1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

$$ \text { The value of } \lim _\limits{x \rightarrow 0} \frac{(27+x)^{1 / 3}-3}{9-(27+x)^{2 / 3}} \text { equals to } $$

A
$$-\frac{1}{3}$$
B
$$\frac{1}{6}$$
C
$$-\frac{1}{6}$$
D
$$\frac{1}{3}$$
2
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

The value of $$\mathop {\lim }\limits_{x \to 0} {{1-\cos (1 - \cos x)} \over {{x^4}}}$$ is

A
$$\frac{1}{6}$$
B
$$\frac{1}{8}$$
C
$$\frac{1}{10}$$
D
$$\frac{1}{12}$$
3
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

The value of $$\mathop {\lim }\limits_{x \to 0} {{{{(1 + x)}^{{1 \over x}}} - e + {1 \over 2}ex} \over {{x^2}}}$$ is

A
$${{11} \over {24}}e$$
B
$$ - {{11} \over {24}}e$$
C
$${e \over {24}}$$
D
None of these
4
BITSAT 2021
MCQ (Single Correct Answer)
+3
-1

The value of $$\mathop {\lim }\limits_{x \to 0} {{\sqrt {1 - {{\cos x}^2}} } \over {1 - \cos x}}$$ is

A
$${1 \over 2}$$
B
2
C
$$\sqrt 2 $$
D
None of these
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