1
JEE Main 2021 (Online) 26th February Morning Shift
+4
-1
The maximum slope of the curve $$y = {1 \over 2}{x^4} - 5{x^3} + 18{x^2} - 19x$$ occurs at the point :
A
$$\left( {3,{{21} \over 2}} \right)$$
B
(0, 0)
C
(2, 9)
D
(2, 2)
2
JEE Main 2021 (Online) 25th February Evening Shift
+4
-1
The minimum value of $$f(x) = {a^{{a^x}}} + {a^{1 - {a^x}}}$$, where a, $$x \in R$$ and a > 0, is equal to :
A
$$a + {1 \over a}$$
B
2a
C
a + 1
D
$$2\sqrt a$$
3
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
If the curves, $${{{x^2}} \over a} + {{{y^2}} \over b} = 1$$ and $${{{x^2}} \over c} + {{{y^2}} \over d} = 1$$ intersect each other at an angle of 90$$^\circ$$, then which of the following relations is TRUE?
A
a $$-$$ c = b + d
B
a + b = c + d
C
$$ab = {{c + d} \over {a + b}}$$
D
a $$-$$ b = c $$-$$ d
4
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
For which of the following curves, the line $$x + \sqrt 3 y = 2\sqrt 3$$ is the tangent at the point $$\left( {{{3\sqrt 3 } \over 2},{1 \over 2}} \right)$$?
A
$$2{x^2} - 18{y^2} = 9$$
B
$${y^2} = {1 \over {6\sqrt 3 }}x$$
C
$${x^2} + 9{y^2} = 9$$
D
$${x^2} + {y^2} = 7$$
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