1
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
2
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
3
KCET 2025
MCQ (Single Correct Answer)
+1
-0

$2 \cos ^{-1} x=\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ is valid for all values of ' $x$ ' satisfying

A
$0 \leq x \leq \frac{1}{\sqrt{2}}$
B
$-1 \leq x \leq 1$
C
$0 \leq x \leq 1$
D
$\frac{1}{\sqrt{2}} \leq x \leq 1$
4
KCET 2025
MCQ (Single Correct Answer)
+1
-0

Consider the following statements:

Statement (I): In a LPP, the objective function is always linear.

Statement (II): Ina LPP, the linear inequalities on variables are called constraints. Which of the following is correct?

A
Statement (I) is true, Statement (II) is true
B
Statement (I) is true, Statement (II) is false
C
Both Statements (I) and (II) are false
D
Statement (I) is false, Statement (II) is true
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