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

The centroid of the triangle formed by the lines $$x+3 y=10$$ and $$6 x^2+x y-y^2=0$$ is

A
$$\left(\frac{1}{3}, \frac{-7}{3}\right)$$
B
$$\left(\frac{-1}{3}, \frac{-7}{3}\right)$$
C
$$\left(\frac{-1}{3}, \frac{7}{3}\right)$$
D
$$\left(\frac{1}{3}, \frac{7}{3}\right)$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

The statement $$[\mathrm{p} \wedge(\mathrm{q} \vee \mathrm{r})] \vee[\sim \mathrm{r} \wedge \sim \mathrm{q} \wedge \mathrm{p}]$$ is equivalent to

A
$$\sim \mathrm{r}$$
B
$$\mathrm{p}$$
C
$$\sim \mathrm{q}$$
D
$$\mathrm{q}$$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$\mathrm{f}(x)=\frac{2 x-3}{3 x-4}, x \neq \frac{4}{3}$$, then the value of $$\mathrm{f}^{-1}(x)$$ is

A
$$\frac{4 x-3}{3 x-2}$$
B
$$\frac{3 x-2}{4 x+3}$$
C
$$\frac{3 x-4}{4 x-2}$$
D
$$\frac{2 x+3}{4 x-3}$$
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
$$5 \sin (\log 12)$$
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