Aspire Faculty ID #18063 · Topic: JEE Main 2026 (24 January Evening Shift) · Just now
JEE Main 2026 (24 January Evening Shift)

Let the angles made with the positive $x$-axis by two straight lines drawn from the point $P(2, 3)$ and meeting the line $x + y = 6$ at a distance $ \sqrt{\frac{2}{3}} $ from the point $P$ be $ \theta_1 $ and $ \theta_2 $. Then the value of $ (\theta_1 + \theta_2) $ is:

Solution



Let $Q$ is $ \left( \sqrt{\frac{2}{3}} \cos\theta + 2,; \sqrt{\frac{2}{3}} \sin\theta + 3 \right) $

so, $ x + y = 6 $

$ \sqrt{\frac{2}{3}} (\cos\theta + \sin\theta) + 5 = 6 $

$ \sin\theta + \cos\theta = \sqrt{\frac{3}{2}} $

$ 1 + \sin 2\theta = \frac{3}{2} $

$ \sin 2\theta = \frac{1}{2} $

$ 2\theta = \frac{\pi}{6},; \frac{5\pi}{6} $

$ \theta = \frac{\pi}{12},; \frac{5\pi}{12} $

So $ \theta_1 + \theta_2 = \frac{\pi}{2} $
← Previous Next →

Previous 10 Questions — JEE Main 2026 (24 January Evening Shift)

Nearest first
1
Let the length of the latus rectum of an ellipse $ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, $ (a > b) $, be $30$. If i…
Topic: JEE Main 2026 (24 January Evening Shift)
 2
Let $ f(x) = \int \frac{7x^{10} + 9x^8}{(1 + x^2 + 2x^9)^2} ,dx $, $ x > 0 $, $ \lim_{x \to 0} f(x) = 0 $ and $ f(1) =…
Topic: JEE Main 2026 (24 January Evening Shift)

Next 10 Questions — JEE Main 2026 (24 January Evening Shift)

Ascending by ID
1
Let $ \vec{a} = 2\hat{i} - \hat{j} - \hat{k}, \vec{b} = \hat{i} + 3\hat{j} - \hat{k} $ and $ \vec{c} = 2\hat{i} + \hat{…
Topic: JEE Main 2026 (24 January Evening Shift)
 2
Let $ \alpha_1, \alpha_2, \alpha_3, \alpha_4 $ be an A.P. of four terms such that each term of the A.P. and its common …
Topic: JEE Main 2026 (24 January Evening Shift)
 3
Let the image of parabola $ x^2 = 4y $, in the line $ x - y = 1 $ be $ (y + \alpha)^2 = b(x - c) $, $ a, b, c \in \math…
Topic: JEE Main 2026 (24 January Evening Shift)
 4
$ \left( \frac{1}{3} + \frac{4}{7} \right) + \left( \frac{1}{3^2} + \frac{1}{3} \times \frac{4}{7} + \frac{4^2}{7^2} \r…
Topic: JEE Main 2026 (24 January Evening Shift)
 5
Let $ P = [p_{ij}] $ and $ Q = [q_{ij}] $ be two square matrices of order $ 3 $ such that $ q_{ij} = 2^{(i + j - 1)} p_…
Topic: JEE Main 2026 (24 January Evening Shift)
 6
The letters of the word "UDAYPUR" are written in all possible ways with or without meaning and these words are arranged…
Topic: JEE Main 2026 (24 January Evening Shift)
 7
The largest value of $ n $, for which $ 40^n $ divides $ 60! $, is:
Topic: JEE Main 2026 (24 January Evening Shift)
 8
The sum of all values of $ \alpha $, for which the shortest distance between the lines $ \frac{x+1}{\alpha} = \frac{y-…
Topic: JEE Main 2026 (24 January Evening Shift)
 9
Let $ f(\alpha) $ denote the area of the region in the first quadrant bounded by $ x = 0, x = 1, y^2 = x $ and $ y = | …
Topic: JEE Main 2026 (24 January Evening Shift)
 10
If the domain of the function $ f(x) = \sin^{-1} \left( \frac{1}{x^2 - 2x - 2} \right) $, is $ (-\infty, \alpha] \cup […
Topic: JEE Main 2026 (24 January Evening Shift)
Ask Your Question or Put Your Review.

loading...