading to the deposition of 300 mg of Cu metal. However, a current of 600 mA was continued to pass through the same solut...
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14Haloalkanes And Haloarenes
Match the List-I with List-II
table {width: 100%; border-collapse: collapse; margin: 20px 0;}th {background-color: blue; color: white; border: 1px solid lightgrey; padding: 10px;}td {border: 1px solid lightgrey; padding: 10px; text-align: l...
table {width: 100%; border-collapse: collapse; margin: 20px 0;}th {background-color: blue; color: white; border: 1px solid lightgrey; padding: 10px;}td {border: 1px solid lightgrey; padding: 10px; text-align: l...
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15Haloalkanes And Haloarenes
Given below are two statements :
Statement I : ' $\mathrm{C}-\mathrm{Cl}$ ' bond is stronger in $\mathrm{CH}_2=\mathrm{CH}-\mathrm{Cl}$ than $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{Cl}$
Statement II : The given optically active molecule, on
h...
Statement I : ' $\mathrm{C}-\mathrm{Cl}$ ' bond is stronger in $\mathrm{CH}_2=\mathrm{CH}-\mathrm{Cl}$ than $\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{Cl}$
Statement II : The given optically active molecule, on
h...
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16Hydrocarbons
\(\text {Arrange the following alkenes in decreasing order of stability. }\)
Choose the correct answer from the options given below:
Choose the correct answer from the options given below:
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17Ionic Equilibrium
Consider two Group IV metal ions $\mathrm{X}^{2+}$ and $\mathrm{Y}^{2+}$.
A solution containing $0.01 \mathrm{M} \mathrm{X}^{2+}$ and $0.01 \mathrm{M} \mathrm{Y}^{2+}$ is saturated with $\mathrm{H}_2 \mathrm{~S}$. The pH at which the metal ...
A solution containing $0.01 \mathrm{M} \mathrm{X}^{2+}$ and $0.01 \mathrm{M} \mathrm{Y}^{2+}$ is saturated with $\mathrm{H}_2 \mathrm{~S}$. The pH at which the metal ...
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18Periodic Table And Periodicity
Given below are two statements :
Statement I : $\mathrm{K}>\mathrm{Mg}>\mathrm{Al}>\mathrm{B}$ is the correct order in terms of metallic character.
Statement II : Atomic radius is always greater than the ionic radius for any element.
In the...
Statement I : $\mathrm{K}>\mathrm{Mg}>\mathrm{Al}>\mathrm{B}$ is the correct order in terms of metallic character.
Statement II : Atomic radius is always greater than the ionic radius for any element.
In the...
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19Practical Organic Chemistry
In Dumas method for estimation of nitrogen, 0.50 g of an organic compound gave 70 mL of nitrogen collected at 300 K and 715 mm pressure. The percentage of nitrogen in the organic compound is $\_\_\_\_$ $\%$.
(Aqueous tension at 300 K is 15 ...
(Aqueous tension at 300 K is 15 ...
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20Redox Reactions
X and Y are the number of electrons involved, respectively during the oxidation of $\mathrm{I}^{-}$to $\mathrm{I}_2$ and $\mathrm{S}^{2-}$ to S by acidified $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$. The value of $\mathrm{X}+\mathrm{Y}$ is ...
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21Salt Analysis
Consider three metal chlorides $\mathrm{x}, \mathrm{y}$ and z , where x is water soluble at room temperature, y is sparingly soluble in water at room temperature and z is soluble in hot water. $\mathrm{x}, \mathrm{y}$ and z are respectively...
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22Solutions
A solution is prepared by dissolving 0.3 g of a non-volatile non-electrolyte solute 'A' of molar mass $60 \mathrm{~g} \mathrm{~mol}^{-1}$ and 0.9 g of a non-volatile non-electrolyte solute ' B ' of molar mass $180 \mathrm{~g} \mathrm{~mol}^...
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23Solutions
' W ' g of a non-volatile electrolyte solid solute of molar mass ' M ' $\mathrm{g} \mathrm{mol}^{-1}$ when dissolved in 100 mL water, decreases vapour pressure of water from 640 mm Hg to 600 mm Hg . If aqueous solution of the electrolyte bo...
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24Structure Of Atom
The hydrogen spectrum consists of several spectral lines in Lyman series $\left(L_1, L_2\right.$, $\mathrm{L}_3 \ldots ; \mathrm{L}_1$ has lowest energy among Lyman series). Similarly it consists of several spectral lines in Balmer series $...
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25Thermodynamics
\(\text { Match the LIST-I with LIST-II }\)
List-I Isothermal process for ideal gas system
List-II Work done (
V
f
>
V
i
V
f
>
V
List-I Isothermal process for ideal gas system
List-II Work done (
>
>
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263d Geometry
Let a line L passing through the point $\mathrm{P}(1,1,1)$ be perpendicular to the lines $\frac{x-4}{4}=\frac{y-1}{1}=\frac{z-1}{1}$ and $\frac{x-17}{1}=\frac{y-71}{1}=\frac{z}{0}$. Let the line L intersect the $y z-$ plane at the point Q ....
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27Application Of Derivatives
Let $(2 \alpha, \alpha)$ be the largest interval in which the function $f(t)=\frac{|t+1|}{t^2}, t<0$, is strictly decreasing. Then the local maximum value of the function $g(x)=2 \log _{\mathrm{e}}(x-2)+\alpha x^2+4 x-\alpha, x>2$, is $\_\_...
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28Area Under The Curves
Let $\mathrm{A}_1$ be the bounded area enclosed by the curves $y=x^2+2, x+y=8$ and $y$-axis that lies in the first quadrant. Let $\mathrm{A}_2$ be the bounded area enclosed by the curves $y=x^2+2, y^2=x, x=2$, and $y$-axis that lies in the ...
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29Binomial Theorem
Let $\mathrm{S}=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+\ldots$ up to 13 terms. If $13 \mathrm{~S}=\frac{2^k}{n!}, k \in \mathrm{~N}$, then $n+k$ is equal to
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30Circle
Let a circle of radius 4 pass through the origin O , the points $\mathrm{A}(-\sqrt{3} a, 0)$ and $\mathrm{B}(0,-\sqrt{2} b)$, where $a$ and $b$ are real parameters and $a b \neq 0$. Then the locus of the centroid of $\triangle \mathrm{OAB}$...
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31Complex Numbers
Let $\mathrm{S}=\left\{z \in \mathbb{C}:\left|\frac{z-6 i}{z-2 i}\right|=1\right.$ and $\left.\left|\frac{z-8+2 i}{z+2 i}\right|=\frac{3}{5}\right\}$.
Then $\sum\limits_{z \in \mathrm{~s}}|z|^2$ is equal to :
Then $\sum\limits_{z \in \mathrm{~s}}|z|^2$ is equal to :
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32Definite Integration
Let a differentiable function $f$ satisfy the equation $\int_0^{36} f\left(\frac{t x}{36}\right) d t=4 \alpha f(x)$. If $y=f(x)$ is a standard parabola passing through the points $(2,1)$ and $(-4, \beta)$, then $\beta^\alpha$ is equal to $\...
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33Ellipse
Let each of the two ellipses $\mathrm{E}_1: \frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ and $\mathrm{E}_2: \frac{x^2}{\mathrm{~A}^2}+\frac{y^2}{\mathrm{~B}^2}=1,(\mathrm{~A}<\mathrm{B})$ have eccentricity $\frac{4}{5}$. Let the lengths of the ...
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34Indefinite Integrals
Let $f(t)=\int\left(\frac{1-\sin \left(\log _e t\right)}{1-\cos \left(\log _e t\right)}\right) d t, t>1$.
If $f\left(e^{\pi / 2}\right)=-e^{\pi / 2}$ and $f\left(e^{\pi / 4}\right)=\alpha e^{\pi / 4}$, then $\alpha$ equals
If $f\left(e^{\pi / 2}\right)=-e^{\pi / 2}$ and $f\left(e^{\pi / 4}\right)=\alpha e^{\pi / 4}$, then $\alpha$ equals
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35Limits Continuity And Differentiability
Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(x)= \begin{cases}2 \alpha\left(x^2-2\right)+2 \beta x & , x<1 \\ (\alpha+3) x+(\alpha-\beta) & , x \geq 1\end{cases}$ be differentiable at all $x \in \mathbb{R}$. Then $34(\alp...
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36Limits Continuity And Differentiability
If the function $f(x)=\frac{e^x\left(e^{\tan x-x}-1\right)+\log _e(\sec x+\tan x)-x}{\tan x-x}$ is continuous at $x=0$, then the value of $f(0)$ is equal to
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37Matrices And Determinants
The number of $3 \times 2$ matrices A , which can be formed using the elements of the set $\{-2,-1,0,1,2\}$ such that the sum of all the diagonal elements of $\mathrm{A}^{\mathrm{T}} \mathrm{A}$ is 5 , is
$\_\_\_\_$
$\_\_\_\_$
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38Permutations And Combinations
The number of numbers greater than 5000 , less than 9000 and divisible by 3 , that can be formed using the digits $0,1,2,5,9$, if the repetition of the digits is allowed, is $\_\_\_\_$
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39Probability
From a lot containing 10 defective and 90 non-defective bulbs, 8 bulbs are selected one by one with replacement. Then the probability of getting at least 7 defective bulbs is
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40Quadratic Equation And Inequalities
If the domain of the function
\(f(x)=\log _{\left(10 x^2-17 x+7\right)}\left(18 x^2-11 x+1\right)\)
is $(-\infty, a) \cup(b, c) \cup(d, \infty)-\{e\}$, then
$90(a+b+c+d+e)$ equals:
\(f(x)=\log _{\left(10 x^2-17 x+7\right)}\left(18 x^2-11 x+1\right)\)
is $(-\infty, a) \cup(b, c) \cup(d, \infty)-\{e\}$, then
$90(a+b+c+d+e)$ equals:
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41Quadratic Equation And Inequalities
The number of the real solutions of the equation: $x|x+3|+|x-1|-2=0$ is
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42Sequences And Series
Consider an A.P.: $a_1, a_2, \ldots, a_{\mathrm{n}} ; a_1>0$. If $a_2-a_1=\frac{-3}{4}, a_{\mathrm{n}}=\frac{1}{4} a_1$, and $\sum\limits_{\mathrm{i}=1}^{\mathrm{n}} a_{\mathrm{i}}=\frac{525}{2}$, then $\sum\limits_{\mathrm{i}=1}^{17} a_{\m...
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43Sequences And Series
Let $729,81,9,1, \ldots$ be a sequence and $\mathrm{P}_n$ denote the product of the first $n$ terms of this sequence.
If $2 \sum\limits_{n=1}^{40}\left(\mathrm{P}_n\right)^{\frac{1}{n}}=\frac{3^\alpha-1}{3^\beta}$ and $\operatorname{gcd}(\a...
If $2 \sum\limits_{n=1}^{40}\left(\mathrm{P}_n\right)^{\frac{1}{n}}=\frac{3^\alpha-1}{3^\beta}$ and $\operatorname{gcd}(\a...
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44Sets And Relations
Let $R$ be a relation defined on the set $\{1,2,3,4\} \times\{1,2,3,4\}$ by
\(\mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\} .\)
Then the number of elements in R is
\(\mathrm{R}=\{((a, b),(c, d)): 2 a+3 b=3 c+4 d\} .\)
Then the number of elements in R is
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45Statistics
The mean and variance of a data of 10 observations are 10 and 2 , respectively. If an observations $\alpha$ in this data is replaced by $\beta$, then the mean and variance become 10.1 and 1.99 , respectively. Then $\alpha+\beta$ equals
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46Straight Lines And Pair Of Straight Lines
Let $A(1,0), B(2,-1)$ and $C\left(\frac{7}{3}, \frac{4}{3}\right)$ be three points. If the equation of the bisector of the angle ABC is $\alpha x+\beta y=5$, then the value of $\alpha^2+\beta^2$ is
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47Trigonometric Ratio And Identites
The value of $\frac{\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}}{\cos 20^{\circ} \cos 40^{\circ} \cos 60^{\circ} \cos 80^{\circ}}$ is equal to
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48Trigonometric Ratio And Identites
If $\cot x=\frac{5}{12}$ for some $x \in\left(\pi, \frac{3 \pi}{2}\right)$, then $\sin 7 x\left(\cos \frac{13 x}{2}+\sin \frac{13 x}{2}\right)+\cos 7 x\left(\cos \frac{13 x}{2}-\sin \frac{13 x}{2}\right)$ is equal to
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49Vector Algebra
Let $\vec{a}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-2 \hat{\mathrm{k}}, \vec{b}=\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and $\vec{c}=\vec{a} \times \vec{b}$. Let $\vec{d}$ be a vector such that $|\vec{d}-\vec{a}|=\sqrt{11},|\vec{c} \times \vec{d}|=...
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50Vector Algebra
Let the lines $\mathrm{L}_1: \vec{r}=\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}}+\lambda(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+4 \hat{\mathrm{k}}), \lambda \in \mathbb{R}$ and $\mathrm{L}_2: \vec{r}=(4 \hat{\mathrm{i}}+\hat{\math...
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