1
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

The sum of all the real roots of the equation

$$({e^{2x}} - 4)(6{e^{2x}} - 5{e^x} + 1) = 0$$ is

A
$${\log _e}3$$
B
$$- {\log _e}3$$
C
$${\log _e}6$$
D
$$- {\log _e}6$$
2
JEE Main 2022 (Online) 24th June Evening Shift
MCQ (Single Correct Answer)
+4
-1

The number of distinct real roots of the equation

x7 $$-$$ 7x $$-$$ 2 = 0 is

A
5
B
7
C
1
D
3
3
JEE Main 2022 (Online) 24th June Morning Shift
MCQ (Single Correct Answer)
+4
-1

If the sum of the squares of the reciprocals of the roots $$\alpha$$ and $$\beta$$ of

the equation 3x2 + $$\lambda$$x $$-$$ 1 = 0 is 15, then 6($$\alpha$$3 + $$\beta$$3)2 is equal to :

A
18
B
24
C
36
D
96
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
The numbers of pairs (a, b) of real numbers, such that whenever $$\alpha$$ is a root of the equation x2 + ax + b = 0, $$\alpha$$2 $$-$$ 2 is also a root of this equation, is :
A
6
B
2
C
4
D
8
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