JEE Main 2026 (Online) 2nd April Morning Shift

If the point of intersection of the lines $ \frac{x+1}{3} = \frac{y+a}{5} = \frac{z+b+1}{7} $ and $ \frac{x-2}{1} = \frac{y-b}{4} = \frac{z-2a}{7} $ lies on xy-plane, then the value of $a+b$ is:

Let a line L passing through the point (1, 1, 1) be perpendicular to both the vectors $2\hat{i} + 2\hat{j} + \hat{k}$ and $\hat{i} + 2\hat{j} + 2\hat{k}$. If $P(a, b, c)$ is the foot of perpendicular from the origin on the line L, then the ...

The number of critical points of the function $f(x) = \begin{cases} |\frac{\sin x}{x}|, & x \neq 0 \\ 1, & x = 0 \end{cases}$ in the interval $(-2\pi, 2\pi)$ is equal to :

Let a circle C have its centre in the first quadrant, intersect the coordinate axes at exactly three points and cut off equal intercepts from the coordinate axes. If the length of the chord of C on the line $x + y = 1$ is $\sqrt{14}$, then ...

Let $x$ and $y$ be real numbers such that $50\left(\frac{2 x}{1+3 i}-\frac{y}{1-2 i}\right)=31+17 i, i=\sqrt{-1}$. Then the value of $10(x-3 y)$ is :

Let [.] denote the greatest integer function. Then the value of $\int\limits_{0}^{3} \left( \frac{e^{x} + e^{-x}}{[x]!} \right) dx$ is :

If $\alpha = \int\limits_{0}^{2\sqrt{3}} \log_{2}(x^{2} + 4) \, dx + \int\limits_{2}^{4} \sqrt{2x - 4} \, dx$, then $\alpha^{2}$ is equal to ________.

If the curve $y = f(x)$ passes through the point $(1, e)$ and satisfies the differential equation $dy = y(2 + \\log_e x) dx$, $x > 0$, then $f(e)$ is equal to :

Let $y = y(x)$ be the solution curve of the differential equation $(1 + \sin x)\dfrac{dy}{dx} + (y + 1)\cos x = 0,\ y(0) = 0.$ If the curve $y = y(x)$ passes through the point $\left( \alpha , \dfrac{-1}{2} \right)$, then a value of $\alph...

Let an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, $a < b$, pass through the point (4, 3) and have eccentricity $\frac{\sqrt{5}}{3}$.Then the length of its latus rectum is :

If the domain of the function $f(x) = \sqrt{\log_{(0.6)} (\left| \frac{2x-5}{x^2-4} \right|)}$ is $(-\infty, a] \cup \{b\} \cup [c, d) \cup (e, \infty)$, then the value of $a + b + c + d + e$ is ________.

If $ \lim\limits_{x\to 2} \frac{\sin\left(x^3 - 5x^2 + ax + b\right)}{\left(\sqrt{x-1}-1\right) \log_e(x-1)} = m $, then $a + b + m$ is equal to :

Let $\alpha, \beta \in \mathbb{R}$ be such that the system of linear equations
$ \begin{aligned} x + 2y + z &= 5 \\ 2x + y + \alpha z &= 5 \\ 8x + 4y + \beta z &= 18 \end{aligned} $
has no solution. Then $\frac{\beta}{\alpha}$ is equal to :

Let $A = \begin{bmatrix} 1 & 2 \\ 1 & \alpha \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 3 \\ \beta & 2 \end{bmatrix}$. If $A^2 - 4A + I = O$ and $B^2 - 5B - 6I = O$, then among the two statements:
(S1) : $[(B-A)(B+A)]^T = \begin{bmatrix} 1...

The number of seven-digit numbers, that can be formed by using the digits 1, 2, 3, 5 and 7 such that each digit is used at least once, is:

The number of elements in the set $S = \left\{ (r, k) : k \in \mathbb{Z} \text{ and } ^{36}C_{r+1} = \frac{6\left(^{35}C_{r}\right)}{(k^2-3)} \right\}$ is :

Let a, b, c ∈ {1, 2, 3, 4}. If the probability, that $a x^2 + 2\sqrt{2} bx + c > 0$ for all $x \in \mathbb{R}$, is $\frac{m}{n}$, $\gcd(m, n) = 1$, then $m + n$ is equal to ________.

Let $\alpha, \alpha+2, \alpha \in \mathbf{Z}$, be the roots of the quadratic equation $x(x+2)+(x+1)(x+3)+(x+2)(x+4)+\ldots .+(x+\mathrm{n}-1)(x+\mathrm{n}+1)=4 \mathrm{n}$ for some $\mathrm{n} \in \mathbf{N}$. Then $\mathrm{n}+\alpha$ is eq...

Let A be the set of first 101 terms of an A.P., whose first term is 1 and the common difference is 5 and let B be the set of first 71 terms of an A.P., whose first term is 9 and the common difference is 7. Then the number of elements in $A ...

If $\sum\limits_{k=1}^{n} a_k = 6 n^3$, then $\sum\limits_{k=1}^{6} \left( \frac{a_{k+1} - a_k}{36} \right)^2$ is equal to ________.

If the mean of the datatable {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: left;}Class5-10...

Let the mid points of the sides of a triangle ABC be $\left(\frac{5}{2}, 7\right)$, $\left(\frac{5}{2}, 3\right)$ and $(4, 5)$. If its incentre is $(h, k)$, then $3h + k$ is equal to :

Let $S = \{x \in [-\pi, \pi] : \sin x (\sin x + \cos x) = a,\ a \in \mathbb{Z} \}$. Then $n(S)$ is equal to:

If $\sin\left(\frac{\pi}{18}\right) \sin\left(\frac{5\pi}{18}\right) \sin\left(\frac{7\pi}{18}\right) = K$, then the value of $\sin\left(\frac{10K\pi}{3}\right)$ is:

If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=2$ and $|\vec{b}|=3$, then the maximum value of $3|(3 \vec{a}+2 \vec{b})|+4|(3 \vec{a}-2 \vec{b})|$ is :