1
COMEDK 2024 Evening Shift
+1
-0

$$\text { If } f(x)=\left\{\begin{array}{cc} x & , \quad 0 \leq x \leq 1 \\ 2 x-1 & , \quad x>1 \end{array}\right. \text { then }$$

A
$$f$$ is not continuous but differentiable at $$x=1$$
B
$$f$$ is differentiable at $$x=1$$
C
$$f$$ is continuous but not differentiable at $$x=1$$
D
$$f$$ is discontinuous at $$x=1$$
2
COMEDK 2024 Morning Shift
+1
-0

$$\text { If } f(x)=\left\{\begin{array}{cc} \frac{1-\sin x}{(\pi-2 x)^2} & , \quad \text { if } x \neq \frac{\pi}{2} \\ \lambda, & \text { if } x=\frac{\pi}{2} \end{array}\right.$$

Then $$f(x)$$ will be continues function at $$x=\frac{\pi}{2}$$, then $$\lambda=$$

A
$$-\frac{1}{8}$$
B
1
C
$$\frac{1}{4}$$
D
$$\frac{1}{8}$$
3
COMEDK 2024 Morning Shift
+1
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{a+x}-\sqrt{a}}{x \sqrt{a(a+x)}}$$ equals to

A
$$a^{-\frac{3}{2}}$$
B
$$\frac{1}{2 a^{\frac{3}{2}}}$$
C
$$\frac{1}{2}$$
D
$$2 a^{-\frac{3}{2}}$$
4
COMEDK 2024 Morning Shift
+1
-0

$$\lim _\limits{x \rightarrow 0}\left(\frac{\sin a x}{\sin b x}\right)^k \text { equals }$$

A
$$\left(\frac{b}{a}\right)^k$$
B
$$\left(\frac{a}{b}\right)^k$$
C
$$\frac{a}{b}$$
D
$$\frac{b}{a}$$
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