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

The centre of the circle whose radius is 3 units and touching internally the circle $$x^2+y^2-4 x-6 y-12=0$$ at the point $$(-1,-1)$$ is

A
$$\left(\frac{4}{5}, \frac{7}{5}\right)$$
B
$$\left(\frac{4}{5}, \frac{-7}{5}\right)$$
C
$$\left(\frac{-4}{5}, \frac{-7}{5}\right)$$
D
$$\left(\frac{-4}{5}, \frac{7}{5}\right)$$
2
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

A fair die with numbers 1 to 6 on their faces is thrown. Let $$\mathrm{X}$$ denote the number of factors of the number, on the uppermost face, then the probability distribution of $$\mathrm{X}$$ is

A
$$\mathrm{X=}x$$ 1 2 3 4
$$\mathrm{P(x=}x)$$ $$\frac{1}{6}$$ $$\frac{1}{2}$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$
B
$$\mathrm{X=}x$$ 1 2 3 4
$$\mathrm{P(x=}x)$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$ $$\frac{1}{2}$$
C
$$\mathrm{X=}x$$ 1 2 3 4
$$\mathrm{P(x=}x)$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$
D
$$\mathrm{X=}x$$ 1 2 3 4
$$\mathrm{P(x=}x)$$ $$\frac{1}{6}$$ $$\frac{1}{6}$$ $$\frac{1}{2}$$ $$\frac{1}{6}$$
3
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

Let $$\overline{\mathrm{u}}, \overline{\mathrm{v}}$$ and $$\overline{\mathrm{w}}$$ be the vectors such that $$|\overline{\mathrm{u}}|=1; |\bar{v}|=2 ;|\bar{w}|=3$$. If the projection of $$\bar{v}$$ along $$\bar{u}$$ is equal to that of $$\overline{\mathrm{w}}$$ along $$\overline{\mathrm{u}}$$ and $$\overline{\mathrm{v}}, \overline{\mathrm{w}}$$ are perpendicular to each other, then $$|\bar{u}-\bar{v}+\bar{w}|$$ is equal to

A
2
B
$$\sqrt{7}$$
C
$$\sqrt{14}$$
D
14
4
MHT CET 2023 14th May Evening Shift
MCQ (Single Correct Answer)
+2
-0

If $$y=4 x-5$$ is a tangent to the curve $$y^2=\mathrm{p} x^3+\mathrm{q}$$ at $$(2,3)$$, then $$\mathrm{p}-\mathrm{q}$$ is

A
$$-$$5
B
5
C
9
D
$$-$$9
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