1
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If the derivative of the function $$f(x) = \left\{ {\matrix{ {b{x^2} + ax + 4;} & {x \ge - 1} \cr {a{x^2} + b;} & {x < - 1} \cr } } \right.$$ is everywhere continuous, then

A
$$a = 2,b = 3$$
B
$$a = 3,b = 2$$
C
$$a = - 2,b = - 3$$
D
$$a = - 3,b = - 2$$
2
COMEDK 2022
MCQ (Single Correct Answer)
+1
-0

If $$\mathop {\lim }\limits_{x \to \infty } {\left( {1 + {a \over x} + {b \over {{x^2}}}} \right)^{2x}} = {e^2}$$, then

A
$$a = 1,b = 2$$
B
$$a = 2,b = 1$$
C
$$a = 1,b \in R$$
D
None of these
3
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0

If $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If L is finite, then

A
$$a = 2$$
B
$$a = 1$$
C
$$a = {1 \over 3}$$
D
None of these
4
COMEDK 2021
MCQ (Single Correct Answer)
+1
-0

If $$f(x) = \left\{ {\matrix{ {ax + 3,} & {x \le 2} \cr {{a^2}x - 1} & {x > 2} \cr } } \right.$$, then the values of a for which f is continuous for all x are

A
1 and $$-$$2
B
1 and 2
C
$$-$$1 and 2
D
$$-$$1 and $$-$$2
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