1
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$\alpha$$ + $$\beta$$ + $$\gamma$$ = 2$$\pi$$, then the system of equations

x + (cos $$\gamma$$)y + (cos $$\beta$$)z = 0

(cos $$\gamma$$)x + y + (cos $$\alpha$$)z = 0

(cos $$\beta$$)x + (cos $$\alpha$$)y + z = 0

has :
A
no solution
B
infinitely many solution
C
exactly two solutions
D
a unique solution
2
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The domain of the function

$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$$ is :
A
$$\left[ {0,{1 \over 4}} \right]$$
B
$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\} $$
D
$$\left[ {0,{1 \over 2}} \right]$$
3
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :
A
$${1 \over {10}}$$
B
$${1 \over {15}}$$
C
$${1 \over {5}}$$
D
$${1 \over {30}}$$
4
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3) is equal to :
A
6
B
54
C
18
D
36
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