1
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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
$${1 \over 2}$$
2
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
Let S = {($$\lambda $$, $$\mu $$) $$ \in $$ R $$ \times $$ R : f(t) = (|$$\lambda $$| e|t| $$-$$ $$\mu $$). sin (2|t|), t $$ \in $$ R, is a differentiable function}. Then S is a subset of :
A
R $$ \times $$ [0, $$\infty $$)
B
[0, $$\infty $$) $$ \times $$ R
C
R $$ \times $$ ($$-$$ $$\infty $$, 0)
D
($$-$$ $$\infty $$, 0) $$ \times $$ R
3
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
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) 8th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
Change Language
$$\mathop {\lim }\limits_{x \to 3} $$ $${{\sqrt {3x} - 3} \over {\sqrt {2x - 4} - \sqrt 2 }}$$ is equal to :
A
$$\sqrt 3 $$
B
$${1 \over {\sqrt 2 }}$$
C
$${{\sqrt 3 } \over 2}$$
D
$${1 \over {2\sqrt 2 }}$$
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