Let $A(1, 2)$ and $C(-3, -6)$ be two diagonally opposite vertices of a rhombus, whose sides $AD$ and $BC$ are parallel to the line $7x - y = 14$. If $B(\alpha, \beta)$ and $D(\gamma, \delta)$ are the other two vertices, then $|\alpha + \beta + \gamma + \delta|$ is equal to:
Next 10 Questions — JEE Main 2026 (23 January Evening Shift)
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Consider two sets
$A = {x \in \mathbb{Z} : |x - 3| - 3 \le 1}$
and
$B = {x \in \mathbb{R} - {1,2} : \dfrac{(x-2)(x-4…
Topic: JEE Main 2026 (23 January Evening Shift)
The system of linear equations
$x + y + z = 6$
$2x + 5y + az = 36$
$x + 2y + 3z = b$
has
Topic: JEE Main 2026 (23 January Evening Shift)
The sum of all the real solutions of the equation
$\log_{x+3}(6x^2 + 28x + 30) - 5 = 2\log_{6x+10}(x^2 + 6x + 9)$
is eq…
Topic: JEE Main 2026 (23 January Evening Shift)
If the points of intersection of the ellipses
$x^2 + 2y^2 - 6x - 12y + 23 = 0$
and
$4x^2 + 2y^2 - 20x - 12y + 35 = 0$
l…
Topic: JEE Main 2026 (23 January Evening Shift)
Let $PQ$ be a chord of the hyperbola$\frac{x^2}{4} - \frac{y^2}{b^2} = 1$,perpendicular to the x-axis such that triangl…
Topic: JEE Main 2026 (23 January Evening Shift)
$\vec{a}, \vec{b}, \vec{c}$ be three vectors such that$\vec{a} \times \vec{b} = 2(\vec{a} \times \vec{c})$.If $|\vec{a}…
Topic: JEE Main 2026 (23 January Evening Shift)
Bag $A$ contains $9$ white and $8$ black balls, while bag $B$ contains $6$ white and $4$ black balls. One ball is rando…
Topic: JEE Main 2026 (23 January Evening Shift)
The area of the region enclosed between the circles$x^2 + y^2 = 4$ and $x^2 + (y-2)^2 = 4$ is:
Topic: JEE Main 2026 (23 January Evening Shift)
The least value of$\cos^2\theta - 6\sin\theta\cos\theta + 3\sin^2\theta + 2$is:
Topic: JEE Main 2026 (23 January Evening Shift)
Let $I(x) = \int \dfrac{3dx}{(4x+6)\sqrt{4x^2 + 8x + 3}}$ and
$I(0) = \dfrac{\sqrt{3}}{4} + 20$. If $I\left(\dfrac{1}{…
Topic: JEE Main 2026 (23 January Evening Shift)
