If y = ${\left[ {x + \sqrt {{x^2} - 1} } \right]^{15}} + {\left[ {x - \sqrt {{x^2} - 1} } \right]^{15}},$ then (x2 $-$ 1) ${{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}}$ is equal to :
Previous 10 Questions — JEE Main 2017 (8 April Morning Shift)
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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)
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)
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)
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)
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)
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)
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)
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)
If
$S = \left\{ {x \in \left[ {0,2\pi } \right]:\left| {\matrix{
0 & {\cos x} & { - \sin x} \cr
{\sin …
Topic: JEE Main 2017 (8 April Morning Shift)
An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :
Topic: JEE Main 2017 (8 April Morning Shift)
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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)
The integral
$\int {\sqrt {1 + 2\cot x(\cos ecx + \cot x)\,} \,\,dx} $
$\left( {0 < x < {\pi \over 2}} \right)$…
Topic: JEE Main 2017 (8 April Morning Shift)
$ \displaystyle \lim_{x\to 3} \frac{\sqrt{3x}-3}{\sqrt{2x}-\sqrt{6}} $
is equal to:
Topic: JEE Main 2017 (8 April Morning Shift)
