1
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The value of $$\int\limits_{{{ - 1} \over {\sqrt 2 }}}^{{1 \over {\sqrt 2 }}} {{{\left( {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right)}^{{1 \over 2}}}dx}$$ is :
A
loge 4
B
loge 16
C
2loge 16
D
4loge (3 + 2$${\sqrt 2 }$$)
2
JEE Main 2021 (Online) 26th August Morning Shift
+4
-1
The value of

$$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\sum\limits_{r = 0}^{2n - 1} {{{{n^2}} \over {{n^2} + 4{r^2}}}}$$ is :
A
$${1 \over 2}{\tan ^{ - 1}}(2)$$
B
$${1 \over 2}{\tan ^{ - 1}}(4)$$
C
$${\tan ^{ - 1}}(4)$$
D
$${1 \over 4}{\tan ^{ - 1}}(4)$$
3
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
The area of the region bounded by y $$-$$ x = 2 and x2 = y is equal to :
A
$${{16} \over 3}$$
B
$${{2} \over 3}$$
C
$${{9} \over 2}$$
D
$${{4} \over 3}$$
4
JEE Main 2021 (Online) 27th July Evening Shift
+4
-1
Let f : (a, b) $$\to$$ R be twice differentiable function such that $$f(x) = \int_a^x {g(t)dt}$$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :
A
twelve roots in (a, b)
B
five roots in (a, b)
C
seven roots in (a, b)
D
three roots in (a, b)
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