JEE Main 2026 (Online) 28th January Morning Shift

\(\text { Consider the following reaction sequence }\)
Compound $(\mathrm{y})$ develops characteristic colour with neutral $\mathrm{FeCl}_3$ solution.
Identify the INCORRECT statement from the following for the above sequence.

\(\text { Given below are the four isomeric compounds }(\mathrm{P}, \mathrm{Q}, \mathrm{R}, \mathrm{~S})\)

Identify correct statements from below.
A. $\mathrm{Q}, \mathrm{R}$ and S will give precipitate with 2, 4-DNP.
B. $P$ and $Q$ will...

\(\text { Given below are two statements for the following reaction sequence. }\)

Statement I : Compound ' $Z$ ' will give yellow precipitate with NaOI .
Statement II : Compound ' Q ' has two different types of ' H ' atoms (aromatic : al...

0.53 g of an organic compound $(\mathrm{x})$ when heated with excess of nitric acid (concentrated) and then with silver nitrate gave 0.75 g of silver bromide precipitate. 1.0 g of $(\mathrm{x})$ gave 1.32 g of $\mathrm{CO}_2$ gas on combust...

CORRECT order of stability for the following is
$\mathrm{CH}_2=\mathrm{CH}^{-}, \mathrm{CH}_3-\mathrm{CH}_2^{-}, \mathrm{CH} \equiv \mathrm{C}^{-}$

In the given pentapeptide, find out an essential amino acid $(\mathrm{Y})$ and the sequence present in the pentapeptide :

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

Given below are two statements :
Statement I : The number of species among $\mathrm{BF}_4^{-}, \mathrm{SiF}_4, \mathrm{XeF}_4$ and $\mathrm{SF}_4$, that have unequal $\mathrm{E}-\mathrm{F}$ bond lengths is two. Here, E is the central atom.
...

An organic compound undergoes first order decomposition. The time taken for decomposition to $\left(\frac{1}{8}\right)^{\text {th }}$ and $\left(\frac{1}{10}\right)^{\text {th }}$ of its initial concentration are $\mathrm{t}_{1 / 8}$ and $\...

The correct statement among the following is:

X is the number of geometrical isomers exhibited by $\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)\left(\mathrm{H}_2 \mathrm{O}\right) \mathrm{BrCl}\right]$.
Y is the number of optically inactive isomer(s) exhibited by $\left[\mathrm{CrCl}_2(...

Given below are two statements :
Statement I : The number of pairs, from the following, in which both the ions are coloured in aqueous solution is 3.
$$ \left[\mathrm{Sc}^{3+}, \mathrm{Ti}^{3+}\right],\left[\mathrm{Mn}^{2+}, \mathrm{Cr}^{2+...

Consider the following redox reaction taking place in acidic medium
\(\mathrm{BH}_4^{-}(a q)+\mathrm{ClO}_3^{-}(a q) \longrightarrow \mathrm{H}_2 \mathrm{BO}_3^{-}(a q)+\mathrm{Cl}^{-}(a q)\)
If the Nernst equation for the above balanced ...

Consider the following reactions giving major product. Identify the correct reaction.

$\mathrm{Ph}-\mathrm{CH}=\mathrm{CH}_2 \xrightarrow[\mathrm{HBr}]{(\mathrm{PhCOO})_2}$ Product
Consider the above reaction
A. The reaction proceeds through a more stable radical intermediate.
B. The role of peroxide is to generate $${H^ \bu...

Consider a weak base ' B ' of $\mathrm{pK}_{\mathrm{b}}=5.699$. ' $x$ ' mL of 0.02 M HCl and ' y ' mL of 0.02 M weak base ' B ' are mixed to make 100 mL of a buffer of pH 9 at $25^{\circ} \mathrm{C}$. The values of ' $x$ ' and ' $y$ ' respe...

Consider the dissociation equilibrium of the following weak acid
\(\mathrm{HA} \rightleftharpoons \mathrm{H}^{+}(\mathrm{aq})+\mathrm{A}^{-}(\mathrm{aq})\)
If the pKa of the acid is 4 , then the pH of 10 mM HA solution is $\_\_\_\_$ .(Nea...

Regarding the hydrides of group 15 elements $\mathrm{EH}_3(\mathrm{E}=\mathrm{N}, \mathrm{P}, \mathrm{As}, \mathrm{Sb})$, select the correct statement from the following :
A. The stability of hydrides decreases down the group.
B. The basici...

In period 4 of the periodic table, the elements with highest and lowest atomic radii are respectively.

Method used for separation of mixture of products ( B and C ) obtained in the following reaction is

500 mL of 1.2 M KI solution is mixed with 500 mL of $0.2 \mathrm{M} \mathrm{KMnO}_4$ solution in basic medium. The liberated iodine was titrated with standard $0.1 \mathrm{M} \mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ solution in the presenc...

Given below are two statements:
Statement I : Griss-Ilosvay test is used for the detection of nitrite ion, which involves the use of sulphanilic acid and $\alpha$-naphthylamine reagent.
Statement II : In the above test, sulphanilic acid is ...

At $\mathrm{T}(\mathrm{K}), 2$ moles of liquid A and 3 moles of liquid B are mixed. The vapour pressure of ideal solution formed is 320 mm Hg . At this stage, one mole of A and one mole of B are added to the solution. The vapour pressure is...

Figure 1. electron probability density for 2 s orbital

Figure 2. wave function for 2s orbital
Which of the following point in Figure 2 most accurately represents the nodal surface as shown in Figure 1?

The wave numbers of three spectral lines of H atom are considered. Identify the set of spectral lines belonging to Balmer series.
( $\mathrm{R}=$ Rydberg constant)

$20.0 \mathrm{dm}^3$ of an ideal gas ' X ' at 600 K and 0.5 MPa undergoes isothermal reversible expansion until pressure of the gas is 0.2 MPa . Which of the following option is correct?
(Given: $\log 2=0.3010$ and $\log 5=0.6989$ )

If the distances of the point $(1,2, a)$ from the line $\frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1}$ along the lines $\mathrm{L}_1: \frac{x-1}{3}=\frac{y-2}{4}=\frac{z-a}{b}$ and $\mathrm{L}_2: \frac{x-1}{1}=\frac{y-2}{4}=\frac{z-a}{c}$ are equ...

The area of the region $\mathrm{R}=\left\{(x, y): x y \leq 8,1 \leq y \leq x^2, x \geq 0\right\}$ is

Let $y=x$ be the equation of a chord of the circle $\mathrm{C}_1$ (in the closed half-plane $x \geq 0$ ) of diameter 10 passing through the origin. Let $\mathrm{C}_2$ be another circle described on the given chord as its diameter. If the eq...

Let $z$ be a complex number such that $|z-6|=5$ and $|z+2-6 i|=5$. Then the value of $z^3+3 z^2-15 z+141$ is equal to :

\(\text { The value of } \sum\limits_{r=1}^{20}\left(\left|\sqrt{\pi\left(\int\limits_0^r x|\sin \pi x| d x\right)}\right|\right) \text { is }\)

Let $f$ be a polynomial function such that $f\left(x^2+1\right)=x^4+5 x^2+2$, for all $x \in \mathbb{R}$.
Then $\int\limits_0^3 f(x) d x$ is equal to

Let $y=y(x)$ be the solution of the differential equation
\(x \frac{d y}{d x}-\sin 2 y=x^3\left(2-x^3\right) \cos ^2 y, x \neq 0 .\)
If $y(2)=0$, then $\tan (y(1))$ is equal to

If $g(x)=3 x^2+2 x-3, f(0)=-3$ and $4 g(f(x))=3 x^2-32 x+72$, then $f(g(2))$ is equal to:

For some $\theta \in\left(0, \frac{\pi}{2}\right)$, let the eccentricity and the length of the latus rectum of the hyperbola $x^2-y^2 \sec ^2 \theta=8$ be $e_1$ and $l_1$, respectively, and let the eccentricity and the length of the latus r...

If $\int\left(\frac{1-5 \cos ^2 x}{\sin ^5 x \cos ^2 x}\right) d x=f(x)+\mathrm{C}$, where C is the constant of integration, then $f\left(\frac{\pi}{6}\right)-f\left(\frac{\pi}{4}\right)$ is equal to

If $k=\tan \left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1}\left(\frac{2}{3}\right)\right)+\tan \left(\frac{1}{2} \sin ^{-1}\left(\frac{2}{3}\right)\right)$, then
the number of solutions of the equation $\sin ^{-1}(k x-1)=\sin ^{-1} x-\cos ^{-1}...

The value of
\(\lim\limits_{x \rightarrow 0} \frac{\log _e\left(\sec (e x) \cdot \sec \left(e^2 x\right) \cdot \ldots \cdot \sec \left(e^{10} x\right)\right)}{e^2-e^{2 \cos x}}\)
is equal to

Let $A, B$ and $C$ be three $2 \times 2$ matrices with real entries such that $B=(I+A)^{-1}$ and $\mathrm{A}+\mathrm{C}=\mathrm{I}$.
If $\mathrm{BC}=\left[\begin{array}{cc}1 & -5 \\ -1 & 2\end{array}\right]$ and $\mathrm{CB}\left[\begin{ar...

Let $\mathrm{S}=\{1,2,3,4,5,6,7,8,9\}$. Let $x$ be the number of 9-digit numbers formed using the digits of the set S such that only one digit is repeated and it is repeated exactly twice. Let $y$ be the number of 9 -digit numbers formed us...

A bag contains 10 balls out of which $k$ are red and $(10-k)$ are black, where $0 \leq k \leq 10$. If three balls are drawn at random without replacement and all of them are found to be black, then the probability that the bag contains 1 re...

Let $\mathrm{S}=\left\{x^3+a x^2+b x+c: a, b, c \in \mathrm{~N}\right.$ and $\left.a, b, c \leq 20\right\}$ be a set of polynomials. Then the number of polynomials in S , which are divisible by $x^2+2$, is

If $\alpha, \beta$, where $\alpha<\beta$, are the roots of the equation $\lambda x^2-(\lambda+3) x+3=0$ such that $\frac{1}{\alpha}-\frac{1}{\beta}=\frac{1}{3}$, then the sum of all possible values of $\lambda$ is

In a G.P., if the product of the first three terms is 27 and the set of all possible values for the sum of its first three terms is $\mathbb{R}-(a, b)$, then $a^2+b^2$ is equal to
$\_\_\_\_$ .

The common difference of the A.P.: $a_1, a_2, \ldots, a_{\mathrm{m}}$ is 13 more than the common difference of the A.P.: $b_1, b_2, \ldots, b_n$. If $b_{31}=-277, b_{43}=-385$ and $a_{78}=327$, then $a_1$ is equal to

The value of $\sum\limits_{k=1}^{\infty}(-1)^{k+1}\left(\frac{k(k+1)}{k!}\right)$ is

The mean and variance of 10 observations are 9 and 34.2 , respectively. If 8 of these observations are $2,3,5,10,11,13,15,21$, then the mean deviation about the median of all the 10 observations is

Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the line $x+2 \sqrt{2} y=4$. If the co-ordinates of the vertex A are $(\alpha, \beta)$, then the greatest integer less than or equal to $|\alpha+\sqrt{2} \...

If $\frac{\tan (\mathrm{A}-\mathrm{B})}{\tan \mathrm{A}}+\frac{\sin ^2 \mathrm{C}}{\sin ^2 \mathrm{~A}}=1, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \in\left(0, \frac{\pi}{2}\right)$, then

For three unit vectors $\vec{a}, \vec{b}, \vec{c}$ satisfying
\(|\vec{a}-\vec{b}|^2+|\vec{b}-\vec{c}|^2+|\vec{c}-\vec{a}|^2=9 \text { and }|2 \vec{a}+k \vec{b}+k \vec{c}|=3 \text {, }\)
the positive value of k is :

Let $P Q R$ be a triangle such that $\overrightarrow{P Q}=-2 \hat{i}-\hat{j}+2 \hat{k}$ and $\overrightarrow{\mathrm{PR}}=a \hat{\mathrm{i}}+b \hat{\mathrm{j}}-4 \hat{\mathrm{k}}, a, b \in \mathrm{Z}$. Let S be the point on QR , which is eq...