JEE Main 2026 (Online) 22nd January Evening Shift

\(\text { 3, 3-Dimethyl-2-butanol cannot be prepared by : }\)

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

The compound $\mathrm{A}, \mathrm{C}_8 \mathrm{H}_8 \mathrm{O}_2$ reacts with acetophenone to form a single product via cross-Aldol condensation. The compound A on reaction with conc. NaOH forms a substituted benzyl alcohol as one of the tw...

\(\text { The IUPAC name of the following compound is : }\)

\(\text { Match List - I with List - II. }\)


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Among $\mathrm{H}_2 \mathrm{~S}, \mathrm{H}_2 \mathrm{O}, \mathrm{NF}_3, \mathrm{NH}_3$ and $\mathrm{CHCl}_3$, identify the molecule $(\mathrm{X})$ with lowest dipole moment value. The number of lone pairs of electrons present on the centra...

Correct statements regarding Arrhenius equation among the following are :
A. Factor $e^{-\mathrm{Ea} / \mathrm{RT}}$ corresponds to fraction of molecules having kinetic energy less than Ea.
B. At a given temperature, lower the Ea, faster is...

Consider $\mathrm{A} \xrightarrow{\mathrm{k}_1} \mathrm{~B}$ and $\mathrm{C} \xrightarrow{\mathrm{k}_2} \mathrm{D}$ are two reactions. If the rate constant $\left(\mathrm{k}_1\right)$ of the $\mathrm{A} \longrightarrow \mathrm{B}$ reaction ...

The mass of benzanilide obtained from the benzoylation reaction of 5.8 g of aniline, if yield of product is $82 \%$, is $\_\_\_\_$ g (nearest integer).
(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathr...

$\left[\mathrm{Ni}\left(\mathrm{PPh}_3\right)_2 \mathrm{Cl}_2\right]$ is a paramagnetic complex. Identify the INCORRECT statements about this complex.
A. The complex exhibits geometrical isomerism.
B. The complex is white in colour.
C. The ...

Given below are two statements :
Statement I : The first ionization enthalpy of Cr is lower than that of Mn .
Statement II : The second and third ionization enthalpies of Cr are higher than those of Mn .
In the light of the above statement...

Among the following oxides of $3 d$ elements, the number of mixed oxides are $\_\_\_\_$ .
$$ \mathrm{Ti}_2 \mathrm{O}_3, \mathrm{~V}_2 \mathrm{O}_4, \mathrm{Cr}_2 \mathrm{O}_3, \mathrm{Mn}_3 \mathrm{O}_4, \mathrm{Fe}_3 \mathrm{O}_4, \mathrm...

Consider the following reduction processes :
$$ \begin{aligned} & \mathrm{Al}^{3+}+3 \mathrm{e}^{-} \longrightarrow \mathrm{Al}(\mathrm{~s}), \mathrm{E}^0=-1.66 \mathrm{~V} \\ & \mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2...

Consider the following electrochemical cell :
\(\mathrm{Pt}\left|\mathrm{O}_2(\mathrm{~g})(1 \mathrm{bar})\right| \mathrm{HCl}(\mathrm{aq}) \| \mathrm{M}^{2+}(\mathrm{aq}, 1.0 \mathrm{M}) \mid \mathrm{M}(\mathrm{~s})\)
The pH above which,...

\(\text { The final product }[\mathrm{B}] \text { is : }\)

Consider the following reaction :

The product Y formed is :

The dibromo compound $[\mathrm{P}]$ (molecular formula: $\mathrm{C}_9 \mathrm{H}_{10} \mathrm{Br}_2$ ) when heated with excess sodamide followed by treatment with dilute HCl gives [Q]. On warming [Q] with mercuric sulphate and dilute sulphu...

Which of the following mixture gives a buffer solution with $\mathrm{pH}=9.25$ ?
Given : $\mathrm{pK}_{\mathrm{b}}\left(\mathrm{NH}_4 \mathrm{OH}\right)=4.75$

Given below are two statements :
Statement I : Elements ' $X$ ' and ' $Y$ ' are the most and least electronegative elements, respectively among $\mathrm{N}, \mathrm{As}, \mathrm{Sb}$ and P . The nature of the oxides $\mathrm{X}_2 \mathrm{O}...

Given below are two statements :
Statement I : $\mathrm{C}<\mathrm{O}<\mathrm{N}<\mathrm{F}$ is the correct order in terms of first ionization enthalpy values.
Statement II : $\mathrm{S}>\mathrm{Se}>\mathrm{Te}>\mathrm{Po}>\mathrm{O}$ is th...

When 1 g of compound $(\mathrm{X})$ is subjected to Kjeldahl's method for estimation of nitrogen, 15 mL 1 M $\mathrm{H}_2 \mathrm{SO}_4$ was neutralized by ammonia evolved. The percentage of nitrogen in compound $(\mathrm{X})$ is :

At $\mathrm{T}(\mathrm{K}), 100 \mathrm{~g}$ of $98 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution is mixed with 100 g of $49 \% \mathrm{H}_2 \mathrm{SO}_4(\mathrm{w} / \mathrm{w})$ aqueous solution. What is the mo...

Identify the correct statements :
A. Hydrated salts can be used as primary standard.
B. Primary standard should not undergo any reaction with air.
C. Reactions of primary standard with another substance should be instantaneous and stoichiom...

$\mathrm{A}+2 \mathrm{~B} \longrightarrow \mathrm{AB}_2$
36.0 g of 'A' (Molar mass : $60 \mathrm{~g} \mathrm{~mol}^{-1}$ ) and 56.0 g of ' B ' (Molar mass : $80 \mathrm{~g} \mathrm{~mol}^{-1}$ ) are allowed to react. Which of the following ...

The energy of first (lowest) Balmer line of H atom is $x \mathrm{~J}$. The energy (in J) of second Balmer line of H atom is :

If the enthalpy of sublimation of Li is $155 \mathrm{~kJ} \mathrm{~mol}^{-1}$, enthalpy of dissociation of $\mathrm{F}_2$ is $150 \mathrm{~kJ} \mathrm{~mol}^{-1}$, ionization enthalpy of Li is $520 \mathrm{~kJ} \mathrm{~mol}^{-1}$, electron...

Let L be the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z+3}{6}$ and let S be the set of all points $(\mathrm{a}, \mathrm{b}, \mathrm{c})$ on L , whose distance from the line $\frac{x+1}{2}=\frac{y+1}{3}=\frac{z-9}{0}$ along the line $L$ is 7 ...

The area of the region $\mathrm{A}=\left\{(x, y): 4 x^2+y^2 \leqslant 8\right.$ and $\left.y^2 \leqslant 4 x\right\}$ is:

Let $\mathrm{C}_{\mathrm{r}}$ denote the coefficient of $x^{\mathrm{r}}$ in the binomial expansion of $(1+x)^{\mathrm{n}}, \mathrm{n} \in \mathrm{N}, 0 \leq \mathrm{r} \leq \mathrm{n}$. If
$P_n=C_0-C_1+\frac{2^2}{3} C_2-\frac{2^3}{4} C_3+\...

Let $\mathrm{S}=\left\{z \in \mathbb{C}: 4 z^2+\bar{z}=0\right\}$. Then $\sum\limits_{z \in \mathrm{~S}}|z|^2$ is equal to:

Let [.] be the greatest integer function. If $\alpha=\int\limits_0^{64}\left(x^{1 / 3}-\left[x^{1 / 3}\right]\right) \mathrm{d} x$, then $\frac{1}{\pi} \int\limits_0^{\alpha \pi}\left(\frac{\sin ^2 \theta}{\sin ^6 \theta+\cos ^6 \theta}\rig...

If $y=y(x)$ satisfies the differential equation $16(\sqrt{x+9 \sqrt{x}})(4+\sqrt{9+\sqrt{x}}) \cos y \mathrm{~d} y=(1+2 \sin y) \mathrm{d} x, x>0$ and $y(256)=\frac{\pi}{2}, y(49)=\alpha$, then $2 \sin \alpha$ is equal to :

Let S and $\mathrm{S}^{\prime}$ be the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ and $\mathrm{P}(\alpha, \beta)$ be a point on the ellipse in the first quadrant. If $(\mathrm{SP})^2+\left(\mathrm{S}^{\prime} \mathrm{P}\right)^2-\...

Let $f(x)=[x]^2-[x+3]-3, x \in \mathbf{R}$, where [.] is the greatest integer funtion. Then

Let the domain of the function $f(x)=\log _3 \log _5\left(7-\log _2\left(x^2-10 x+85\right)\right)+\sin ^{-1}\left(\left|\frac{3 x-7}{17-x}\right|\right)$ be $(\alpha, \beta]$. Then $\alpha+\beta$ is equal to :

Let $f$ and $g$ be functions satisfying $f(x+y)=f(x) f(y), f(1)=7$ and $g(x+y)=g(x y), g(1)=1$, for all $x, y \in \mathbf{N}$. If $\sum\limits_{x=1}^{\mathrm{n}}\left(\frac{f(x)}{\mathrm{g}(x)}\right)=19607$, then n is equal to :

Let $\mathrm{P}(10,2 \sqrt{15})$ be a point on the hyperbola $\frac{x^2}{\mathrm{a}^2}-\frac{y^2}{\mathrm{~b}^2}=1$, whose foci are S and $\mathrm{S}^{\prime}$. If the length of its latus rectum is 8 , then the square of the area of $\Delta...

If $\lim\limits_{x \rightarrow 0} \frac{\mathrm{e}^{(\mathrm{a}-1) x}+2 \cos \mathrm{~b} x+(\mathrm{c}-2) \mathrm{e}^{-x}}{x \cos x-\log _{\mathrm{e}}(1+x)}=2$, then $\mathrm{a}^2+\mathrm{b}^2+\mathrm{c}^2$ is equal to :

Let $[\cdot]$ denote the greatest integer function, and let $f(x)=\min \left\{\sqrt{2} x, x^2\right\}$.
Let $\mathrm{S}=\left\{x \in(-2,2)\right.$ : the function $\mathrm{g}(x)=|x|\left[x^2\right]$ is discontinuous at $\left.x\right\}$.
The...

Let n be the number obtained on rolling a fair die. If the probability that the system
$$ \begin{aligned} & x-\mathrm{n} y+z=6 \\ & x+(\mathrm{n}-2) y+(\mathrm{n}+1) z=8 \\ & \quad(\mathrm{n}-1) y+z=1 \end{aligned} $$
has a unique solution ...

If $X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$ is a solution of the system of equations $A X=B$, where $\operatorname{adj} A=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & 5 \\ 1 & -2 & 3\end{array}\right]$ and $\mathrm{B}=\left[...

Let the locus of the mid-point of the chord through the origin $O$ of the parabola $y^2=4 x$ be the curve S . Let P be any point on S . Then the locus of the point, which internally divides OP in the ratio 3 : 1, is :

Let $\alpha, \beta$ be the roots of the quadratic equation $12 x^2-20 x+3 \lambda=0, \lambda \in \mathbf{Z}$. If $\frac{1}{2} \leqslant|\beta-\alpha| \leqslant \frac{3}{2}$, then the sum of all possible values of $\lambda$ is :

Suppose $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are in A.P. and $\mathrm{a}^2, 2 \mathrm{~b}^2, \mathrm{c}^2$ are in G.P. If $\mathrm{a}<\mathrm{b}<\mathrm{c}$ and $\mathrm{a}+\mathrm{b}+\mathrm{c}=1$, then $9\left(\mathrm{a}^2+\mathrm{b}^2+\m...

The number of elements in the relation $\mathrm{R}=\left\{(x, y): 4 x^2+y^2<52, x, y \in \mathbf{Z}\right\}$ is

Let S be the set of the first 11 natural numbers. Then the number of elements in $A=\{B \subseteq S: n(B) \geqslant 2$ and the product of all elements of $B$ is even $\}$ is $\_\_\_\_$ .

If the mean deviation about the median of the numbers $\mathrm{k}, 2 \mathrm{k}, 3 \mathrm{k}, \ldots ., 1000 \mathrm{k}$ is 500 , then $\mathrm{k}^2$ is equal to :

Among the statements
$(S 1)$ : If $A(5,-1)$ and $B(-2,3)$ are two vertices of a triangle, whose orthocentre is $(0,0)$, then its third vertex is $(-4,-7)$
and
(S2) : If positive numbers $2 a, b, c$ are three consecutive terms of an A.P., th...

Let $\cos (\alpha+\beta)=-\frac{1}{10}$ and $\sin (\alpha-\beta)=\frac{3}{8}$, where $0<\alpha<\frac{\pi}{3}$ and $0<\beta<\frac{\pi}{4}$. If $\tan 2 \alpha=\frac{3(1-r \sqrt{5})}{\sqrt{11}(s+\sqrt{5})}, r, s \in N$, then $r+s$ is equal to ...

Let $\vec{a}=2 \hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\lambda \hat{j}+2 \hat{k}, \lambda \in \boldsymbol{Z}$ be two vectors. Let $\vec{c}=\vec{a} \times \vec{b}$ and $\vec{d}$ be a vector of magnitude 2 in $y z$-plane. If $|\vec{c}|=\sqrt{53...

Let a vector $\overrightarrow{\mathrm{a}}=\sqrt{2} \hat{i}-\hat{j}+\lambda \hat{k}, \lambda>0$, make an obtuse angle with the vector $\overrightarrow{\mathrm{b}}=-\lambda^2 \hat{i}+4 \sqrt{2} \hat{j}+4 \sqrt{2} \hat{k}$ and an angle $\theta...