1
KCET 2021
MCQ (Single Correct Answer)
+1
-0

Consider the following statements

statement 1: $$\lim _\limits{x \rightarrow 1} \frac{a x^2+b x+c}{x^2+b x+a}$$ is 1

(where $$a+b+c \neq 0$$).

statement 2: $$\lim _\limits{x \rightarrow 2} \frac{\frac{1}{x}+\frac{1}{2}}{x+2}$$ is $$\frac{1}{4}$$.

A
Only statement 2 is true.
B
Only statement 1 is true.
C
Both statements 1 and 2 are true.
D
Both statements 1 and 2 are false.
2
KCET 2021
MCQ (Single Correct Answer)
+1
-0

If $$f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$$, then $$\lim _\limits{x \rightarrow \pi} f(x)$$ is equal to

A
$$-$$1
B
1
C
0
D
3
3
KCET 2021
MCQ (Single Correct Answer)
+1
-0

At $$x=1$$, the function

$$f(x)=\left\{\begin{array}{cc} x^3-1, & 1< x < \infty \\ x-1, & -\infty< x \leq 1 \end{array}\right. \text { is }$$

A
continuous and differentiable.
B
continuous and non-differentiable.
C
discontinuous and differentiable.
D
discontinuous and non-differentiable.
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