1
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
$$\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}$$ equals :
A
$${1 \over 4}$$
B
1
C
$${1 \over 2}$$
D
$$-$$ $${1 \over 2}$$
2
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Let f(x) = $$\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {,x = 2} \cr } } \right.$$

Thevaue of k for which f s continuous at x = 2 is :
A
1
B
e
C
e-1
D
e-2
3
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
$$\sqrt 3 {\log _e}\, 3$$
4
JEE Main 2018 (Online) 15th April Evening Slot
+4
-1
Let f(x) be a polynomial of degree $$4$$ having extreme values at $$x = 1$$ and $$x = 2.$$

If   $$\mathop {lim}\limits_{x \to 0} \left( {{{f\left( x \right)} \over {{x^2}}} + 1} \right) = 3$$   then f($$-$$1) is equal to :
A
$${9 \over 2}$$
B
$${5 \over 2}$$
C
$${3 \over 2}$$
D
$${1 \over 2}$$
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