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1
JEE Main 2020 (Online) 9th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
Given : $$f(x) = \left\{ {\matrix{ {x\,\,\,\,\,,} & {0 \le x < {1 \over 2}} \cr {{1 \over 2}\,\,\,\,,} & {x = {1 \over 2}} \cr {1 - x\,\,\,,} & {{1 \over 2} < x \le 1} \cr } } \right.$$

and $$g(x) = \left( {x - {1 \over 2}} \right)^2,x \in R$$

Then the area (in sq. units) of the region bounded by the curves, y = ƒ(x) and y = g(x) between the lines, 2x = 1 and 2x = $$\sqrt 3 $$, is :
A
$${1 \over 2} + {{\sqrt 3 } \over 4}$$
B
$${1 \over 2} - {{\sqrt 3 } \over 4}$$
C
$${1 \over 3} + {{\sqrt 3 } \over 4}$$
D
$${{\sqrt 3 } \over 4} - {1 \over 3}$$
2
JEE Main 2020 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
The value of
$$\int\limits_0^{2\pi } {{{x{{\sin }^8}x} \over {{{\sin }^8}x + {{\cos }^8}x}}} dx$$ is equal to :
A
4$$\pi $$
B
2$$\pi $$
C
$$\pi $$2
D
2$$\pi $$2
3
JEE Main 2020 (Online) 9th January Morning Slot
MCQ (Single Correct Answer)
+4
-1
If for all real triplets (a, b, c), ƒ(x) = a + bx + cx2; then $$\int\limits_0^1 {f(x)dx} $$ is equal to :
A
$${1 \over 6}\left\{ {f(0) + f(1) + 4f\left( {{1 \over 2}} \right)} \right\}$$
B
$$2\left\{ 3{f(1) + 2f\left( {{1 \over 2}} \right)} \right\}$$
C
$${1 \over 3}\left\{ {f(0) + f\left( {{1 \over 2}} \right)} \right\}$$
D
$${1 \over 2}\left\{ {f(1) + 3f\left( {{1 \over 2}} \right)} \right\}$$
4
JEE Main 2020 (Online) 8th January Evening Slot
MCQ (Single Correct Answer)
+4
-1
The area (in sq. units) of the region
{(x,y) $$ \in $$ R2 : x2 $$ \le $$ y $$ \le $$ 3 – 2x}, is
A
$${{34} \over 3}$$
B
$${{29} \over 3}$$
C
$${{31} \over 3}$$
D
$${{32} \over 3}$$
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