AP EAPCET 2024 - 23th May Morning Shift | Limits, Continuity and Differentiability Question 2 | Mathematics

Let $[P]$ denote the greatest integer $\leq P$. If $0 \leq a \leq 2$, then the number of integral values of ' $a$ ' such that $\lim \limits_{x \rightarrow a}\left(\left[x^2\right]-[x]^2\right)$ does not exist is

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

-0

If $f(x)=\left\{\begin{array}{cl}\frac{\sqrt{a^2-a x+x^2}-\sqrt{x^2+a x+a^2}}{\sqrt{a+x}-\sqrt{a-x}}, & x \neq 0 \text { is } \\ K & x=0\end{array}\right.$ continuous at $x=0$, then $K$ is equal to

$-\sqrt{a}$

$\sqrt{a}$

-1

$a+\sqrt{a}$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

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If $f(x)=\left\{\begin{array}{cc}a x^2+b x-\frac{13}{8}, & x \leq 1 \\ 3 x-3, & 1 < x \leq 2 \text { is differentiable } \\ b x^3+1, & x > 2\end{array}\right.$ $\forall x \in R$, then $a-b$ is equal to

$\frac{9}{8}$

$\frac{5}{4}$

$\frac{11}{8}$

$\frac{1}{4}$

AP EAPCET 2024 - 23th May Morning Shift

MCQ (Single Correct Answer)

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In each of the following options, a function and an interval are given. Choose the option containing the function and the interval for which Lagrange's mean value theorem is not applicable

$f(x)=|x|, 1 \leq x \leq 5$

$f(x)=[x],[\sqrt{2}, \sqrt{3}]$

$f(x)=\log \left(x^2-1\right),\left[\frac{1}{e}, e-2\right]$

$f(x)=e^x,[-e, e]$

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