MHT CET 2024 11th May Evening Shift | MHT CET Year Wise Previous Years Questions

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

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The parametric equations of the circle $x^2+y^2-\mathrm{a} x-b y=0$ are

$x=\frac{\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{2} \cos \theta, y=\frac{\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{2} \sin \theta$

$x=\frac{-\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \sin \theta, y=\frac{-\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \cos \theta$

$x=\frac{\mathrm{a}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{2}} \sin \theta, y=\frac{\mathrm{b}}{2}+\sqrt{\frac{\mathrm{a}^2+\mathrm{b}^2}{2}} \cos \theta$

$x=\frac{\mathrm{a}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \cos \theta, y=\frac{\mathrm{b}}{2}+\frac{\sqrt{\mathrm{a}^2+\mathrm{b}^2}}{4} \sin \theta$

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

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The curve $y=a x^3+b x^2+c x+5$ touches the X - axis at $(-2,0)$ and cuts the Y -axis at a point Q where its gradient is 3 , then values of $a, b, c$ respectively, are

$3,-\frac{1}{2},-\frac{3}{4}$

$-\frac{3}{4},-\frac{1}{2}, 3$

$-\frac{1}{2},-\frac{3}{4}, 3$

$-\frac{1}{2}, 3,-\frac{3}{4}$

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

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A variable plane passes through the fixed point $(3,2,1)$ and meets $X, Y$ and $Z$ axes at points $A$, B and C respectively. A plane is drawn parallel to YZ - plane through A , a second plane is drawn parallel to ZX -plan through B , a third plane is drawn parallel to XY - plane through C . Then locus of the point of intersection of these three planes, is

$\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=\frac{11}{6}$

$\frac{x}{3}+\frac{y}{2}+\frac{z}{1}=1$

$\frac{3}{x}+\frac{2}{y}+\frac{1}{z}=1$

$x+y+z=6$

MHT CET 2024 11th May Evening Shift

MCQ (Single Correct Answer)

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The value of $\sin \left(\cos ^{-1}\left(-\frac{1}{3}\right)-\sin ^{-1}\left(\frac{1}{3}\right)\right)$ is