A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1: 2x+y+6=0$ and $L_2: 4x+2y-p=0,; p>0$ at the points $A$ and $B$, respectively. If $|AB|=\dfrac{9}{\sqrt{2}}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\dfrac{AM}{BM}$ is equal to
Previous 10 Questions — JEE Main 2025 (3 April Morning Shift)
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\text { If } y(x)=\left|\begin{array}{ccc}
\sin x & \cos x & \sin x+\cos x+1 \\
27 & 28 & 27 \\
1 & 1 & 1
\end{array}…
Topic: JEE Main 2025 (3 April Morning Shift)
Let $z \in \mathbb{C}$ be such that $\dfrac{z^2+3i}{z-2+i}=2+3i$. Then the sum of all possible values of $z^2$ is:
Topic: JEE Main 2025 (3 April Morning Shift)
If $\displaystyle \sum_{r=1}^{9} \left(\dfrac{r + 3}{2^r}\right) \cdot {^9C_r} = \alpha \left(\dfrac{3}{2}\right)^9 - \…
Topic: JEE Main 2025 (3 April Morning Shift)
The sum of all rational terms in the expansion of $(2 + \sqrt{3})^8$ is:
Topic: JEE Main 2025 (3 April Morning Shift)
Let $g$ be a differentiable function such that
$\displaystyle \int_0^x g(t),dt = x - \int_0^x t g(t),dt,; x \ge 0$
and …
Topic: JEE Main 2025 (3 April Morning Shift)
Line $L_1$ passes through the point $(1, 2, 3)$ and is parallel to the $z$-axis.
Line $L_2$ passes through the point $(…
Topic: JEE Main 2025 (3 April Morning Shift)
A line passing through the point $P(\sqrt{5}, \sqrt{5})$ intersects the ellipse
$\dfrac{x^2}{36} + \dfrac{y^2}{25} = 1$…
Topic: JEE Main 2025 (3 April Morning Shift)
Let $\quad f(x)= \begin{cases}(1+a x)^{1 / x} & , x0\end{cases}$ be continuous at $x=0$. Then $e^a b c$ is equal to:
Topic: JEE Main 2025 (3 April Morning Shift)
Let a line passing through the point $(4,1,0)$ intersect the line $\mathrm{L}_1: \frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}…
Topic: JEE Main 2025 (3 April Morning Shift)
Let $\alpha$ and $\beta$ be the roots of $x^2 + \sqrt{3}x - 16 = 0$, and $\gamma$ and $\delta$ be the roots of $x^2 + 3…
Topic: JEE Main 2025 (3 April Morning Shift)
