Let the values of $\lambda$ for which the shortest distance between the lines $\frac{x-1}{2} = \frac{y-2}{3} = \frac{z-3}{4}$
and $\frac{x-\lambda}{3} = \frac{y-4}{4} = \frac{z-5}{5}$ is $\frac{1}{\sqrt{6}}$ be $\lambda_1$ and $\lambda_2$. Then the radius of the circle passing through the
points $(0, 0), (\lambda_1, \lambda_2)$ and $(\lambda_2, \lambda_1)$ is
Next 10 Questions — JEE Main 2025 (8 April Evening Shift)
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Let $f(x)=x-1$ and $g(x)=e^x$ for $x\in\mathbb{R}$. If $\dfrac{dy}{dx}=e^{-2\sqrt{x}}g\big(f(f(x))\big)-\dfrac{y}{\sqrt…
Topic: JEE Main 2025 (8 April Evening Shift)
If $ \frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots \infty= \frac{\pi^4}{90} $, $\frac{1}{1^4} + \frac{1}{3^4} …
Topic: JEE Main 2025 (8 April Evening Shift)
Let a be the length of a side of a square OABC with O being the origin. Its side OA makes an acute angle $\alpha $ with…
Topic: JEE Main 2025 (8 April Evening Shift)
A line passing through the point $P(a, 0)$ makes an acute angle $\alpha$ with the positive x-axis. Let this line be rot…
Topic: JEE Main 2025 (8 April Evening Shift)
Let the ellipse $3x^2 + py^2 = 4$ pass through the centre $C$ of the circle $x^2 + y^2 - 2x - 4y - 11 = 0$ of radius $r…
Topic: JEE Main 2025 (8 April Evening Shift)
The sum of the squares of the roots of $|x - 2|^2 + |x - 2| - 2 = 0$ and the squares of the roots of $x^2 - 2|x - 3| - …
Topic: JEE Main 2025 (8 April Evening Shift)
The value of $ \cot^{-1} \left( \frac{\sqrt{1 + \tan^2(2)} - 1}{\tan(2)} \right) - \cot^{-1} \left( \frac{\sqrt{1 + \ta…
Topic: JEE Main 2025 (8 April Evening Shift)
Let $A = {\theta \in [0,2\pi] : 1 + 10,\mathrm{Re}\left(\dfrac{2\cos\theta + i\sin\theta}{\cos\theta - 3i\sin\theta}\ri…
Topic: JEE Main 2025 (8 April Evening Shift)
Given below are two statements:
Statement I:
$\displaystyle \lim_{x \to 0} \left( \tan^{-1}x + \log_e \dfrac{\sqrt{1+x…
Topic: JEE Main 2025 (8 April Evening Shift)
The integral $\displaystyle \int_{-1}^{\tfrac{3}{2}} \left( |\pi^2 x \sin(\pi x)| \right) dx$ is equal to
Topic: JEE Main 2025 (8 April Evening Shift)
