1
JEE Main 2022 (Online) 25th June Evening Shift
+4
-1

Let a, b $$\in$$ R be such that the equation $$a{x^2} - 2bx + 15 = 0$$ has a repeated root $$\alpha$$. If $$\alpha$$ and $$\beta$$ are the roots of the equation $${x^2} - 2bx + 21 = 0$$, then $${\alpha ^2} + {\beta ^2}$$ is equal to :

A
37
B
58
C
68
D
92
2
JEE Main 2022 (Online) 24th June Evening Shift
+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
$$- {\log _e}6$$
3
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

The number of distinct real roots of the equation

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

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