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1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Let g(x) = cosx2, f(x) = $$\sqrt x $$ and $$\alpha ,\beta \left( {\alpha < \beta } \right)$$ be the roots of the quadratic equation 18x2 - 9$$\pi $$x + $${\pi ^2}$$ = 0. Then the area (in sq. units) bounded by the curve
y = (gof)(x) and the lines $$x = \alpha $$, $$x = \beta $$ and y = 0 is
A
$${1 \over 2}\left( {\sqrt 2 - 1} \right)$$
B
$${1 \over 2}\left( {\sqrt 3 - 1} \right)$$
C
$${1 \over 2}\left( {\sqrt 3 + 1} \right)$$
D
$${1 \over 2}\left( {\sqrt 3 - \sqrt 2 } \right)$$
2
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_{ - \pi /2}^{\pi /2} {{{{{\sin }^2}x} \over {1 + {2^x}}}} dx$$ is
A
$${\pi \over 4}$$
B
$${\pi \over 8}$$
C
$${\pi \over 2}$$
D
$${4\pi }$$
3
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of integral $$\int_{{\pi \over 4}}^{{{3\pi } \over 4}} {{x \over {1 + \sin x}}dx} $$ is :
A
$$\pi \sqrt 2 $$
B
$$\pi \left( {\sqrt 2 - 1} \right)$$
C
$${\pi \over 2}\left( {\sqrt 2 + 1} \right)$$
D
$$2\pi \left( {\sqrt 2 - 1} \right)$$
4
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If   $${I_1} = \int_0^1 {{e^{ - x}}} {\cos ^2}x{\mkern 1mu} dx;$$

   $${I_2} = \int_0^1 {{e^{ - {x^2}}}} {\cos ^2}x{\mkern 1mu} dx$$  and

$${I_3} = \int_0^1 {{e^{ - {x^3}}}} dx;$$ then
A
I2  >  I3  >  I1
B
I2  >  I1  >  I3
C
I3  >  I2  >  I1
D
I3  >  I1  >  I2
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