1
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
$$-$$$${{{30} \over 4}}$$
2
JEE Main 2021 (Online) 17th March Morning Shift
+4
-1
If cot$$-$$1($$\alpha$$) = cot$$-$$1 2 + cot$$-$$1 8 + cot$$-$$1 18 + cot$$-$$1 32 + ...... upto 100 terms, then $$\alpha$$ is :
A
1.02
B
1.03
C
1.01
D
1.00
3
JEE Main 2021 (Online) 16th March Evening Shift
+4
-1
Given that the inverse trigonometric functions take principal values only. Then, the number of real values of x which satisfy

$${\sin ^{ - 1}}\left( {{{3x} \over 5}} \right) + {\sin ^{ - 1}}\left( {{{4x} \over 5}} \right) = {\sin ^{ - 1}}x$$ is equal to :
A
2
B
0
C
3
D
1
4
JEE Main 2021 (Online) 26th February Evening Shift
+4
-1
If 0 < a, b < 1, and tan$$-$$1a + tan$$-$$1b = $${\pi \over 4}$$, then the value of

$$(a + b) - \left( {{{{a^2} + {b^2}} \over 2}} \right) + \left( {{{{a^3} + {b^3}} \over 3}} \right) - \left( {{{{a^4} + {b^4}} \over 4}} \right) + .....$$ is :
A
$${\log _e}$$2
B
e
C
$${\log _e}\left( {{e \over 2}} \right)$$
D
e2 = 1
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