An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

1

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

Topic: JEE Main 2023 (11 April Morning Shift)

2

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)

3

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)

4

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)

5

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)

6

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)

7

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)

8

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)

9

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)

10

Let $y = y(x)$ be a solution curve of the differential equation \[ (1 - x^2 y^2)\,dx = y\,dx + x\,dy. \] If the line …

Topic: JEE Main 2023 (11 April Morning Shift)

1

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

Topic: JEE Main 2023 (11 April Morning Shift)