1
KCET 2023
+1
-0

The function $$f(x)=\cot x$$ is discontinuous on every point of the set

A
$$\{x=2 n \pi ; n \in Z\}$$
B
$$\left\{x=(2 n+1) \frac{\pi}{2} ; n \in Z\right\}$$
C
$$\left\{x=\frac{n \pi}{2} ; n \in Z\right\}$$
D
$$\{x=n \pi ; n \in Z\}$$
2
KCET 2022
+1
-0

If $$f(x)=\left\{\begin{array}{cc}x^2-1, & 0< x<2 \\ 2 x+3, & 2 \leq x<3\end{array}\right.$$,

the quadratic equation whose roots are $$\lim _\limits{x \rightarrow 2^{-}} f(x)$$ and $$\lim _\limits{x \rightarrow 2^{+}} f(x)$$ is

A
$$x^2-14 x+49=0$$
B
$$x^2-10 x+21=0$$
C
$$x^2-6 x+9=0$$
D
$$x^2-7 x+8=0$$
3
KCET 2022
+1
-0

$$\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=$$

A
$$\frac{1}{2 \sqrt{3}}$$
B
$$\frac{1}{3 \sqrt{2}}$$
C
$$2 \sqrt{3}$$
D
$$3 \sqrt{2}$$
4
KCET 2021
+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.
EXAM MAP
Medical
NEET