If the domain of the function $f(x)=\sqrt{\dfrac{x^{2}-25}{4-x^{2}}}+\log_{10}(x^{2}+2x-15)$ is $(-\infty,\alpha)\cup[\beta,\infty)$, then $\alpha^{2}+\beta^{3}$ is equal to:
Next 10 Questions — JEE Main 2024 (1 February Evening Shift)
Ascending by ID
1
2
3
4
5
6
7
8
9
10
If $z$ is a complex number such that $|z|\le1$, then the minimum value of
$\left|z+\dfrac{1}{2}(3+4i)\right|$ is:
Topic: JEE Main 2024 (1 February Evening Shift)
Consider a $\triangle ABC$ where $A(1,3,2)$, $B(-2,8,0)$ and $C(3,6,7)$.
If the angle bisector of $\angle BAC$ meets …
Topic: JEE Main 2024 (1 February Evening Shift)
Consider the relations $R_1$ and $R_2$ defined as
$a\,R_1\,b \iff a^2 + b^2 = 1$ for all $a,b\in\mathbb{R}$,
and …
Topic: JEE Main 2024 (1 February Evening Shift)
Let the system of equations
$x+2y+3z=5,\quad 2x+3y+z=9,\quad 4x+3y+\lambda z=\mu$
have infinite number of solutions. T…
Topic: JEE Main 2024 (1 February Evening Shift)
If $\displaystyle \int_{0}^{\pi/3}\!\cos^{4}x\,dx=a\pi+b\sqrt{3}$, where $a$ and $b$ are rational numbers, then $9a+8b$…
Topic: JEE Main 2024 (1 February Evening Shift)
Let $\alpha$ and $\beta$ be the roots of the equation $p x^{2}+q x-r=0$, where $p\ne 0$.
If $p,q,r$ are consecutive ter…
Topic: JEE Main 2024 (1 February Evening Shift)
Let Ajay will not appear in JEE exam with probability $p=\dfrac{2}{7}$,
while both Ajay and Vijay will appear in the e…
Topic: JEE Main 2024 (1 February Evening Shift)
Let $P$ be a point on the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{4}=1$.
Let the line passing through $P$ and parallel …
Topic: JEE Main 2024 (1 February Evening Shift)
Consider $10$ observations $x_{1},x_{2},\ldots,x_{10}$ such that
$\displaystyle \sum_{i=1}^{10}(x_{i}-\alpha)=2$ and $\…
Topic: JEE Main 2024 (1 February Evening Shift)
Let $f(x)=\left|2x^{2}+5|x|-3\right|,\; x\in\mathbb{R}$.
If $m$ and $n$ denote the number of points where $f$ is not …
Topic: JEE Main 2024 (1 February Evening Shift)
