1
JEE Main 2021 (Online) 20th July Evening Shift
+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
$${{151} \over {63}}$$
2
JEE Main 2021 (Online) 20th July Morning Shift
+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
3
JEE Main 2021 (Online) 17th March Evening Shift
+4
-1
The number of solutions of the equation

$${\sin ^{ - 1}}\left[ {{x^2} + {1 \over 3}} \right] + {\cos ^{ - 1}}\left[ {{x^2} - {2 \over 3}} \right] = {x^2}$$, for x$$\in$$[$$-$$1, 1], and [x] denotes the greatest integer less than or equal to x, is :
A
0
B
Infinite
C
2
D
4
4
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
The sum of possible values of x for

tan$$-$$1(x + 1) + cot$$-$$1$$\left( {{1 \over {x - 1}}} \right)$$ = tan$$-$$1$$\left( {{8 \over {31}}} \right)$$ is :
A
$$-$$$${{{32} \over 4}}$$
B
$$-$$$${{{33} \over 4}}$$
C
$$-$$$${{{31} \over 4}}$$
D
$$-$$$${{{30} \over 4}}$$
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