1
MHT CET 2021 23rd September Evening Shift
+2
-0

If $$\mathrm{G}(\overline{\mathrm{g}}), \mathrm{H}(\overline{\mathrm{h}})$$ and $$\mathrm{P}(\overline{\mathrm{p}})$$ are respectively centroid, orthocenter and circumcentre of a triangle and $$\mathrm{x} \overline{\mathrm{p}}+\mathrm{y} \overline{\mathrm{h}}+z \overline{\mathrm{g}}=\overline{0}$$, then $$\mathrm{x}, \mathrm{y}, \mathrm{z}$$ are respectively.

A
$$1,1,-2$$
B
$$1,3,-4$$
C
$$2,1,-3$$
D
$$2,3,-5$$
2
MHT CET 2021 23rd September Evening Shift
+2
-0

With usual notations in $$\triangle$$ABC, if $$\frac{\sin A}{\sin C}=\frac{\sin (A-B)}{\sin (B-C)}$$, then $$a^2, b^2, c^2$$ are in

A
Not in AP
B
HP
C
AP
D
GP
3
MHT CET 2021 23rd September Evening Shift
+2
-0

The area of the triangle $$\mathrm{ABC}$$ is $$10 \sqrt{3} \mathrm{~cm}^2$$, angle $$\mathrm{B}$$ is $$60^{\circ}$$ and its perimeter is $$20 \mathrm{~cm}$$, then $$\ell(\mathrm{AC})=$$

A
10 cm
B
8 cm
C
5 cm
D
7 cm
4
MHT CET 2021 23th September Morning Shift
+2
-0

In a triangle $$\mathrm{ABC}$$, with usual notations $$\mathrm{a}=2, \mathrm{~b}=3, \mathrm{c}=5$$, then $$\frac{\cos \mathrm{A}}{\mathrm{a}}+\frac{\cos \mathrm{B}}{\mathrm{b}}+\frac{\cos \mathrm{C}}{\mathrm{c}}=$$

A
$$\frac{19}{30}$$
B
$$\frac{19}{60}$$
C
$$\frac{23}{60}$$
D
$$\frac{38}{35}$$
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