1
JEE Main 2022 (Online) 24th June Evening Shift
+4
-1

Let $$x * y = {x^2} + {y^3}$$ and $$(x * 1) * 1 = x * (1 * 1)$$.

Then a value of $$2{\sin ^{ - 1}}\left( {{{{x^4} + {x^2} - 2} \over {{x^4} + {x^2} + 2}}} \right)$$ is

A
$${\pi \over 4}$$
B
$${\pi \over 3}$$
C
$${\pi \over 2}$$
D
$${\pi \over 6}$$
2
JEE Main 2022 (Online) 24th June Morning Shift
+4
-1

The set of all values of k for which

$${({\tan ^{ - 1}}x)^3} + {({\cot ^{ - 1}}x)^3} = k{\pi ^3},\,x \in R$$, is the interval :

A
$$\left[ {{1 \over {32}},{7 \over 8}} \right)$$
B
$$\left( {{1 \over {24}},{{13} \over {16}}} \right)$$
C
$$\left[ {{1 \over {48}},{{13} \over {16}}} \right]$$
D
$$\left[ {{1 \over {32}},{9 \over 8}} \right)$$
3
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
$${\cos ^{ - 1}}(\cos ( - 5)) + {\sin ^{ - 1}}(\sin (6)) - {\tan ^{ - 1}}(\tan (12))$$ is equal to :

(The inverse trigonometric functions take the principal values)
A
3$$\pi$$ $$-$$ 11
B
4$$\pi$$ $$-$$ 9
C
4$$\pi$$ $$-$$ 11
D
3$$\pi$$ + 1
4
JEE Main 2021 (Online) 27th August Evening Shift
+4
-1
Let M and m respectively be the maximum and minimum values of the function
f(x) = tan$$-$$1 (sin x + cos x) in $$\left[ {0,{\pi \over 2}} \right]$$, then the value of tan(M $$-$$ m) is equal to :
A
$$2 + \sqrt 3$$
B
$$2 - \sqrt 3$$
C
$$3 + 2\sqrt 2$$
D
$$3 - 2\sqrt 2$$
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