1
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+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
2
JEE Main 2018 (Online) 15th April Evening Slot
MCQ (Single Correct Answer)
+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
$${1 \over 2}$$
3
JEE Main 2018 (Online) 15th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
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
4
JEE Main 2017 (Online) 9th April Morning Slot
MCQ (Single Correct Answer)
+4
-1
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
$$-$$ $${{2} \over {5}}$$
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