1
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
2
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
$(-\infty, 3] \cup(5, \infty)$
3
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
$f(\pi)=-1$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0
Which of the following is not correct?
A
$\cos 5 \pi=\cos 4 \pi$
B
$\sin 2 \pi=\sin (-2 \pi)$
C
$\sin 4 \pi=\sin 6 \pi$
D
$\tan 45^{\circ}=\tan \left(-315^{\circ}\right)$
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