Let $ A, B $ and $ C $ be three $ 2 \times 2 $ matrices with real entries such that $ B = (I + A)^{-1} $ and $ A + C = I $. If $ BC = \left[ \matrix{ 1 & -5 \cr -1 & 2 } \right] $ and $ CB \left[ \matrix{ x_1 \cr x_2 } \right] = \left[ \matrix{ 12 \cr -6 } \right] $, then $ x_1 + x_2 $ is
Previous 10 Questions — JEE Main 2026 (28 January Morning Shift)
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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)
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 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)
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)
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)
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)
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)
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)
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 $ 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)
Next 10 Questions — JEE Main 2026 (28 January Morning Shift)
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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)
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)
For three unit vectors $ \vec{a}, \vec{b}, \vec{c} $ satisfying$ |\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{…
Topic: JEE Main 2026 (28 January Morning Shift)
Let $ y = y(x) $ be the solution of the differential equation$ x \frac{dy}{dx} - \sin 2y = x^3(2 - x^3)\cos^2 y,; x \ne…
Topic: JEE Main 2026 (28 January Morning Shift)
In a G.P., if the product of the first three terms is $ 27 $ and the set of all possible values for the sum of its firs…
Topic: JEE Main 2026 (28 January Morning Shift)
For some $ \theta \in \left( 0, \frac{\pi}{2} \right) $, let the eccentricity and the length of the latus rectum of the…
Topic: JEE Main 2026 (28 January Morning Shift)
If $ k = \tan\left( \frac{\pi}{4} + \frac{1}{2}\cos^{-1}\left(\frac{2}{3}\right) \right) + \tan\left( \frac{1}{2}\sin^{…
Topic: JEE Main 2026 (28 January Morning Shift)
The value of $ \sum_{n=1}^{20} \left[ \sqrt{\pi} \int_0^\pi [x]\sin(nx),dx \right] $ is ______
Topic: JEE Main 2026 (28 January Morning Shift)
Let $ PQR $ be a triangle such that $ \overrightarrow{PQ} = -2\hat{i} - \hat{j} + 2\hat{k} $ and $ \overrightarrow{PR} …
Topic: JEE Main 2026 (28 January Morning Shift)
