1
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\mathrm{P}(x)$$ be a polynomial of degree 2, with $$\mathrm{P}(2)=-1, \mathrm{P}^{\prime}(2)=0, \mathrm{P}^{\prime \prime}(2)=2$$, then $$\mathrm{P}(1.001)$$ is

A
0.002
B
$$-$$0.002
C
0.004
D
$$-$$0.004
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=\sqrt{(x-\sin x)+\sqrt{(x-\sin x)+\sqrt{(x-\sin x) \ldots.}}}$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}=$$

A
$$\frac{1-\cos x}{2 y-1}$$
B
$$\frac{1+\cos x}{2 y-1}$$
C
$$\frac{1-\cos x}{2 y+1}$$
D
$$\frac{1-\sin x}{2 y-1}$$
3
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+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
4
MHT CET 2023 14th May Morning Shift
MCQ (Single Correct Answer)
+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
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