1
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${4\pi }$$
2
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
Let y = y(x) be the solution of the differential equation

$$\sin x{{dy} \over {dx}} + y\cos x = 4x$$, $$x \in \left( {0,\pi } \right)$$.

If $$y\left( {{\pi \over 2}} \right) = 0$$, then $$y\left( {{\pi \over 6}} \right)$$ is equal to :
A
$$ - {4 \over 9}{\pi ^2}$$
B
$${4 \over {9\sqrt 3 }}{\pi ^2}$$
C
$$ - {8 \over {9\sqrt 3 }}{\pi ^2}$$
D
$$ - {8 \over 9}{\pi ^2}$$
3
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
Let the orthocentre and centroid of a triangle be A(-3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is :
A
$${{3\sqrt 5 } \over 2}$$
B
$$\sqrt {10} $$
C
$$2\sqrt {10} $$
D
$$3\sqrt {{5 \over 2}} $$
4
JEE Main 2018 (Offline)
MCQ (Single Correct Answer)
+4
-1
Out of Syllabus
Change Language
If the tangent at (1, 7) to the curve x2 = y - 6

touches the circle x2 + y2 + 16x + 12y + c = 0, then the value of c is :
A
95
B
195
C
185
D
85
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