1
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.
2
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
3
JEE Main 2020 (Online) 7th January Evening Slot
+4
-1
Let $$\alpha$$ and $$\beta$$ be the roots of the equation x2 - x - 1 = 0.
If pk = $${\left( \alpha \right)^k} + {\left( \beta \right)^k}$$ , k $$\ge$$ 1, then which one of the following statements is not true?
A
(p1 + p2 + p3 + p4 + p5) = 26
B
p5 = 11
C
p3 = p5 – p4
D
p5 = p2 · p3
4
JEE Main 2020 (Online) 7th January Morning Slot
+4
-1
Let $$\alpha$$ and $$\beta$$ be two real roots of the equation
(k + 1)tan2x - $$\sqrt 2$$ . $$\lambda$$tanx = (1 - k), where k($$\ne$$ - 1) and $$\lambda$$ are real numbers. if tan2 ($$\alpha$$ + $$\beta$$) = 50, then a value of $$\lambda$$ is:
A
5$$\sqrt 2$$
B
10
C
5
D
10$$\sqrt 2$$
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