1
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=a \sin x+b \cos x \quad$ (where $\mathrm{a}$ and $\mathrm{b}$ are constants), then $y^2+\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)^2$ is

A
a function of $x$.
B
a function of $x$ and $y$.
C
a function of $y$.
D
a constant.
2
MHT CET 2024 2nd May Morning Shift
MCQ (Single Correct Answer)
+2
-0

If $y=\sqrt{\frac{1-\sin ^{-1} x}{1+\sin ^{-1} x}}$, then $\left(\frac{d y}{d x}\right)$ at $x=0$ is

A
1
B
2
C
$-$2
D
$-$1
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$x=\sqrt{\mathrm{e}^{\sin ^{-1} t}}$$ and $$y=\sqrt{\mathrm{e}^{\cos ^{-1} t}}$$, then $$\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$$ is

A
$$\frac{-y}{x^2}$$
B
$$\frac{y^2}{2 x^2}$$
C
$$\frac{2 y}{x^2}$$
D
$$\frac{-2 y}{x^2}$$
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}^{\prime}(x)=\sin (\log x)$$ and $$y=\mathrm{f}\left(\frac{2 x+3}{3-2 x}\right)$$, then $$\frac{\mathrm{d} y}{\mathrm{~d} x}$$ at $$x=1$$ is

A
$$6 \sin (\log 5)$$
B
$$5 \sin (\log 6)$$
C
$$12 \sin (\log 5)$$
D
$$5 \sin (\log 12)$$
MHT CET Subjects
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