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, one word is selected at random. The probability that the selected word will NOT have vowels in alphabetical order is:

1

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)

2

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)

3

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)

4

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)

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

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)

7

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)

8

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)

9

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)

10

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

Topic: JEE Main 2025 (28 January Evening Shift)

1

If A and B are the points of intersection of the circle $x^2 + y^2 - 8x = 0$ and the hyperbola $\frac{x^2}{9} - \frac{y…

Topic: JEE Main 2025 (28 January Evening Shift)

2

If $\sum\limits_{r=1}^{13}\left\{\frac{1}{\sin \left(\frac{\pi}{4}+(r-1) \frac{\pi}{6}\right) \sin \left(\frac{\pi}{4}+…

Topic: JEE Main 2025 (28 January Evening Shift)

3

If $\alpha + i\beta$ and $\gamma + i\delta$ are the roots of $x^2 - (3 - 2i)x - (2i - 2) = 0$, $i = \sqrt{-1}$, then $\…

Topic: JEE Main 2025 (28 January Evening Shift)

4

>Let $A, B, C$ be three points in xy-plane, whose position vector are given by $\sqrt{3} \hat{i}+\hat{j}, \hat{i}+\sqrt…

Topic: JEE Main 2025 (28 January Evening Shift)

5

If $f(x)=\displaystyle\int \frac{1}{x^{1/4}\left(1+x^{1/4}\right)},dx,; f(0)=-6$, then $f(1)$ is equal to:

Topic: JEE Main 2025 (28 January Evening Shift)

6

Let $\mathrm{A}=\left[\begin{array}{cc}\frac{1}{\sqrt{2}} & -2 \\ 0 & 1\end{array}\right]$ and $\mathrm{P}=\left[\begin…

Topic: JEE Main 2025 (28 January Evening Shift)

7

Let $f$ be a real valued continuous function defined on the positive real axis such that $g(x)=\int\limits_0^x t f(t) d…

Topic: JEE Main 2025 (28 January Evening Shift)

8

et $f:[0,3]\to A$ be defined by $,f(x)=2x^3-15x^2+36x+7,$ and $g:[0,\infty)\to B$ be defined by $,g(x)=\dfrac{x^{2025}}…

Topic: JEE Main 2025 (28 January Evening Shift)

9

For positive integers $n$, if $4a_n=(n^2+5n+6)$ and $S_n=\displaystyle\sum_{k=1}^{n}\frac{1}{a_k},$ then the value of $…

Topic: JEE Main 2025 (28 January Evening Shift)