1
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
$$3 - 2\sqrt 2$$
2
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
$$\sin \left( {{{4a} \over \pi }} \right)$$
3
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
$$\left[ { - {1 \over 2},\infty } \right) - \{ 0\}$$
4
JEE Main 2021 (Online) 26th August Evening Shift
+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
$${{51} \over {50}}$$
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