1
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
$${1 \over {{3^2} - 1}} + {1 \over {{5^2} - 1}} + {1 \over {{7^2} - 1}} + .... + {1 \over {{{(201)}^2} - 1}}$$ is equal to
A
$${{101} \over {404}}$$
B
$${{25} \over {101}}$$
C
$${{101} \over {408}}$$
D
$${{99} \over {400}}$$
2
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the functions are defined as $$f(x) = \sqrt x $$ and $$g(x) = \sqrt {1 - x} $$, then what is the common domain of the following functions :

f + g, f $$-$$ g, f/g, g/f, g $$-$$ f where $$(f \pm g)(x) = f(x) \pm g(x),(f/g)x = {{f(x)} \over {g(x)}}$$
A
$$0 \le x \le 1$$
B
$$0 \le x < 1$$
C
$$0 < x < 1$$
D
$$0 < x \le 1$$
3
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If $$f(x) = \left\{ {\matrix{ {{1 \over {|x|}}} & {;\,|x|\, \ge 1} \cr {a{x^2} + b} & {;\,|x|\, < 1} \cr } } \right.$$ is differentiable at every point of the domain, then the values of a and b are respectively :
A
$${1 \over 2},{1 \over 2}$$
B
$${1 \over 2}, - {3 \over 2}$$
C
$${5 \over 2}, - {3 \over 2}$$
D
$$ - {1 \over 2},{3 \over 2}$$
4
JEE Main 2021 (Online) 18th March Morning Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let $$A + 2B = \left[ {\matrix{ 1 & 2 & 0 \cr 6 & { - 3} & 3 \cr { - 5} & 3 & 1 \cr } } \right]$$ and $$2A - B = \left[ {\matrix{ 2 & { - 1} & 5 \cr 2 & { - 1} & 6 \cr 0 & 1 & 2 \cr } } \right]$$. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) $$-$$ Tr(B) has value equal to
A
1
B
2
C
0
D
3
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