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

Let $$f: R \rightarrow R$$ be a function such that $$\mathrm{f}(x)=x^3+x^2 \mathrm{f}^{\prime}(1)+x \mathrm{f}^{\prime \prime}(2)+6, x \in \mathrm{R}$$, then $$\mathrm{f}(2)$$ equals

A
30
B
$$-$$4
C
$$-$$2
D
8
2
MHT CET 2023 14th May Morning Shift
+2
-0

$$\text { If } y=\left(\sin ^{-1} x\right)^2+\left(\cos ^{-1} x\right)^2, \text { then }\left(1-x^2\right) y_2-x y_1=$$

A
1
B
4
C
$$-$$4
D
$$-$$1
3
MHT CET 2023 14th May Morning Shift
+2
-0

If $$y=[(x+1)(2 x+1)(3 x+1) \ldots \ldots(\mathrm{n} x+1)]^n$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=0$$ is

A
$$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$$
B
$$\frac{\mathrm{n}^2(\mathrm{n}+1)}{2}$$
C
$$\frac{\mathrm{n}(\mathrm{n}+1)}{4}$$
D
$$\frac{\mathrm{n}^2(\mathrm{n}-1)}{2}$$
4
MHT CET 2023 14th May Morning Shift
+2
-0

The money invested in a company is compounded continuously. If ₹ 200 invested today becomes ₹ 400 in 6 years, then at the end of 33 years it will become ₹

A
$$1600 \sqrt{2}$$
B
$$3200 \sqrt{2}$$
C
$$12800 \sqrt{2}$$
D
$$6400 \sqrt{2}$$
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