1
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
The local maximum value of the function $$f(x) = {\left( {{2 \over x}} \right)^{{x^2}}}$$, x > 0, is
A
$${\left( {2\sqrt e } \right)^{{1 \over e}}}$$
B
$${\left( {{4 \over {\sqrt e }}} \right)^{{e \over 4}}}$$
C
$${(e)^{{2 \over e}}}$$
D
1
2
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
If the value of the integral
$$\int\limits_0^5 {{{x + [x]} \over {{e^{x - [x]}}}}dx = \alpha {e^{ - 1}} + \beta } $$, where $$\alpha$$, $$\beta$$ $$\in$$ R, 5$$\alpha$$ + 6$$\beta$$ = 0, and [x] denotes the greatest integer less than or equal to x; then the value of ($$\alpha$$ + $$\beta$$)2 is equal to :
A
100
B
25
C
16
D
36
3
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
The point $$P\left( { - 2\sqrt 6 ,\sqrt 3 } \right)$$ lies on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ having eccentricity $${{\sqrt 5 } \over 2}$$. If the tangent and normal at P to the hyperbola intersect its conjugate axis at the point Q and R respectively, then QR is equal to :
A
$$4\sqrt 3 $$
B
6
C
$$6\sqrt 3 $$
D
$$3\sqrt 6 $$
4
JEE Main 2021 (Online) 26th August Evening Shift
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y(x) be the solution of the differential equation

2x2 dy + (ey $$-$$ 2x)dx = 0, x > 0. If y(e) = 1, then y(1) is equal to :
A
0
B
2
C
loge 2
D
loge (2e)
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