Let $S$ denote the set of $4$-digit numbers $abcd$ such that $a > b > c > d$ and $P$ denote the set of $5$-digit numbers having product of its digits equal to $20$. Then $n(S) + n(P)$ is equal to ______.

1

Let \( A = \begin{bmatrix} 0 & 2 & -3 \\ -2 & 0 & 1 \\ 3 & -1 & 0 \end{bmatrix} \) and \( B \) be a matrix such that…

Topic: JEE Main 2026 (23 January Evening Shift)

2

The number of elements in the set\( S = \{ x : x \in [0,100], \int_{0}^{x} t^2 \sin(x-t)\,dt = x^2 \} \)is ______.

Topic: JEE Main 2026 (23 January Evening Shift)

3

If the image of the point $P(a, 2, a)$ in the line $\dfrac{x}{2} = \dfrac{y + a}{1} = \dfrac{z}{1}$ is $Q$ and the im…

Topic: JEE Main 2026 (23 January Evening Shift)

4

If the solution curve $y = f(x)$ of the differential equation $(x^2 - 4)y' - 2xy + 2x(4 - x)^2 = 0,; x > 2$, passes t…

Topic: JEE Main 2026 (23 January Evening Shift)

5

Let $\sum a_k = \alpha n^2 + \beta n$. If $a_{10} = 59$ and $a_6 = 7a_4$, then $\alpha + \beta$ is equal to:

Topic: JEE Main 2026 (23 January Evening Shift)

6

An equilateral triangle $OAB$ is inscribed in the parabola $y^2 = 4x$ with vertex at origin. Then the minimum distance …

Topic: JEE Main 2026 (23 January Evening Shift)

7

Question

Topic: JEE Main 2026 (23 January Evening Shift)

8

If $z = \dfrac{\sqrt{3}}{2} + \dfrac{i}{2},; i = \sqrt{-1}$, then $(z^{201} - i)^5$ is equal to:

Topic: JEE Main 2026 (23 January Evening Shift)

9

Let $A = {0,1,2,\ldots,9}$. Let $R$ be a relation on $A$ defined by $(x,y) \in R$ iff $|x-y|$ is a multiple of $3$. Gi…

Topic: JEE Main 2026 (23 January Evening Shift)

10

The number of ways, in which $16$ oranges can be distributed to four children such that each child gets at least one or…

Topic: JEE Main 2026 (23 January Evening Shift)