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

If $\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}\right.$ is an integer and $\left.\mathrm{x}^2-9=0\right\}$

$B=\{x: x$ is a natural number and $2 \leq x<5\}$

$\mathrm{C}=\{\mathrm{x}: \mathrm{x}$ is a prime number $\leq 4\}$

Then $(B-C) \cup A$ is,

A
$\{-3,3,4\}$
B
$\{2,3,4\}$
C
$\{3,4,5\}$
D
$\{2,3,5\}$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$A$ and $B$ are two sets having 3 and 6 elements respectively. Consider the following statements.

Statement (I): Minimum number of elements in AUB is 3

Statement (II): Maximum number of elements in AB is 3 Which of the following is correct?

A
Statement (I) is true, statement (II) is false
B
Statement (1) is false, statement (II) is true
C
Both statements (1) and (II) are true
D
Both statements (I) and (II) are false
3
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
$(-\infty, 3] \cup(5, \infty)$
4
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
$f(\pi)=-1$
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