Let $f(x) = x^3 + x^2 f'(1) + 2x f''(2) + f'''(3)$, $x \in R$. Then the value of $f'(5)$ is:

1

Let $f : R \to R$ be a twice differentiable function such that $f''(x) > 0$ for all $x \in R$ and $f'(a-1) = 0$, whe…

Topic: JEE Main 2026 (21 January Evening Shift)

2

The positive integer $n$, for which the solutions of the equation $x(x+2) + (x+2)(x+4) + \cdots + (x+2n-2)(x+2n) = \fra…

Topic: JEE Main 2026 (21 January Evening Shift)

1

In the line $ax + 4y = \sqrt{7}$, where $a \in R$, touches the ellipse $3x^2 + 4y^2 = 1$ at the point $P$ in the first …

Topic: JEE Main 2026 (21 January Evening Shift)

2

Let $y^2 = 12x$ be the parabola with its vertex at $O$. Let $P$ be a point on the parabola and $A$ be a point on the y-…

Topic: JEE Main 2026 (21 January Evening Shift)

3

Let one end of a focal chord of the parabola $y^2 = 16x$ be $(16, 16)$. If $P(\alpha, \beta)$ divides this focal chord …

Topic: JEE Main 2026 (21 January Evening Shift)

4

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)

5

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)

6

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)

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

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)

9

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)

10

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

Topic: JEE Main 2026 (21 January Evening Shift)