1
JEE Main 2021 (Online) 25th February Morning Slot
+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
2
JEE Main 2021 (Online) 24th February Evening Slot
+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
$${x^2} + {y^2} = 7$$
3
JEE Main 2021 (Online) 24th February Evening Slot
+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
$$( - \infty , - 5) \cup ( - 4,\infty )$$
4
JEE Main 2021 (Online) 24th February Evening Slot
+4
-1
If the curve y = ax2 + bx + c, x$$\in$$R, passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are :
A
a = $$-$$ 1, b = 1, c = 1
B
a = 1, b = 1, c = 0
C
a = $${1 \over 2}$$, b = $${1 \over 2}$$, c = 1
D
a = 1, b = 0, c = 1
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