1
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let P1, P2, ......, P15 be 15 points on a circle. The number of distinct triangles formed by points Pi, Pj, Pk such that i +j + k $$\ne$$ 15, is :
A
12
B
419
C
443
D
455
2
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
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]
3
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let a1, a2, ..........., a21 be an AP such that $$\sum\limits_{n = 1}^{20} {{1 \over {{a_n}{a_{n + 1}}}} = {4 \over 9}} $$. If the sum of this AP is 189, then a6a16 is equal to :
A
57
B
72
C
48
D
36
4
JEE Main 2021 (Online) 1st September Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The function f(x), that satisfies the condition
$$f(x) = x + \int\limits_0^{\pi /2} {\sin x.\cos y\,f(y)\,dy} $$, is :
A
$$x + {2 \over 3}(\pi - 2)\sin x$$
B
$$x + (\pi + 2)\sin x$$
C
$$x + {\pi \over 2}\sin x$$
D
$$x + (\pi - 2)\sin x$$
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