1
JEE Main 2023 (Online) 15th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The number of real roots of the equation $x|x|-5|x+2|+6=0$, is :
A
4
B
3
C
5
D
6
2
JEE Main 2023 (Online) 13th April Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha, \beta$$ be the roots of the equation $$x^{2}-\sqrt{2} x+2=0$$. Then $$\alpha^{14}+\beta^{14}$$ is equal to

A
$$-64$$
B
$$-64 \sqrt{2}$$
C
$$-128 \sqrt{2}$$
D
$$-128$$
3
JEE Main 2023 (Online) 13th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

The set of all $$a \in \mathbb{R}$$ for which the equation $$x|x-1|+|x+2|+a=0$$ has exactly one real root, is :

A
$$(-\infty, \infty)$$
B
$$(-6, \infty)$$
C
$$(-\infty,-3)$$
D
$$(-6,-3)$$
4
JEE Main 2023 (Online) 12th April Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language

Let $$\alpha, \beta$$ be the roots of the quadratic equation $$x^{2}+\sqrt{6} x+3=0$$. Then $$\frac{\alpha^{23}+\beta^{23}+\alpha^{14}+\beta^{14}}{\alpha^{15}+\beta^{15}+\alpha^{10}+\beta^{10}}$$ is equal to :

A
72
B
9
C
729
D
81
JEE Main Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Civil Services
UPSC Civil Service
Defence
NDA
CBSE
Class 12