1
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If $$[\cdot]$$ denotes greatest integer function, then $$\lim _\limits{x \rightarrow \frac{-3}{5}} \frac{1}{\dot{x}}\left[\frac{-1}{x}\right]=$$

A
$$-5 / 3$$
B
$$5 / 3$$
C
$$10 / 3$$
D
$$-10 / 3$$
2
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

If $$l, m(l< m)$$ are roots of $$a x^2+b x+c=0$$, then $$\lim _\limits{x \rightarrow \alpha} \frac{\left|a x^2+b x+c\right|}{a x^2+b x+c}=$$

A
$$\frac{|a|}{a}, \forall \alpha \in R$$
B
$$\frac{-|a|}{a} \text {, when } \alpha \notin(l, m)$$
C
$$\frac{-|a|}{a} \text {, when } \alpha \in(1, m)$$
D
$$\frac{|a|}{a} \text {, when } \alpha \in(i, m)$$
3
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

Let $$f(x)=\left\{\begin{array}{cl}\frac{1}{|x|}, & \text { for }|x|>1 \\ a x^2+b, & \text { for }|x| \leq 1\end{array}\right.$$. If $$\lim _\limits{x \rightarrow 1^{+}} f(x)$$ and $$\lim _\limits{x \rightarrow 1^{-}} f(x)$$ exist, then the possible values for $$a$$ and $$b$$ are

A
$$a=b=1$$
B
$$a=-1 / 2, b=-3 / 2$$
C
$$a=3 / 2, b=-1 / 2$$
D
$$a=1 / 2, b=-3 / 2$$
4
AP EAPCET 2022 - 4th July Evening Shift
+1
-0

$$\frac{d}{d x}\left(\lim _{x \rightarrow 2} \frac{1}{y-2}\left(\frac{1}{x}-\frac{1}{x+y-2}\right)\right)=$$

A
$$1 / x^2$$
B
$$2 / x^3$$
C
$$-2 / x^3$$
D
$$1 / x^3$$
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