Let \( f(x) = \begin{cases} \dfrac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x \ne -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases} \) be continuous at \( x = -\frac{3}{2} \). If \( f \circ f(x) = \frac{7}{5} \), then \( x \) is equal to:

1

A building construction work can be completed by two masons $A$ and $B$ together in $22.5$ days. Mason $A$ alone can co…

Topic: JEE Main 2026 (23 January Morning Shift)

2

Let $\alpha$ and $\beta$ respectively be the maximum and the minimum values of the function$f(\theta) = 4\left(\sin^4\l…

Topic: JEE Main 2026 (23 January Morning Shift)

3

Let $S = {z : 3 \le |2z - 3(1 + i)| \le 7}$ be a set of complex numbers. Then $\min_{z \in S} \left|z + \frac{1}{2}(5 +…

Topic: JEE Main 2026 (23 January Morning Shift)

4

Number of solutions of $\sqrt{3}\cos2\theta + 8\cos\theta + 3\sqrt{3} = 0,; \theta \in [-3\pi, 2\pi]$ is:

Topic: JEE Main 2026 (23 January Morning Shift)

5

The vertices $B$ and $C$ of a triangle $ABC$ lie on the line $\frac{x}{1} = \frac{1 - y}{-2} = \frac{z - 2}{3}$. The …

Topic: JEE Main 2026 (23 January Morning Shift)

6

The sum of all possible values of $n \in \mathbb{N}$, so that the coefficients of $x$, $x^2$ and $x^3$ in the expansion…

Topic: JEE Main 2026 (23 January Morning Shift)

7

If $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation$(-2+\sqrt{3})\left(|\sqrt{x}-3|\right) + (x…

Topic: JEE Main 2026 (23 January Morning Shift)

8

Let $y = y(x)$ be the solution of the differential equation $x^4dy + (4x^3y + 2\sin x)dx = 0,; x > 0,; y\left(\frac{…

Topic: JEE Main 2026 (23 January Morning Shift)

9

Let $A = {-2, -1, 0, 1, 2, 3, 4}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $2x + y \le 2$. Let $\e…

Topic: JEE Main 2026 (23 January Morning Shift)

10

Let the line $y - x = 1$ intersect the ellipse $\frac{x^2}{2} + \frac{y^2}{1} = 1$ at the points $A$ and $B$. Then the …

Topic: JEE Main 2026 (23 January Morning Shift)

1

The value of the integral $\displaystyle \int_{\pi/24}^{5\pi/24} \frac{dx}{1 + \sqrt{3}\tan 2x}$ is:

Topic: JEE Main 2026 (23 January Morning Shift)

2

Among the statements: I : \( \begin{vmatrix} 1 & \cos\alpha & \cos\beta \\ \cos\alpha & 1 & \cos\gamma \\ \cos\beta & …

Topic: JEE Main 2026 (23 January Morning Shift)

3

The value of $\dfrac{{}^{100}C_{50}}{51} + \dfrac{{}^{100}C_{51}}{52} + \cdots + \dfrac{{}^{100}C_{100}}{101}$ is:

Topic: JEE Main 2026 (23 January Morning Shift)

4

Let the mean and variance of $8$ numbers $-10,; -7,; -1,; x,; y,; 9,; 2,; 16$ be $\dfrac{7}{2}$ and $\dfrac{293}{4}$,…

Topic: JEE Main 2026 (23 January Morning Shift)

5

Let the direction cosines of two lines satisfy the equations: $4\ell + m - n = 0$ and $2mn + 10n\ell + 3\ell m = 0$. …

Topic: JEE Main 2026 (23 January Morning Shift)

6

Let $|A| = 6$, where $A$ is a $3 \times 3$ matrix. If $|\text{adj}(3\text{adj}(A^2 \cdot \text{adj}(2A)))| = 2^m \cdot…

Topic: JEE Main 2026 (23 January Morning Shift)

7

Let the area of the region bounded by the curve $y = \max{\sin x, \cos x}$, lines $x = 0,; x = \frac{3\pi}{2}$, and th…

Topic: JEE Main 2026 (23 January Morning Shift)

8

Let $f$ be a twice differentiable non-negative function such that$(f(x))^2 = 25 + \int_0^x \big((f(t))^2 + (f'(t))^2\bi…

Topic: JEE Main 2026 (23 January Morning Shift)

9

From the first $100$ natural numbers, two numbers first $a$ and then $b$ are selected randomly without replacement. If …

Topic: JEE Main 2026 (23 January Morning Shift)

10

The number of $4$-letter words, with or without meaning, which can be formed using the letters $PQRPRSTUVP$, is ______.

Topic: JEE Main 2026 (23 January Morning Shift)