1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If    f(x) = sin-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :
A
$$- \sqrt 3 {\log _e}\sqrt 3$$
B
$$\sqrt 3 {\log _e}\sqrt 3$$
C
$$- \sqrt 3 {\log _e}\, 3$$
D
$$\sqrt 3 {\log _e}\, 3$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Let f(x) be a polynomial of degree $$4$$ having extreme values at $$x = 1$$ and $$x = 2.$$

If   $$\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$$   then f($$-$$1) is equal to :
A
$${9 \over 2}$$
B
$${5 \over 2}$$
C
$${3 \over 2}$$
D
$${1 \over 2}$$
3
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
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
+4
-1
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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