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

A die has two face each with number ' 1 ', three faces each with number ' 2 ' and one face with number ' 3 '. If the die is rolled once, then $\mathrm{P}(1$ or 3$)$ is

A
$\frac{2}{3}$
B
$\frac{1}{2}$
C
$\frac{1}{3}$
D
$\frac{1}{6}$
2
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$$ \text { Let } A=\{a, b, c\} \text {, then the number of equivalence relations on A containing }(b, c) \text { is } $$

A
1
B
3
C
2
D
4
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 2025
MCQ (Single Correct Answer)
+1
-0

$$ \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right)= $$

A
1
B
5
C
15
D
10
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