1
TG EAPCET 2025 (Online) 3rd May Morning Shift
MCQ (Single Correct Answer)
+1
-0

The value of $x$ at which the real valued function $f(x)=7|2 x+1|-19|3 x-5|$ is not differentiable is

A

1,-1

B

$\frac{1}{2},-\frac{5}{3}$

C

$-\frac{1}{2}, \frac{5}{3}$

D

0,1

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

If $f(x)=\frac{x\left(a^x-1\right)}{1-\cos x}$ and $g(x)=\frac{x\left(1-a^x\right)}{a^x\left(\sqrt{1-x^2}-\sqrt{1+x^2}\right)}$, then $\lim _{x \rightarrow 0}(f(x)-g(x))=$

A

$3 \log a$

B

$e^a$

C

$2 \log a$

D

$\log a$

3
TG EAPCET 2025 (Online) 2nd May Evening Shift
MCQ (Single Correct Answer)
+1
-0

If $f(x)=\left\{\begin{array}{cc}\frac{a \sin x-b x+c x^2+x^3}{2 \log (1+x)-2 x^3+x^4} & , x \neq 0 \\ 0 & , x=0\end{array}\right.$

is continuous at $x=0$, then

A

$a=2 b$

B

$a=b$

C

$a=b=c$

D

$b=c$

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

If the function $g(x)=\left\{\begin{array}{cl}K \sqrt{x+1} & , 0 \leq x \leq 3 \\ m x+2 & , 3 < x \leq 5\end{array}\right.$ is differentiable, then $K+m=$

A

4

B

2

C

6

D

0

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