1
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Let $$A=\{x: x \in R, x$$ is not a positive integer) Define $$f: A \rightarrow R$$ as $$f(x)=\frac{2 x}{x-1}$$, then $$f$$ is

A
injective but not surjective.
B
surjective but not injective.
C
bijective.
D
neither injective nor surjective.
2
KCET 2021
MCQ (Single Correct Answer)
+1
-0

The function $$f(x)=\sqrt{3} \sin 2 x-\cos 2 x+4$$ is one-one in the interval

A
$$\left[\frac{-\pi}{6}, \frac{\pi}{3}\right]$$
B
$$\left[\frac{\pi}{6}, \frac{-\pi}{3}\right]$$
C
$$\left[\frac{-\pi}{2}, \frac{\pi}{2}\right]$$
D
$$\left[\frac{-\pi}{6}, \frac{-\pi}{3}\right]$$
3
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Domain of the function

$$f(x)=\frac{1}{\sqrt{\left[x^2\right]-[x]-6}},$$

where $$[x]$$ is greatest integer $$\leq x$$ is

A
$$(-\infty,-2) \cup[4, \infty)$$
B
$$(-\infty,-2 \cup[3, \infty]$$
C
$$[-\infty,-2] \cup[4, \infty]$$
D
$$[-\infty,-2] \cup[3, \infty)$$
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