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

The value of $$\lim _\limits{x \rightarrow 0} \frac{8}{x^8}\left(1-\cos \frac{x^2}{2}-\cos \frac{x^2}{4}+\cos \frac{x^2}{2} \cos \frac{x^2}{4}\right)$$ is

A
$$\frac{1}{32}$$
B
$$\frac{1}{8}$$
C
$$\frac{1}{64}$$
D
$$\frac{1}{16}$$
2
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
$$\frac{1}{3}$$
3
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
$$\frac{1}{12}$$
4
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
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