Let $\mathrm{A}=\left[\begin{array}{cc}\alpha & -1 \\ 6 & \beta\end{array}\right], \alpha>0$, such that $\operatorname{det}(\mathrm{A})=0$ and $\alpha+\beta=1$. If I denotes $2 \times 2$ identity matrix, then the matrix $(I+A)^8$ is :

1

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}…

Topic: JEE Main 2025 (2 April Morning Shift)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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)

10

The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:

Topic: JEE Main 2025 (2 April Morning Shift)