1
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
The domain of the function

$$f(x) = {\sin ^{ - 1}}\left( {{{3{x^2} + x - 1} \over {{{(x - 1)}^2}}}} \right) + {\cos ^{ - 1}}\left( {{{x - 1} \over {x + 1}}} \right)$$ is :
A
$$\left[ {0,{1 \over 4}} \right]$$
B
$$[ - 2,0] \cup \left[ {{1 \over 4},{1 \over 2}} \right]$$
C
$$\left[ {{1 \over 4},{1 \over 2}} \right] \cup \{ 0\}$$
D
$$\left[ {0,{1 \over 2}} \right]$$
2
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
$$3 - 2\sqrt 2$$
3
JEE Main 2021 (Online) 27th August Morning Shift
+4
-1
If $${({\sin ^{ - 1}}x)^2} - {({\cos ^{ - 1}}x)^2} = a$$; 0 < x < 1, a $$\ne$$ 0, then the value of 2x2 $$-$$ 1 is :
A
$$\cos \left( {{{4a} \over \pi }} \right)$$
B
$$\sin \left( {{{2a} \over \pi }} \right)$$
C
$$\cos \left( {{{2a} \over \pi }} \right)$$
D
$$\sin \left( {{{4a} \over \pi }} \right)$$
4
JEE Main 2021 (Online) 26th August Evening Shift
+4
-1
The domain of the function $${{\mathop{\rm cosec}\nolimits} ^{ - 1}}\left( {{{1 + x} \over x}} \right)$$ is :
A
$$\left( { - 1, - {1 \over 2}} \right] \cup (0,\infty )$$
B
$$\left[ { - {1 \over 2},0} \right) \cup [1,\infty )$$
C
$$\left( { - {1 \over 2},\infty } \right) - \{ 0\}$$
D
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\}$$
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