1
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
2
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)
3
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Out of Syllabus
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
$${x^2} + {y^2} = 7$$
4
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Let $$f:R \to R$$ be defined as

$$f(x) = \left\{ {\matrix{ { - 55x,} & {if\,x < - 5} \cr {2{x^3} - 3{x^2} - 120x,} & {if\, - 5 \le x \le 4} \cr {2{x^3} - 3{x^2} - 36x - 336,} & {if\,x > 4,} \cr } } \right.$$

Let A = {x $$\in$$ R : f is increasing}. Then A is equal to :
A
$$( - 5,\infty )$$
B
$$( - \infty , - 5) \cup (4,\infty )$$
C
$$( - 5, - 4) \cup (4,\infty )$$
D
$$( - \infty , - 5) \cup ( - 4,\infty )$$
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