1
JEE Main 2021 (Online) 1st September Evening Shift
+4
-1
The range of the function,

$$f(x) = {\log _{\sqrt 5 }}\left( {3 + \cos \left( {{{3\pi } \over 4} + x} \right) + \cos \left( {{\pi \over 4} + x} \right) + \cos \left( {{\pi \over 4} - x} \right) - \cos \left( {{{3\pi } \over 4} - x} \right)} \right)$$ is :
A
$$\left( {0,\sqrt 5 } \right)$$
B
[$$-$$2, 2]
C
$$\left[ {{1 \over {\sqrt 5 }},\sqrt 5 } \right]$$
D
[0, 2]
2
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
$$\left[ {0,{1 \over 2}} \right]$$
3
JEE Main 2021 (Online) 31st August Evening Shift
+4
-1
Let f : N $$\to$$ N be a function such that f(m + n) = f(m) + f(n) for every m, n$$\in$$N. If f(6) = 18, then f(2) . f(3) is equal to :
A
6
B
54
C
18
D
36
4
JEE Main 2021 (Online) 31st August Morning Shift
+4
-1
Which of the following is not correct for relation R on the set of real numbers ?
A
(x, y) $$\in$$ R $$\Leftrightarrow$$ 0 < |x| $$-$$ |y| $$\le$$ 1 is neither transitive nor symmetric.
B
(x, y) $$\in$$ R $$\Leftrightarrow$$ 0 < |x $$-$$ y| $$\le$$ 1 is symmetric and transitive.
C
(x, y) $$\in$$ R $$\Leftrightarrow$$ |x| $$-$$ |y| $$\le$$ 1 is reflexive but not symmetric.
D
(x, y) $$\in$$ R $$\Leftrightarrow$$ |x $$-$$ y| $$\le$$ 1 is reflexive nd symmetric.
JEE Main Subjects
Physics
Mechanics
Electricity
Optics
Modern Physics
Chemistry
Physical Chemistry
Inorganic Chemistry
Organic Chemistry
Mathematics
Algebra
Trigonometry
Coordinate Geometry
Calculus
EXAM MAP
Joint Entrance Examination