Let the lines $L_1:\ \vec r=\hat i+2\hat j+3\hat k+\lambda(2\hat i+3\hat j+4\hat k)$ and $L_2:\ \vec r=(4\hat i+\hat j)+\mu(5\hat i+2\hat j+\hat k)$ intersect at point $R$. Let $P$ and $Q$ be points on $L_1$ and $L_2$ such that $|PR|=\sqrt{29}$ and $|OQ|=\sqrt{\frac{47}{3}}$. If $P$ lies in the first octant, then $27(OR)^2$ is equal to:
Previous 10 Questions — JEE Main 2026 (24 January Morning Shift)
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Let a circle of radius $4$ pass through the origin $O$, the point $A(-\sqrt{3}a,0)$ and $B(0,-\sqrt{2}b)$, where $a$ an…
Topic: JEE Main 2026 (24 January Morning Shift)
If the function
$f(x)=\dfrac{e^x\left(e^{\tan x}-1\right)+\ln(\sec x+\tan x)-x}{\tan x-x}$
is continuous at $x=0$, then…
Topic: JEE Main 2026 (24 January Morning Shift)
Next 10 Questions — JEE Main 2026 (24 January Morning Shift)
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Let $729, 81, 9, 1, \ldots$ be a sequence and $P_n$ denote the product of the first $n$ terms of this sequence.
If $2\s…
Topic: JEE Main 2026 (24 January Morning Shift)
Let $\vec a = 2\hat i + \hat j - 2\hat k,; \vec b = \hat i + \hat j$ and $\vec c = \vec a \times \vec b$.
Let $\vec d$…
Topic: JEE Main 2026 (24 January Morning Shift)
If the domain of the function
$f(x)=\log_{(10x^2-17x+7)}(18x^2-11x+1)$
is $(-\infty,a)\cup(b,c)\cup(d,\infty)-{e}$, t…
Topic: JEE Main 2026 (24 January Morning Shift)
Let each of the two ellipses
\( E_1:\ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \ (a > b) \)
and
\( E_2:\ \frac{x^…
Topic: JEE Main 2026 (24 January Morning Shift)
The value of
$\dfrac{\sqrt{3}\csc20^\circ-\sec20^\circ}{\cos20^\circ\cos40^\circ\cos60^\circ\cos80^\circ}$
is equal t…
Topic: JEE Main 2026 (24 January Morning Shift)
Let
$S={z\in\mathbb{C}:\left|\frac{z-6i}{z-2i}\right|=1 \text{ and } \left|\frac{z-8+2i}{z+2i}\right|=\frac{3}{5}}$
T…
Topic: JEE Main 2026 (24 January Morning Shift)
If $\cot x=\frac{5}{12}$ for some $x\in\left(\frac{\pi}{2},\frac{3\pi}{2}\right)$, then
$\sin7x\left(\cos\frac{13x}{2}…
Topic: JEE Main 2026 (24 January Morning Shift)
Let
$f(t)=\int \frac{1-\sin(\log_e t)}{1-\cos(\log_e t)}dt,; t>1$
If $f(e^{\pi/2})=-e^{-\pi/2}$ and $f(e^{\pi/4})=\al…
Topic: JEE Main 2026 (24 January Morning Shift)
Let $R$ be a relation defined on ${1,2,3,4}\times{1,2,3,4}$ by
$R={((a,b),(c,d)):2a+3b=3c+4d}$
Then the number of ele…
Topic: JEE Main 2026 (24 January Morning Shift)
Let $A(1,0),; B(2,-1)$ and $C\left(\frac{7}{3},\frac{4}{3}\right)$ be three points.
If equation of bisector of angle $…
Topic: JEE Main 2026 (24 January Morning Shift)
