1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
If $$\sum\limits_{r = 1}^{50} {{{\tan }^{ - 1}}{1 \over {2{r^2}}} = p} $$, then the value of tan p is :
A
$${{101} \over {102}}$$
B
$${{50} \over {51}}$$
C
100
D
$${{51} \over {50}}$$
2
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
Let $$f(x) = \cos \left( {2{{\tan }^{ - 1}}\sin \left( {{{\cot }^{ - 1}}\sqrt {{{1 - x} \over x}} } \right)} \right)$$, 0 < x < 1. Then :
A
$${(1 - x)^2}f'(x) - 2{(f(x))^2} = 0$$
B
$${(1 + x)^2}f'(x) + 2{(f(x))^2} = 0$$
C
$${(1 - x)^2}f'(x) + 2{(f(x))^2} = 0$$
D
$${(1 + x)^2}f'(x) - 2{(f(x))^2} = 0$$
3
JEE Main 2021 (Online) 20th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
The value of $$\tan \left( {2{{\tan }^{ - 1}}\left( {{3 \over 5}} \right) + {{\sin }^{ - 1}}\left( {{5 \over {13}}} \right)} \right)$$ is equal to :
A
$${{ - 181} \over {69}}$$
B
$${{220} \over {21}}$$
C
$${{ - 291} \over {76}}$$
D
$${{151} \over {63}}$$
4
JEE Main 2021 (Online) 20th July Morning Shift
MCQ (Single Correct Answer)
+4
-1
The number of real roots of the equation $${\tan ^{ - 1}}\sqrt {x(x + 1)} + {\sin ^{ - 1}}\sqrt {{x^2} + x + 1} = {\pi \over 4}$$ is :
A
1
B
2
C
4
D
0
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