1
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$A = \{ 1,2,3,....,10\} $$ and $$f:A \to A$$ be defined as

$$f(k) = \left\{ {\matrix{ {k + 1} & {if\,k\,is\,odd} \cr k & {if\,k\,is\,even} \cr } } \right.$$

Then the number of possible functions $$g:A \to A$$ such that $$gof = f$$ is :
A
55
B
105
C
5!
D
10C5
2
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A1 be the area of the region bounded by the curves y = sinx, y = cosx and y-axis in the first quadrant. Also, let A2 be the area of the region bounded by the curves y = sinx, y = cosx, x-axis and x = $${\pi \over 2}$$ in the first quadrant. Then,
A
$${A_1}:{A_2} = 1:\sqrt 2 $$ and $${A_1} + {A_2} = 1$$
B
$${A_1} = {A_2}$$ and $${A_1} + {A_2} = \sqrt 2 $$
C
$$2{A_1} = {A_2}$$ and $${A_1} + {A_2} = 1 + \sqrt 2 $$
D
$${A_1}:{A_2} = 1:2$$ and $${A_1} + {A_2} = 1$$
3
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$f(x) = {\sin ^{ - 1}}x$$ and $$g(x) = {{{x^2} - x - 2} \over {2{x^2} - x - 6}}$$. If $$g(2) = \mathop {\lim }\limits_{x \to 2} g(x)$$, then the domain of the function fog is :
A
$$( - \infty , - 2] \cup \left[ { - {4 \over 3},\infty } \right)$$
B
$$( - \infty , - 2] \cup [ - 1,\infty )$$
C
$$( - \infty , - 2] \cup \left[ { - {3 \over 2},\infty } \right)$$
D
$$( - \infty , - 1] \cup [2,\infty )$$
4
JEE Main 2021 (Online) 26th February Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f : R $$ \to $$ R be defined as

$$f(x) = \left\{ \matrix{ 2\sin \left( { - {{\pi x} \over 2}} \right),if\,x < - 1 \hfill \cr |a{x^2} + x + b|,\,if - 1 \le x \le 1 \hfill \cr \sin (\pi x),\,if\,x > 1 \hfill \cr} \right.$$ If f(x) is continuous on R, then a + b equals :
A
$$-$$3
B
3
C
$$-$$1
D
1
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