1
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
$${x^2} + {y^2} = 7$$
2
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
$$( - \infty , - 5) \cup ( - 4,\infty )$$
3
JEE Main 2021 (Online) 24th February Evening Shift
+4
-1
Out of Syllabus
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
4
JEE Main 2021 (Online) 24th February Morning Shift
+4
-1
The function
f(x) = $${{4{x^3} - 3{x^2}} \over 6} - 2\sin x + \left( {2x - 1} \right)\cos x$$ :
A
increases in $$\left( { - \infty ,{1 \over 2}} \right]$$
B
decreases in $$\left( { - \infty ,{1 \over 2}} \right]$$
C
increases in $$\left[ {{1 \over 2},\infty } \right)$$
D
decreases in $$\left[ {{1 \over 2},\infty } \right)$$
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