The area of the region bounded by the curves $x(1+y^{2})=1$ and $y^{2}=2x$ is:

1

Bag $B_1$ contains 6 white and 4 blue balls, Bag $B_2$ contains 4 white and 6 blue balls, and Bag $B_3$ contains 5 whit…

Topic: JEE Main 2025 (28 January Evening Shift)

2

Let $f:\mathbb{R}\to\mathbb{R}$ be a twice differentiable function such that $f(2)=1$. If $F(x)=x f(x)$ for all $x\in\m…

Topic: JEE Main 2025 (28 January Evening Shift)

3

If the midpoint of a chord of the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{4}=1$ is $\left(\sqrt{2},,\dfrac{4}{3}\right)…

Topic: JEE Main 2025 (28 January Evening Shift)

4

The square of the distance of the point $\left(\dfrac{15}{7},,\dfrac{32}{7},,7\right)$ from the line $\dfrac{x+1}{3}=\d…

Topic: JEE Main 2025 (28 January Evening Shift)

5

Two equal sides of an isosceles triangle are along $-x+2y=4$ and $x+y=4$. If $m$ is the slope of its third side, then t…

Topic: JEE Main 2025 (28 January Evening Shift)

6

Let the coefficients of three consecutive terms $T_r, T_{r+1}$ and $T_{r+2}$ in the binomial expansion of $(a+b)^{12}$ …

Topic: JEE Main 2025 (28 January Evening Shift)

7

If the components of $\vec a=\alpha,\hat i+\beta,\hat j+\gamma,\hat k$ along and perpendicular to $\vec b=3\hat i+\hat …

Topic: JEE Main 2025 (28 January Evening Shift)

8

Let $f:\mathbb{R}-{0}\to(-\infty,1)$ be a polynomial of degree $2$, satisfying $f(x)f\left(\dfrac{1}{x}\right)=f(x)+f\l…

Topic: JEE Main 2025 (28 January Evening Shift)

9

Let [x] denote the greatest integer less than or equal to x. Then the domain of $ f(x) = \sec^{-1}(2[x] + 1) $ is:

Topic: JEE Main 2025 (28 January Evening Shift)

10

Let S be the set of all the words that can be formed by arranging all the letters of the word GARDEN. From the set S, o…

Topic: JEE Main 2025 (28 January Evening Shift)