1
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If the function

$$ f(x)=\left\{\begin{array}{cc} \frac{\cos a x-\cos 9 x}{x^2} & \text {, if } x \neq 0 \\ 16 & \text {, if } x=0 \end{array}\right. $$

is continuous at $x=0$, then $a=$

A
$\pm 8$
B
$\pm 7$
C
$\pm 6$
D
$\pm 5$
2
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0

If $ f(x)=\left\{\begin{array}{ll}\frac{8}{x^{3}}-6 x & \text {, if } 0 < x \leq 1 \\\\ \frac{x-1}{\sqrt{x}-1} & \text {,if } x > 1\end{array}\right. $ is a real valued function, then at $ x=1, f $ is

A
continuous and differentiable
B
continuous but not differentiable
C
neither continuous nor differentiable
D
differentiable but not continuous
3
TG EAPCET 2024 (Online) 9th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\right) \ldots .(2)\right]^{1 / n}=$
A
$16 e^{-1}$
B
$2 e^{\left(\frac{\pi-4}{2}\right)}$
C
$2 \log 2-1$
D
$2+e^{\left(\frac{\pi-4}{2}\right)}$
4
TS EAMCET 2023 (Online) 12th May Evening Shift
MCQ (Single Correct Answer)
+1
-0

$$ \lim\limits_{x \rightarrow 1}(1-x) \tan \left(\frac{\pi}{2} x\right)= $$

A
$\pi / 2$
B
$2 / \pi$
C
1
D
0
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