$\displaystyle 4 \int_0^1 \left(\dfrac{1}{\sqrt{3 + x^2} + \sqrt{1 + x^2}}\right) dx - 3 \log_e(\sqrt{3})$ is equal to:

1

If $\displaystyle \sum_{r=0}^{10} \left(\dfrac{10^{r+1}-1}{10^r}\right) , {}^{11}C_{r+1} = \dfrac{\alpha^{11} - 11^{11}…

Topic: JEE Main 2025 (2 April Evening Shift)

2

If the length of the minor axis of an ellipse is equal to one-fourth of the distance between the foci, then the eccentr…

Topic: JEE Main 2025 (2 April Evening Shift)

3

Let $(a, b)$ be the point of intersection of the curve $x^2 = 2y$ and the straight line $y - 2x - 6 = 0$ in the second …

Topic: JEE Main 2025 (2 April Evening Shift)

4

The number of terms of an A.P. is even. The sum of all the odd terms is $24$, the sum of all the even terms is $30$, an…

Topic: JEE Main 2025 (2 April Evening Shift)

5

The line $L_1$ is parallel to the vector $\vec{a} = -3\hat{i} + 2\hat{j} + 4\hat{k}$ and passes through the point $(7, …

Topic: JEE Main 2025 (2 April Evening Shift)

6

If the domain of the function $f(x) = \dfrac{1}{\sqrt{10 + 3x - x^2}} + \dfrac{1}{\sqrt{x + |x|}}$ is $(a, b)$, then $(…

Topic: JEE Main 2025 (2 April Evening Shift)

7

If the domain of the function $f(x) = \dfrac{1}{\sqrt{10 + 3x - x^2}} + \dfrac{1}{\sqrt{x + |x|}}$ is $(a, b)$, then $(…

Topic: JEE Main 2025 (2 April Evening Shift)

8

Let $A = {1, 2, 3, \ldots, 100}$ and $R$ be a relation on $A$ such that $R = {(a, b) : a = 2b + 1}$. Let $(a_1, a_2), (…

Topic: JEE Main 2025 (2 April Evening Shift)

9

If $\theta \in \left[-\dfrac{7\pi}{6}, \dfrac{4\pi}{3}\right]$, then the number of solutions of $\sqrt{3}\csc^2\theta -…

Topic: JEE Main 2025 (2 April Evening Shift)

10

If the image of the point $P(1, 0, 3)$ in the line joining the points $A(4, 7, 1)$ and $B(3, 5, 3)$ is $Q(\alpha, \beta…

Topic: JEE Main 2025 (2 April Evening Shift)

1

Let $\vec{a} = 2\hat{i} - 3\hat{j} + \hat{k}$, $\vec{b} = 3\hat{i} + 2\hat{j} + 5\hat{k}$, and a vector $\vec{c}$ be su…

Topic: JEE Main 2025 (2 April Evening Shift)

2

$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $ $ \begin{a…

Topic: JEE Main 2025 (2 April Evening Shift)

3

The integral $\displaystyle \int_{-1}^{\tfrac{3}{2}} \left( |\pi^2 x \sin(\pi x)| \right) dx$ is equal to

Topic: JEE Main 2025 (2 April Evening Shift)