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1
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
The number of solutions of sin7x + cos7x = 1, x$$\in$$ [0, 4$$\pi$$] is equal to
A
11
B
7
C
5
D
9
2
JEE Main 2021 (Online) 22th July Evening Shift
+4
-1
If the domain of the function $$f(x) = {{{{\cos }^{ - 1}}\sqrt {{x^2} - x + 1} } \over {\sqrt {{{\sin }^{ - 1}}\left( {{{2x - 1} \over 2}} \right)} }}$$ is the interval ($$\alpha$$, $$\beta$$], then $$\alpha$$ + $$\beta$$ is equal to :
A
$${3 \over 2}$$
B
2
C
$${1 \over 2}$$
D
1
3
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
Let $$f:R - \left\{ {{\alpha \over 6}} \right\} \to R$$ be defined by $$f(x) = {{5x + 3} \over {6x - \alpha }}$$. Then the value of $$\alpha$$ for which (fof)(x) = x, for all $$x \in R - \left\{ {{\alpha \over 6}} \right\}$$, is :
A
No such $$\alpha$$ exists
B
5
C
8
D
6
4
JEE Main 2021 (Online) 20th July Morning Shift
Let [ x ] denote the greatest integer $$\le$$ x, where x $$\in$$ R. If the domain of the real valued function $$f(x) = \sqrt {{{\left| {[x]} \right| - 2} \over {\left| {[x]} \right| - 3}}}$$ is ($$-$$ $$\infty$$, a) $$]\cup$$ [b, c) $$\cup$$ [4, $$\infty$$), a < b < c, then the value of a + b + c is :
$$-$$2
$$-$$3