1
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The function $f(x)=|\cos x|$ is

A
Everywhere continuous and differentiable
B
Everywhere continuous but not differentiable at odd multiples of $\pi / 2$
C
Neither continuous nor differentiable at $(2 n+1) \frac{\pi}{2}, n \in Z$
D
Not differentiable everywhere
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0

$$\lim _\limits{n \rightarrow \infty}\left(\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+\ldots+\frac{1}{5 n}\right)= $$

A
$\pi / 4$
B
$\tan ^{-1} 3$
C
$\tan ^{-1} 2$
D
$\pi / 2$
3
KCET 2023
MCQ (Single Correct Answer)
+1
-0

If $$\lim _\limits{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=A \cos B$$, then the values of $$A$$ and $$B$$ respectively are

A
$$1,2$$
B
$$2, 1$$
C
$$1, 1$$
D
$$2,2$$
4
KCET 2023
MCQ (Single Correct Answer)
+1
-0

The function $$f(x)=\cot x$$ is discontinuous on every point of the set

A
$$\{x=2 n \pi ; n \in Z\}$$
B
$$\left\{x=(2 n+1) \frac{\pi}{2} ; n \in Z\right\}$$
C
$$\left\{x=\frac{n \pi}{2} ; n \in Z\right\}$$
D
$$\{x=n \pi ; n \in Z\}$$
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