1
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$\alpha$$, $$\beta$$ be two roots of the

equation x2 + (20)1/4x + (5)1/2 = 0. Then $$\alpha$$8 + $$\beta$$8 is equal to
A
10
B
100
C
50
D
160
2
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The probability that a randomly selected 2-digit number belongs to the set {n $$\in$$ N : (2n $$-$$ 2) is a multiple of 3} is equal to :
A
$${1 \over 6}$$
B
$${2 \over 3}$$
C
$${1 \over 2}$$
D
$${1 \over 3}$$
3
JEE Main 2021 (Online) 27th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$A = \{ (x,y) \in R \times R|2{x^2} + 2{y^2} - 2x - 2y = 1\} $$, $$B = \{ (x,y) \in R \times R|4{x^2} + 4{y^2} - 16y + 7 = 0\} $$ and $$C = \{ (x,y) \in R \times R|{x^2} + {y^2} - 4x - 2y + 5 \le {r^2}\} $$.

Then the minimum value of |r| such that $$A \cup B \subseteq C$$ is equal to
A
$${{3 + \sqrt {10} } \over 2}$$
B
$${{2 + \sqrt {10} } \over 2}$$
C
$${{3 + 2\sqrt 5 } \over 2}$$
D
$$1 + \sqrt 5 $$
4
JEE Main 2021 (Online) 27th July Morning Shift
Numerical
+4
-1
Change Language
For real numbers $$\alpha$$ and $$\beta$$, consider the following system of linear equations :

x + y $$-$$ z = 2, x + 2y + $$\alpha$$z = 1, 2x $$-$$ y + z = $$\beta$$. If the system has infinite solutions, then $$\alpha$$ + $$\beta$$ is equal to ______________.
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