1
KCET 2024
MCQ (Single Correct Answer)
+1
-0

Let $f(x)=\left|\begin{array}{ccc}\cos x & x & 1 \\ 2 \sin x & x & 2 x \\ \sin x & x & x\end{array}\right|$. Then, $\lim _\limits{x \rightarrow 0} \frac{f(x)}{x^2}$ is

A
$-$1
B
0
C
3
D
2
2
KCET 2024
MCQ (Single Correct Answer)
+1
-0

Which one of the following observations is correct for the features of logarithm function to any base $b>1$ ?

A
The domain of the logarithm function is $R$, the set of real numbers.
B
The range of the logarithm function is $R^{+}$, the set of all positive real numbers.
C
The point $(1,0)$ is always on the graph of the logarithm function.
D
The graph of the logarithm function is decreasing as we move from left to right.
3
KCET 2024
MCQ (Single Correct Answer)
+1
-0

The function $f(x)=|\cos x|$ is

A
Everywhere continuous and differentiable
B
Everywhere continuous but not differentiable at odd multiples of $\pi / 2$
C
Neither continuous nor differentiable at $(2 n+1) \frac{\pi}{2}, n \in Z$
D
Not differentiable everywhere
4
KCET 2024
MCQ (Single Correct Answer)
+1
-0

If $y=2 x^{3 x}$, then $d y / d x$ at $x=1$ is

A
2
B
6
C
3
D
1
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