The domain of the function \[ f(x)=\frac{1}{\sqrt{[x]^2-3[x]-10}} \] (where $[x]$ denotes the greatest integer less than or equal to $x$) is:

1

Let the function $f:[0,2]\to\mathbb{R}$ be defined as \[ f(x)= \begin{cases} e^{\min\{x^2,\; x-[x]\}}, & x\in[0,1),\\[4…

Topic: JEE Main 2023 (11 April Evening Shift)

2

Let $y=y(x)$ be the solution of the differential equation \[ \frac{dy}{dx}+\frac{5}{x(x^5+1)}\,y=\frac{(x^5+1)^2}{x^7},…

Topic: JEE Main 2023 (11 April Evening Shift)

3

Let $f$ and $g$ be two functions defined by \[ f(x)= \begin{cases} x+1, & x

Topic: JEE Main 2023 (11 April Evening Shift)

4

If $f:\mathbb{R}\to\mathbb{R}$ is a continuous function satisfying \[ \int_{0}^{\pi/2} f(\sin 2x)\,\sin x\,dx \;+\; \al…

Topic: JEE Main 2023 (11 April Evening Shift)

5

Let the mean of 6 observations $1, 2, 4, 5, x, y$ be $5$ and their variance be $10$. Then their mean deviation about t…

Topic: JEE Main 2023 (11 April Evening Shift)

6

If \[ \begin{vmatrix} x+1 & x & x \\ x & x+\lambda & x \\ x & x & x+\lambda^2 \end{vmatrix} = \dfrac{9}{8}\,(103x+81),…

Topic: JEE Main 2023 (11 April Evening Shift)

7

If the $1011^{\text{th}}$ term from the end in the binomial expansion of \(\left(\dfrac{4x}{5}-\dfrac{5}{2x}\right)^{2…

Topic: JEE Main 2023 (11 April Evening Shift)

8

Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let $R$ be a relation defined on $A\times B$ such that $R=\{\,((a_1,b_1…

Topic: JEE Main 2023 (11 April Evening Shift)

9

If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with ser…

Topic: JEE Main 2023 (11 April Evening Shift)

10

Let $a,b,c,d$ be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5 b^3 c^2 d$ is $3750\beta$,…

Topic: JEE Main 2023 (11 April Evening Shift)