1
MHT CET 2021 24th September Evening Shift
+2
-0

In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 2 \mathrm{~B}}{\mathrm{~b}^2}$$ is

A
$$\frac{5}{36}$$
B
$$\frac{1}{4}$$
C
$$\frac{1}{9}$$
D
$$\frac{13}{36}$$
2
MHT CET 2021 24th September Morning Shift
+2
-0

In any $$\triangle A B C$$, with usual notations, $$c(a \cos B-b \cos A)=$$

A
$$a^2-b^2$$
B
$$\frac{1}{a^2}-\frac{1}{b^2}$$
C
$$a^2+b^2$$
D
$$\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}$$
3
MHT CET 2021 24th September Morning Shift
+2
-0

If in a $$\triangle A B C$$, with usual notations, $$\mathrm{a}^2, \mathrm{~b}^2, \mathrm{c}^2$$ are in A.P. then $$\frac{\sin 3 B}{\sin B}=$$

A
$$\frac{a^2-c^2}{2 a c}$$
B
$$\left(\frac{a^2-c^2}{2 a c}\right)^2$$
C
$$\frac{\mathrm{a}^2-\mathrm{c}^2}{\mathrm{ac}}$$
D
$$\left(\frac{a^2-c^2}{a c}\right)^2$$
4
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
$$2,3,-5$$
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