If the set $\left\{\operatorname{Re}\!\left(\dfrac{z-\overline{z}+z\overline{z}}{\,2-3z+5\overline{z}\,}\right): z\in\mathbb{C},\ \operatorname{Re}(z)=3\right\}$ is equal to the interval $(\alpha,\beta]$, then $24(\beta-\alpha)$ is equal to:

1

Let $S$ be the set of all values of $\lambda$ for which the shortest distance between the lines $\dfrac{x-\lambda}{0}=…

Topic: JEE Main 2023 (15 April Morning Shift)

2

Let $A_1$ and $A_2$ be two arithmetic means and $G_1, G_2, G_3$ be three geometric means of two distinct positive numbe…

Topic: JEE Main 2023 (15 April Morning Shift)

3

If $(\alpha,\beta)$ is the orthocenter of the triangle $ABC$ with vertices $A(3,-7)$, $B(-1,2)$ and $C(4,5)$, then $9\a…

Topic: JEE Main 2023 (15 April Morning Shift)

4

The number of real roots of the equation $x|x|-5|x+2|+6=0$ is:

Topic: JEE Main 2023 (15 April Morning Shift)

5

A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on …

Topic: JEE Main 2023 (15 April Morning Shift)

6

Let $\left(a+bx+cx^2\right)^{10}=\displaystyle\sum_{i=0}^{20} p_i x^i,\ a,b,c\in\mathbb{N}.$ If $p_1=20$ and $p_2=210$…

Topic: JEE Main 2023 (15 April Morning Shift)

7

Let $[x]$ denote the greatest integer function and $f(x)=\max\{\,1+x+[x],\ 2+x,\ x+2[x]\,\},\ 0\le x\le 2.$ Let $m$ b…

Topic: JEE Main 2023 (15 April Morning Shift)

8

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observ…

Topic: JEE Main 2023 (15 April Morning Shift)

9

If the domain of the function $f(x)=\log_e(4x^2+11x+6)+\sin^{-1}(4x+3)+\cos^{-1}\!\left(\dfrac{10x+6}{3}\right)$ is $(\…

Topic: JEE Main 2023 (15 April Morning Shift)

10

Let ABCD be a quadrilateral. If E and F are the mid points of the diagonals AC and BD respectively and $\overrightarrow…

Topic: JEE Main 2023 (15 April Morning Shift)