1
MHT CET 2021 22th September Morning Shift
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{\cos (m x)-\cos (n x)}{x^2}=$$

A
$$\frac{m^2-n^2}{2}$$
B
$$m^2-n^2$$
C
$$\frac{n^2-m^2}{2}$$
D
$$n^2-m^2$$
2
MHT CET 2021 21th September Evening Shift
+2
-0

\begin{aligned} & \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x<0 \\ & =\frac{2 x+1}{x-2} \quad \text {, if } 0 \leq x \leq 1 \\ \end{aligned}

is continuous in the interval $$[-1,1]$$, then $$p=$$

A
1
B
$$-$$1
C
$$\frac{-1}{2}$$
D
$$\frac{1}{2}$$
3
MHT CET 2021 21th September Evening Shift
+2
-0

If $$\lim _\limits{x \rightarrow 5} \frac{x^k-5^k}{x-5}=500$$, then the value of $$k$$, where $$k \in N$$ is

A
5
B
3
C
4
D
6
4
MHT CET 2021 21th September Morning Shift
+2
-0

\begin{aligned} & \text { If the function } \mathrm{f}(\mathrm{x})=1+\sin \frac{\pi}{2}, \quad-\infty<\mathrm{x} \leq 1 \\ & =\mathrm{ax}+\mathrm{b}, \quad 1<\mathrm{x}<3 \\ & =6 \tan \frac{x \pi}{12}, \quad 3 \leq x<6 \\ \end{aligned}

is continuous in $$(-\infty, 6)$$, then the values of $$\mathrm{a}$$ and $$\mathrm{b}$$ are respectively.

A
1, 1
B
2, 1
C
0, 2
D
2, 0
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