Let $A = {2,3,5,7,9}$. Let $R$ be the relation on $A$ defined by $xRy$ if and only if $2x \le 3y$. Let $\ell$ be the number of elements in $R$, and $m$ be the minimum number of elements required to be added in $R$ to make it a symmetric relation. Then $\ell + m$ is equal to:

1

Let $y = y(x)$ be the solution of differential equation $\sec x \frac{dy}{dx} - 2y = 2 + 3\sin x$, $x \in \left(-\frac{…

Topic: JEE Main 2026 (21 January Evening Shift)

2

For a triangle $ABC$, let $\vec{p} = \overrightarrow{BC},; \vec{q} = \overrightarrow{CA}$ and $\vec{r} = \overrightarro…

Topic: JEE Main 2026 (21 January Evening Shift)

3

For the matrices $A = \begin{bmatrix} 3 & -4 \ 1 & -1 \end{bmatrix}, \quad B = \begin{bmatrix} -29 & 49 \ -13 & 18 \en…

Topic: JEE Main 2026 (21 January Evening Shift)

4

Let $A = {x : |x^2 - 10| \le 6}$ and $B = {x : |x - 2| > 1}$. Then

Topic: JEE Main 2026 (21 January Evening Shift)

5

Let $a_1, \frac{a_2}{2}, \frac{a_3}{2^2},; \ldots, \frac{a_{10}}{2^9}$ be a G.P. of common ratio $\frac{1}{\sqrt{2}}$. …

Topic: JEE Main 2026 (21 January Evening Shift)

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If the area of the region ${(x,y) : 1 - 2x \le y \le 4 - x^2,; x \ge 0,; y \ge 0}$ is $\frac{\alpha}{\beta}$, $\alpha, …

Topic: JEE Main 2026 (21 January Evening Shift)

7

A random variable $X$ takes values $0, 1, 2, 3$ with probabilities $\frac{2a+1}{30}, \frac{8a-1}{30}, \frac{4a+1}{30},b…

Topic: JEE Main 2026 (21 January Evening Shift)

8

Let $\alpha$ and $\beta$ be the roots of equation $x^2 + 2ax + (3a + 10) = 0$ such that $\alpha < 1 < \beta$. Then the …

Topic: JEE Main 2026 (21 January Evening Shift)

9

Let the line $L_1$ be parallel to the vector $-3\hat{i} + 2\hat{j} + 4\hat{k}$ and pass through the point $(2, 6, 7)$, …

Topic: JEE Main 2026 (21 January Evening Shift)

10

Let the line $L$ pass through the point $(-3, 5, 2)$ and make equal angles with the positive coordinate axes. If the di…

Topic: JEE Main 2026 (21 January Evening Shift)

1

The system of equations$3x + y + 4z = 3$$2x + ay - z = -3$$x + 2y + z = 4$has no solution, then the value of $\alpha$ i…

Topic: JEE Main 2026 (21 January Evening Shift)

2

Let $z$ be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34\left|…

Topic: JEE Main 2026 (21 January Evening Shift)

3

The largest $n \in \mathbb{N}$, for which $7^n$ divides $101!$, is:

Topic: JEE Main 2026 (21 January Evening Shift)

4

Let $[ \cdot ]$ denote the greatest integer function and $f(x) = \lim_{n \to \infty} \frac{1}{n} \sum_{k=1}^{n} \left[…

Topic: JEE Main 2026 (21 January Evening Shift)

5

If $\displaystyle \int_{0}^{1} 4\cot^{-1}(1 - 2x + 4x^2),dx = a\tan^{-1}(2) - b\log_e(5)$, where $a,b \in \mathbb{N}$, …

Topic: JEE Main 2026 (21 January Evening Shift)

6

Let the maximum value of $(\sin^{-1}x)^2 + (\cos^{-1}x)^2$ for $x \in \left[-\frac{\sqrt{3}}{2}, \frac{1}{\sqrt{2}}\rig…

Topic: JEE Main 2026 (21 January Evening Shift)

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If $\displaystyle \left(\frac{1}{^{15}C_0} + \frac{1}{^{15}C_1}\right)\left(\frac{1}{^{15}C_1} + \frac{1}{^{15}C_2}\ri…

Topic: JEE Main 2026 (21 January Evening Shift)

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If $P$ is a point on the circle $x^2 + y^2 = 4$, $Q$ is a point on the straight line $5x + y + 2 = 0$ and $x - y + 1 = …

Topic: JEE Main 2026 (21 January Evening Shift)