1
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

Let $f:[-1,2] \rightarrow R$ be defined by $f(x)=\left[x^2-3\right]$ where $[$. denotes greatest integer function, then the number of points of discontinuity for the function $f$ in $(-1,2)$ is

A

5

B

4

C

3

D

2

2
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left\{\begin{array}{cc}x^2\left|\cos \frac{\pi}{2}\right|, & x \neq 0 \\ 0, & x=0\end{array}\right.$, then at $x=2, f(x)$ is

A

Differentiable

B

Continuous but not differentiable

C

Right differentiable only

D

Left differentiable only

3
TG EAPCET 2025 (Online) 4th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

The set of all values of $x$ for which $f(x)=\| x|-1|$ is differentiable is

A

$\{-1,1\}$

B

$R-\{-1,1,0\}$

C

$R$

D

$(0, \infty)$

4
TG EAPCET 2025 (Online) 4th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $\mathop {\lim }\limits_{x \to 0} \frac{3^{x^3}-\left(1-x^3\right)^{\frac{2}{3}}}{x^2 \sin x}=p+\log q$, then $p q=$

A

$\frac{2}{3}$

B

2

C

3

D

-2

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