1
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The integral $$\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}} $$ is equal to
A
2
B
4
C
$$-$$ 1
D
$$-$$ 2
2
JEE Main 2017 (Offline)
MCQ (Single Correct Answer)
+4
-1
Change Language
The area (in sq. units) of the region

$$\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}$$ is
A
$${3 \over 2}$$
B
$${7 \over 3}$$
C
$${5 \over 2}$$
D
$${59 \over 12}$$
3
JEE Main 2016 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
The value of the integral

$$\int\limits_4^{10} {{{\left[ {{x^2}} \right]dx} \over {\left[ {{x^2} - 28x + 196} \right] + \left[ {{x^2}} \right]}}} ,$$

where [x] denotes the greatest integer less than or equal to x, is :
A
6
B
3
C
7
D
$${1 \over 3}$$
4
JEE Main 2016 (Online) 10th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
For x $$ \in $$ R, x $$ \ne $$ 0, if y(x) is a differentiable function such that

x $$\int\limits_1^x y $$ (t) dt = (x + 1) $$\int\limits_1^x ty $$ (t) dt,  then y (x) equals :

(where C is a constant.)
A
$${C \over x}{e^{ - {1 \over x}}}$$
B
$${C \over {{x^2}}}{e^{ - {1 \over x}}}$$
C
$${C \over {{x^3}}}{e^{ - {1 \over x}}}$$
D
$$C{x^3}\,{1 \over {{e^x}}}$$
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