1
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Domain of the function $f$, given by $f(x)=\frac{1}{\sqrt{(x-2)(x-5)}}$ is

A
$(-\infty, 2] \cup[5, \infty)$
B
$(-\infty, 2) \cup(5, \infty)$
C
$(-\infty, 3) \cup[5, \infty)$
D
$(-\infty, 3] \cup(5, \infty)$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x$, where $[x]=$ greatest integer $\leq x$, then which of the following is not true?

A
$f(0)=0$
B
$f\left(\frac{\pi}{2}\right)=1$
C
$f\left(\frac{\pi}{4}\right)=1+\frac{1}{\sqrt{2}}$
D
$f(\pi)=-1$
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Let the functions " f " and " g " be $\mathrm{f}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $\mathrm{f}(\mathrm{x})=\sin \mathrm{x}$ and $\mathrm{g}:\left[0, \frac{\pi}{2}\right] \rightarrow \mathrm{R}$ given by $g(x)=\cos x$, where $R$ is the set of real numbers

Consider the following statements:

Statement (I): $f$ and $g$ are one-one

Statement (II): $\mathrm{f}+\mathrm{g}$ is one-one

Which of the following is correct?

A
Statement (I) is true, statement (II) is false
B
Statement (I) is false, statement (II) is true
C
Both statements (I) and (I) are true
D
Both statements (I) and (II) are false
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0

If $[x]^2-5[x]+6=0$, where $[x]$ denotes the greatest integer function, then

A
$x \in[3,4]$
B
$x \in[2,4)$
C
$x \in[2,3]$
D
$x \in(2,3]$
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