Let the vertices $Q$ and $R$ of the triangle $PQR$ lie on the line $\dfrac{x + 3}{5} = \dfrac{y - 1}{2} = \dfrac{z + 4}{3}$, $QR = 5$ and the coordinates of the point $P$ be $(0, 2, 3)$. If the area of the triangle $PQR$ is $\dfrac{m}{n}$, then:
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Let $a \in R$ and $A$ be a matrix of order $3 \times 3$ such that $\operatorname{det}(A)=-4$ and $A+I=\left[\begin{arra…
Topic: JEE Main 2025 (2 April Morning Shift)
If $\theta \in[-2 \pi, 2 \pi]$, then the number of solutions of $2 \sqrt{2} \cos ^2 \theta+(2-\sqrt{6}) \cos \theta-\sq…
Topic: JEE Main 2025 (2 April Morning Shift)
If $S$ and $S'$ are the foci of the ellipse $\dfrac{x^2}{18} + \dfrac{y^2}{9} = 1$ and $P$ be a point on the ellipse, t…
Topic: JEE Main 2025 (2 April Morning Shift)
Let the focal chord $PQ$ of the parabola $y^2 = 4x$ make an angle of $60^\circ$ with the positive $x$-axis, where $P$ l…
Topic: JEE Main 2025 (2 April Morning Shift)
If the function $f(x) = 2x^3 - 9ax^2 + 12a^2x + 1$, where $a > 0$, attains its local maximum and local minimum values a…
Topic: JEE Main 2025 (2 April Morning Shift)
Let $ABCD$ be a tetrahedron such that the edges $AB$, $AC$ and $AD$ are mutually perpendicular.
Let the areas of the tr…
Topic: JEE Main 2025 (2 April Morning Shift)
Let $z$ be a complex number such that $|z| = 1$.
If $\dfrac{2 + k\bar{z}}{k + z} = kz$, $k \in \mathbb{R}$, then the ma…
Topic: JEE Main 2025 (2 April Morning Shift)
Let one focus of the hyperbola $\textbf{H}: \dfrac{x^2}{a^2} - \dfrac{y^2}{b^2} = 1$ be at $(\sqrt{10}, 0)$ and the cor…
Topic: JEE Main 2025 (2 April Morning Shift)
The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:
Topic: JEE Main 2025 (2 April Morning Shift)
Let $P_n = \alpha^n + \beta^n$, $n \in \mathbb{N}$.
If $P_{10} = 123$, $P_9 = 76$, $P_8 = 47$ and $P_1 = 1$, then the q…
Topic: JEE Main 2025 (2 April Morning Shift)
