1
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let A be the set of all points ($$\alpha$$, $$\beta$$) such that the area of triangle formed by the points (5, 6), (3, 2) and ($$\alpha$$, $$\beta$$) is 12 square units. Then the least possible length of a line segment joining the origin to a point in A, is :
A
$${4 \over {\sqrt 5 }}$$
B
$${16 \over {\sqrt 5 }}$$
C
$${8 \over {\sqrt 5 }}$$
D
$${12 \over {\sqrt 5 }}$$
2
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The number of solutions of the equation $${32^{{{\tan }^2}x}} + {32^{{{\sec }^2}x}} = 81,\,0 \le x \le {\pi \over 4}$$ is :
A
3
B
1
C
0
D
2
3
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let f be any continuous function on [0, 2] and twice differentiable on (0, 2). If f(0) = 0, f(1) = 1 and f(2) = 2, then
A
f''(x) = 0 for all x $$\in$$ (0, 2)
B
f''(x) = 0 for some x $$\in$$ (0, 2)
C
f'(x) = 0 for some x $$\in$$ [0, 2]
D
f''(x) > 0 for all x $$\in$$ (0, 2)
4
JEE Main 2021 (Online) 31st August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If [x] is the greatest integer $$\le$$ x, then

$${\pi ^2}\int\limits_0^2 {\left( {\sin {{\pi x} \over 2}} \right)(x - [x]} {)^{[x]}}dx$$ is equal to :
A
2($$\pi$$ $$-$$ 1)
B
4($$\pi$$ $$-$$ 1)
C
4($$\pi$$ + 1)
D
2($$\pi$$ + 1)
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