1
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
Let a, b $$\in$$ R, a $$\ne$$ 0 be such that the equation, ax2 – 2bx + 5 = 0 has a repeated root $$\alpha$$, which is also a root of the equation, x2 – 2bx – 10 = 0. If $$\beta$$ is the other root of this equation, then $$\alpha$$2 + $$\beta$$2 is equal to :
A
28
B
24
C
26
D
25
2
JEE Main 2020 (Online) 9th January Morning Slot
+4
-1
The number of real roots of the equation,
e4x + e3x – 4e2x + ex + 1 = 0 is :
A
1
B
2
C
3
D
4
3
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let S be the set of all real roots of the equation,
3x(3x – 1) + 2 = |3x – 1| + |3x – 2|. Then S :
A
contains exactly two elements.
B
is an empty set.
C
is a singleton.
D
contains at least four elements.
4
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
Let $$\alpha = {{ - 1 + i\sqrt 3 } \over 2}$$.
If $$a = \left( {1 + \alpha } \right)\sum\limits_{k = 0}^{100} {{\alpha ^{2k}}}$$ and
$$b = \sum\limits_{k = 0}^{100} {{\alpha ^{3k}}}$$, then a and b are the roots of the quadratic equation :
A
x2 + 101x + 100 = 0
B
x2 + 102x + 101 = 0
C
x2 – 102x + 101 = 0
D
x2 – 101x + 100 = 0
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