1
TS EAMCET 2023 (Online) 14th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The period of the function $f(x)=e^{\log (\sin x)}+(\tan x)^3-\operatorname{cosec}(3 x-5)$ is

A

$\pi$

B

$\pi / 2$

C

$2 \pi$

D

$2 \pi / 3$

2
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Which one of the following functions is a bijection?

A

$f: R-Z \rightarrow[0,1]$ defined by $f(x)=\sqrt{x-[x]}$. (Here $[x]$ represents the greatest integer function)

B

$f: R \rightarrow(-\infty, 2)$ defined by $f(x)=4 x-x^2-3$

C

$f:(5, \infty) \rightarrow R-\{0\}$ defined by $f(x)=\frac{1}{\sqrt{x-5}}$

D

$f:[0,4] \rightarrow[0,4]$ defined by $f(x)=\sqrt{16-x^2}$

3
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The domain of the real valued function $f(x)=\frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is

A

Z

B

$\phi$

C

$R-Z$

D

$R$

4
TS EAMCET 2023 (Online) 13th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The range of the function defined by

$$ f(x)=\left\{\begin{array}{lc} 2 x-3, & \text { if } x<-1 \\ 1-x^2, & \text { if }-1 \leq x \leq 1 \text { is } \\ 3 x^2+2, & \text { if } x>1 \end{array}\right. $$

A

$R$

B

$(-\infty,-5) \cup[0,1] \cup(5, \infty)$

C

$(-\infty,-1] \cup(1, \infty)$

D

$(-\infty,-3) \cup(0,1) \cup(3, \infty)$

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