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) 26th February Morning Shift
+4
-1
Out of Syllabus
Let f be any function defined on R and let it satisfy the condition : $$|f(x) - f(y)|\, \le \,|{(x - y)^2}|,\forall (x,y) \in R$$

If f(0) = 1, then :
A
f(x) can take any value in R
B
$$f(x) < 0,\forall x \in R$$
C
$$f(x) > 0,\forall x \in R$$
D
$$f(x) = 0,\forall x \in R$$
3
JEE Main 2021 (Online) 25th February Morning Shift
+4
-1
Out of Syllabus
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) 25th February Morning Shift
+4
-1
Out of Syllabus
If Rolle's theorem holds for the function $$f(x) = {x^3} - a{x^2} + bx - 4$$, $$x \in [1,2]$$ with $$f'\left( {{4 \over 3}} \right) = 0$$, then ordered pair (a, b) is equal to :
A
($$-$$5, $$-$$8)
B
(5, $$-$$8)
C
($$-$$5, 8)
D
(5, 8)
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