1
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
$$2\pi \left( {\sqrt 2 - 1} \right)$$
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
If    $$\int {{{2x + 5} \over {\sqrt {7 - 6x - {x^2}} }}} \,\,dx = A\sqrt {7 - 6x - {x^2}} + B{\sin ^{ - 1}}\left( {{{x + 3} \over 4}} \right) + C$$
(where C is a constant of integration), then the ordered pair (A, B) is equal to :
A
(2,  1)
B
($$-$$ 2,   $$-$$1)
C
($$-$$ 2,  1)
D
(2,   $$-$$1)
3
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${1 \over 2}$$
4
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$$ \sqrt 3 {\log _e}\, 3 $$
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