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1
JEE Main 2019 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_0^{\pi /2} {{{{{\sin }^3}x} \over {\sin x + \cos x}}dx} $$ is
A
$${{\pi - 2} \over 8}$$
B
$${{\pi - 2} \over 4}$$
C
$${{\pi - 1} \over 2}$$
D
$${{\pi - 1} \over 4}$$
2
JEE Main 2019 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
The area (in sq. units) of the region

A = {(x, y) : x2 $$ \le $$ y $$ \le $$ x + 2} is
A
$${{31 \over 6}}$$
B
$${{10 \over 3}}$$
C
$${{13 \over 6}}$$
D
$${{9 \over 2}}$$
3
JEE Main 2019 (Online) 8th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Let S($$\alpha $$) = {(x, y) : y2 $$ \le $$ x, 0 $$ \le $$ x $$ \le $$ $$\alpha $$} and A($$\alpha $$) is area of the region S($$\alpha $$). If for a $$\lambda $$, 0 < $$\lambda $$ < 4, A($$\lambda $$) : A(4) = 2 : 5, then $$\lambda $$ equals
A
$$2{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$
B
$$2{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$
C
$$4{\left( {{4 \over {25}}} \right)^{{1 \over 3}}}$$
D
$$4{\left( {{2 \over {5}}} \right)^{{1 \over 3}}}$$
4
JEE Main 2019 (Online) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
If $$f(x) = {{2 - x\cos x} \over {2 + x\cos x}}$$ and g(x) = logex, (x > 0) then the value of integral

$$\int\limits_{ - {\pi \over 4}}^{{\pi \over 4}} {g\left( {f\left( x \right)} \right)dx{\rm{ }}} $$ is
A
loge3
B
loge2
C
loge1
D
logee
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