Let $ S = { x^3 + ax^2 + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20 } $ be a set of polynomials. Then the number of polynomials in $ S $, which are divisible by $ x^2 + 2 $, is

1

Let $ S = {1, 2, 3, 4, 5, 6, 7, 8, 9} $. Let $ x $ be the number of 9-digit numbers formed using the digits of the set …

Topic: JEE Main 2026 (28 January Morning Shift)

2

Let $ ABC $ be an equilateral triangle with orthocenter at the origin and the side $ BC $ on the line $ x + 2\sqrt{2}y …

Topic: JEE Main 2026 (28 January Morning Shift)

3

Let $ z $ be a complex number such that $ |z - 6| = 5 $ and $ |z + 2 - 6i| = 5 $. Then the value of $ z^3 + 3z^2 - 15z …

Topic: JEE Main 2026 (28 January Morning Shift)

4

If $ \frac{\tan(A - B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1 $, $ A, B, C \in \left( 0, \frac{\pi}{2} \right) $, then

Topic: JEE Main 2026 (28 January Morning Shift)

5

Let $ y = x $ be the equation of a chord of the circle $ C_1 $ (in the closed half-plane $ x \ge 0 $) of diameter 10 pa…

Topic: JEE Main 2026 (28 January Morning Shift)

6

The value of $ \sum_{k=1}^{\infty} (-1)^{k+1} \frac{k(k+1)}{k!} $ is:

Topic: JEE Main 2026 (28 January Morning Shift)

1

A bag contains 10 balls out of which $ k $ are red and $ (10 - k) $ are black, where $ 0 \le k \le 10 $. If three balls…

Topic: JEE Main 2026 (28 January Morning Shift)

2

If $ \alpha, \beta $, where $ \alpha < \beta $, are the roots of the equation $ \lambda x^2 - (\lambda + 3)x + 3 = 0 $…

Topic: JEE Main 2026 (28 January Morning Shift)

3

If $ \int \frac{1 - 5\cos^2 x}{\sin^5 x \cos^2 x} dx = f(x) + C $ where $ C $ is the constant of integration, then $ f\…

Topic: JEE Main 2026 (28 January Morning Shift)

4

Let $ f $ be a polynomial function such that $ f(x^2 + 1) = x^4 + 5x^2 + 2 $, for all $ x \in \mathbb{R} $. Then $ \int…

Topic: JEE Main 2026 (28 January Morning Shift)

5

The area of the region $ R = {(x, y) : xy \le 8,; 1 \le y \le x^2,; x \ge 0 } $ is

Topic: JEE Main 2026 (28 January Morning Shift)

6

The value of $ \lim_{x \to 0} \frac{\log_e(\sec(ex))\sec(e^2x)\ldots\sec(e^{10}x)}{e^2 - e^{2\cos x}} $ is equal to

Topic: JEE Main 2026 (28 January Morning Shift)

7

The mean and variance of 10 observations are 9 and 34.2, respectively. If 8 of these observations are $ 2, 3, 5, 10, 11…

Topic: JEE Main 2026 (28 January Morning Shift)

8

Let $ A, B $ and $ C $ be three $ 2 \times 2 $ matrices with real entries such that $ B = (I + A)^{-1} $ and $ A + C = …

Topic: JEE Main 2026 (28 January Morning Shift)

9

The common difference of the A.P.: $ a_1, a_2, \ldots, a_n $ is 13 more than the common difference of the A.P.: $ b_1, …

Topic: JEE Main 2026 (28 January Morning Shift)

10

If the distances of the point $ (1, 2, a) $ from the line$ \frac{x - 1}{1} = \frac{y}{2} = \frac{z - 1}{1} $along the l…

Topic: JEE Main 2026 (28 January Morning Shift)