Competishun Header
Competishun
Contact Us
Back

Report Issue

JEE MAIN 2023
02-04-2023-S2
Question
Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{1 / 4} x+a=0$. If $\alpha^4+\beta^4=-30$, then the product of all possible values of $a$ is $\_\_\_\_$ .
Write Your Answer
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Solution Image
Question Tags
JEE Main
Mathematics
Easy
Start Preparing for JEE with Competishun
YouTube
Books
App
Tests
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
Q JEE MAIN 20262026
Given below are two statements
Statement I: $\mathrm{H}_2 \mathrm{O}$ molecules move from the chamber 1 to chamber 2 .
Statement II:...
JEE MainChemistryMedium
View Solution→
QJEE MAIN 20232023
A triangle is formed by $X$-axis, $Y$-axis and the line $3 x+4 y=60$. Then the number of points $P(a, b)$...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
$25 \%$ of the population are smokers. A smoker has 27 times more chances to develop lung cancer then a...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
If the shortest distance between the line joining the points $(1,2,3)$ and $(2,3,4)$, and the line $\frac{x-1}{2}=\frac{y+1}{-1}=\frac{z-2}{0}$ is $\alpha$, then...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
The remainder when $(2023)^{2023}$ is divided by 35 is $\_\_\_\_$ .
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
If $\int_{\frac{1}{3}}^3\left|\log _e x\right| d x=\frac{m}{n} \log _e\left(\frac{n^2}{e}\right)$, where $m$ and $n$ are coprime natural numbers, then $m^2+n^2-5$ is equal...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
If $m$ and $n$ respectively are the numbers of positive and negative value of $\theta$ in the interval $[-\pi, \pi]$...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Let $a \in R$ and let $\alpha, \beta$ be the roots of the equation $x^2+60^{1 / 4} x+a=0$. If $\alpha^4+\beta^4=-30$,...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Points $\mathrm{P}(-3,2), \mathrm{Q}(9,10)$ and $\mathrm{R}(\alpha, 4)$ lie on a circle C with PR as its diameter. The tangents to C...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
For the two positive numbers $a, b$, if $a, b$ and $\frac{1}{18}$ are in a geometric progression, while $\frac{1}{a}, 10$...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
The foot of perpendicular of the point $(2,0,5)$ on the line $\frac{x+1}{2}=\frac{y-1}{5}=\frac{z+1}{-1}$ is $(\alpha, \beta, \gamma)$. Then. Which of the...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Let $\vec{a}=-\hat{i}-\hat{j}+\hat{k}, \vec{a} \cdot \vec{b}=1$ and $\vec{a} \times \vec{b}=\hat{i}-\hat{j}$. Then $\vec{a}-6 \vec{b}$ is equal to
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Let $T$ and $C$ respectively be the transverse and conjugate axes of the hyperbola $16 x^2-y^2+64 x+4 y+ 44=0$. Then...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
The integral $16 \int_1^2 \frac{\mathrm{dx}}{\mathrm{x}^3\left(\mathrm{x}^2+2\right)^2}$ is equal to
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
Let N be the sum of the numbers appeared when two fair dice are rolled and let the probability that...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
\text { The shortest distance between the lines } x+1=2 y=-12 z \text { and } x=y+2=6 z-6 \text {...
JEE MainMathematicsEasy
View Solution→
QJEE MAIN 20232023
\sum_{k=0}^6{ }^{51-k} \mathrm{C}_3 \text { is equal to }
JEE MainMathematicsEasy
View Solution→