1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
If    f(x) = sin-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :
A
$$- \sqrt 3 {\log _e}\sqrt 3$$
B
$$\sqrt 3 {\log _e}\sqrt 3$$
C
$$- \sqrt 3 {\log _e}\, 3$$
D
$$\sqrt 3 {\log _e}\, 3$$
2
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If $$f\left( x \right) = \left| {\matrix{ {\cos x} & x & 1 \cr {2\sin x} & {{x^2}} & {2x} \cr {\tan x} & x & 1 \cr } } \right|,$$ then $$\mathop {\lim }\limits_{x \to 0} {{f'\left( x \right)} \over x}$$
A
does not exist.
B
exists and is equal to 2.
C
existsand is equal to 0.
D
exists and is equal to $$-$$ 2.
3
JEE Main 2018 (Online) 15th April Morning Slot
+4
-1
If   x2 + y2 + sin y = 4, then the value of $${{{d^2}y} \over {d{x^2}}}$$ at the point ($$-$$2,0) is :
A
$$-$$ 34
B
$$-$$ 32
C
4
D
$$-$$ 2
4
JEE Main 2017 (Online) 9th April Morning Slot
+4
-1
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
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