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 + 141 $ is equal to
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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)
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)
The value of $ \sum_{k=1}^{\infty} (-1)^{k+1} \frac{k(k+1)}{k!} $ is:
Topic: JEE Main 2026 (28 January Morning Shift)
Next 10 Questions — JEE Main 2026 (28 January Morning Shift)
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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)
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)
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 …
Topic: JEE Main 2026 (28 January Morning Shift)
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)
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)
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)
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)
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)
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)
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)
