1
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $\alpha$ and $\beta$ be the roots of the equation $p x^2+q x-r=0$, where $p \neq 0$. If $p, q$ and $r$ be the consecutive terms of a non constant G.P. and $\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}$, then the value of $(\alpha-\beta)^2$ is :
A
8
B
9
C
$\frac{20}{3}$
D
$\frac{80}{9}$
2
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let Ajay will not appear in JEE exam with probability $\mathrm{p}=\frac{2}{7}$, while both Ajay and Vijay will appear in the exam with probability $\mathrm{q}=\frac{1}{5}$. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :
A
$\frac{9}{35}$
B
$\frac{3}{35}$
C
$\frac{24}{35}$
D
$\frac{18}{35}$
3
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $\mathrm{P}$ be a point on the ellipse $\frac{x^2}{9}+\frac{y^2}{4}=1$. Let the line passing through $\mathrm{P}$ and parallel to $y$-axis meet the circle $x^2+y^2=9$ at point $\mathrm{Q}$ such that $\mathrm{P}$ and $\mathrm{Q}$ are on the same side of the $x$-axis. Then, the eccentricity of the locus of the point $R$ on $P Q$ such that $P R: R Q=4: 3$ as $P$ moves on the ellipse, is :
A
$\frac{13}{21}$
B
$\frac{\sqrt{139}}{23}$
C
$\frac{\sqrt{13}}{7}$
D
$\frac{11}{19}$
4
JEE Main 2024 (Online) 1st February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Consider 10 observations $x_1, x_2, \ldots, x_{10}$ such that $\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2$ and $\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40$, where $\alpha, \beta$ are positive integers. Let the mean and the variance of the observations be $\frac{6}{5}$ and $\frac{84}{25}$ respectively. Then $\frac{\beta}{\alpha}$ is equal to :
A
2
B
1
C
$\frac{5}{2}$
D
$\frac{3}{2}$
JEE Main Papers
2023
2021
EXAM MAP
Medical
NEETAIIMS
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
Staff Selection Commission
SSC CGL Tier I
CBSE
Class 12