The integral

$\int {\sqrt {1 + 2\cot x(\cos ecx + \cot x)\,} \,\,dx} $

$\left( {0 < x < {\pi \over 2}} \right)$ is equal to :

(where C is a constant of integration)

1

If a point P has co-ordinates (0,-2) and Q is any point on the circle $x^{2}+y^{2}-5x-y+5=0$, then the maximum value of…

Topic: JEE Main 2017 (8 April Morning Shift)

2

If y = ${\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}},$ then (x2 $-$ …

Topic: JEE Main 2017 (8 April Morning Shift)

3

The curve satisfying the differential equation $y,dx-(x+3y^{2}),dy=0$ and passing through the point (1,1), also passes …

Topic: JEE Main 2017 (8 April Morning Shift)

4

The locus of the point of intersection of the straight lines, $tx-2y-3t=0$, $x-2ty+3=0\ (t\in\mathbb{R}),$ is :

Topic: JEE Main 2017 (8 April Morning Shift)

5

The area (in sq. units) of the smaller portion enclosed between the curves $x^2 + y^2 = 4$ and $y^2 = 3x$, is :

Topic: JEE Main 2017 (8 April Morning Shift)

6

The integral $\int_{{\pi \over {12}}}^{{\pi \over 4}} {\,\,{{8\cos 2x} \over {{{\left( {\tan x + \cot x} \right)}^3}}…

Topic: JEE Main 2017 (8 April Morning Shift)

7

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles…

Topic: JEE Main 2017 (8 April Morning Shift)

8

The area (in sq. units) of the parallelogram whose diagonals are along the vectors $8\hat{i}-6\hat{j}$ and $3\hat{i}+4\…

Topic: JEE Main 2017 (8 April Morning Shift)

9

The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appo…

Topic: JEE Main 2017 (8 April Morning Shift)

10

Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are $\dfra…

Topic: JEE Main 2017 (8 April Morning Shift)

1

$ \displaystyle \lim_{x\to 3} \frac{\sqrt{3x}-3}{\sqrt{2x}-\sqrt{6}} $ is equal to:

Topic: JEE Main 2017 (8 April Morning Shift)