The number of integral solutions $x$ of $\log _{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2 x-3}\right)^{2} \geq 0$ is :

1

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 m…

Topic: JEE Main 2023 (11 April Morning Shift)

2

The number of triplets , where  are distinct non negative integers satisfying , is :

Topic: JEE Main 2023 (11 April Morning Shift)

3

Let $\vec{a}$ be a non-zero vector parallel to the line of intersection of the two planes described by $\hat{i} + \ha…

Topic: JEE Main 2023 (11 April Morning Shift)

4

Area of the region \[ \{(x, y) : x^2 + (y - 2)^2 \le 4, \; x^2 \ge 2y\} \] is:

Topic: JEE Main 2023 (11 April Morning Shift)

5

Consider ellipses $\mathbf{E_k} : kx^2 + k^2y^2 = 1, \; k = 1, 2, \ldots, 20$. Let $\mathbf{C_k}$ be the circle which…

Topic: JEE Main 2023 (11 April Morning Shift)

6

Let $f(x) = \lfloor x^2 - x \rfloor + | -x + \lfloor x \rfloor |$, where $x \in \mathbb{R}$ and $\lfloor t \rfloor$ d…

Topic: JEE Main 2023 (11 April Morning Shift)

7

Let $\mathbf{A}$ be a $2 \times 2$ matrix with real entries such that $\mathbf{A}' = \alpha \mathbf{A} + \mathbf{I}$,…

Topic: JEE Main 2023 (11 April Morning Shift)

8

For any vector $\vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k}$, with $10|a_i| < 1, \; i = 1, 2, 3$, consider the …

Topic: JEE Main 2023 (11 April Morning Shift)

9

Let sets A and B have 5 elements each. Let the mean of the elements in sets A and B be 5 and 8 respectively and the var…

Topic: JEE Main 2023 (11 April Morning Shift)

10

The value of the integral \[ \int_{-\log_e 2}^{\log_e 2} e^x \left( \log_e\!\left( e^x + \sqrt{1 + e^{2x}} \right) \r…

Topic: JEE Main 2023 (11 April Morning Shift)