1
JEE Main 2022 (Online) 25th July Morning Shift
+4
-1

If $$\alpha, \beta, \gamma, \delta$$ are the roots of the equation $$x^{4}+x^{3}+x^{2}+x+1=0$$, then $$\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$$ is equal to :

A
$$-$$4
B
$$-$$1
C
1
D
4
2
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Let $${S_1} = \left\{ {x \in R - \{ 1,2\} :{{(x + 2)({x^2} + 3x + 5)} \over { - 2 + 3x - {x^2}}} \ge 0} \right\}$$ and $${S_2} = \left\{ {x \in R:{3^{2x}} - {3^{x + 1}} - {3^{x + 2}} + 27 \le 0} \right\}$$. Then, $${S_1} \cup {S_2}$$ is equal to :

A
$$( - \infty , - 2] \cup (1,2)$$
B
$$( - \infty , - 2] \cup [1,2]$$
C
$$( - 2,1] \cup [2,\infty )$$
D
$$( - \infty ,2]$$
3
JEE Main 2022 (Online) 30th June Morning Shift
+4
-1

Let S be the set of all integral values of $$\alpha$$ for which the sum of squares of two real roots of the quadratic equation $$3{x^2} + (\alpha - 6)x + (\alpha + 3) = 0$$ is minimum. Then S :

A
is an empty set
B
is a singleton
C
contains exactly two elements
D
contains more than two elements
4
JEE Main 2022 (Online) 29th June Evening Shift
+4
-1

Let $$\alpha$$ be a root of the equation 1 + x2 + x4 = 0. Then, the value of $$\alpha$$1011 + $$\alpha$$2022 $$-$$ $$\alpha$$3033 is equal to :

A
1
B
$$\alpha$$
C
1 + $$\alpha$$
D
1 + 2$$\alpha$$
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