1

### JEE Main 2017 (Online) 8th April Morning Slot

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 :
A
125 y
B
124 y2
C
225 y2
D
225 y
2

### JEE Main 2017 (Online) 9th April Morning Slot

If 2x = y${^{{1 \over 5}}}$ + y${^{ - {1 \over 5}}}$ and

(x2 $-$ 1) ${{{d^2}y} \over {d{x^2}}}$ + $\lambda$x ${{dy} \over {dx}}$ + ky = 0,

then $\lambda$ + k is equal to :
A
$-$ 23
B
$-$ 24
C
26
D
$-$ 26
3

### JEE Main 2017 (Online) 9th April Morning Slot

The value of k for which the function

$f\left( x \right) = \left\{ {\matrix{ {{{\left( {{4 \over 5}} \right)}^{{{\tan \,4x} \over {\tan \,5x}}}}\,\,,} & {0 < x < {\pi \over 2}} \cr {k + {2 \over 5}\,\,\,,} & {x = {\pi \over 2}} \cr } } \right.$

is continuous at x = ${\pi \over 2},$ is :
A
${{17} \over {20}}$
B
${{2} \over {5}}$
C
${{3} \over {5}}$
D
$-$ ${{2} \over {5}}$
4

### JEE Main 2017 (Online) 9th April Morning Slot

Let f be a polynomial function such that

f (3x) = f ' (x) . f '' (x), for all x $\in$ R. Then :
A
f (2) + f ' (2) = 28
B
f '' (2) $-$ f ' (2) = 0
C
f '' (2) $-$ f (2) = 4
D
f (2) $-$ f ' (2) + f '' (2) = 10