1
MHT CET 2023 14th May Morning Shift
+2
-0

$$\lim _\limits{x \rightarrow \infty} x^3\left\{\sqrt{x^2+\sqrt{1+x^4}}-x \sqrt{2}\right\}=$$

A
$$\frac{1}{\sqrt{2}}$$
B
$$\frac{1}{4 \sqrt{2}}$$
C
$$\frac{-1}{4 \sqrt{2}}$$
D
$$\frac{-1}{\sqrt{2}}$$
2
MHT CET 2023 13th May Evening Shift
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1+x \sin x}-\sqrt{\cos x}}{\tan ^2 \frac{x}{2}}=$$

A
1
B
2
C
3
D
$$-$$1
3
MHT CET 2023 13th May Evening Shift
+2
-0

If $$f(x)$$ is continuous on its domain $$[-2,2]$$, where

$$f(x)=\left\{\begin{array}{cc} \frac{\sin a x}{x}+3 & , \text { for }-2 \leq x<0 \\ 2 x+7 & , \text { for } 0 \leq x \leq 1 \\ \sqrt{x^2+8}-b & , \text { for } 1< x \leq 2 \end{array}\right.$$ $$\text { then the value of } 2 a+3 b \text { is }$$

A
$$-$$12
B
$$-$$10
C
10
D
12
4
MHT CET 2023 13th May Morning Shift
+2
-0

The function $$\mathrm{f}(\mathrm{t})=\frac{1}{\mathrm{t}^2+\mathrm{t}-2}$$ where $$\mathrm{t}=\frac{1}{x-1}$$ is discontinuous at

A
$$-2,1$$
B
$$2, \frac{1}{2}$$
C
$$\frac{1}{2}, 1$$
D
$$2,1$$
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