1
MHT CET 2023 14th May Morning Shift
+2
-0

In $$\triangle \mathrm{ABC}$$, with usual notations, $$2 \mathrm{ac} \sin \left(\frac{1}{2}(\mathrm{~A}-\mathrm{B}+\mathrm{C})\right)$$ is equal to

A
$$\mathrm{a^2+b^2-c^2}$$
B
$$\mathrm{c}^2+\mathrm{a}^2-\mathrm{b}^2$$
C
$$\mathrm{b}^2-\mathrm{c}^2-\mathrm{a}^2$$
D
$$\mathrm{c}^2-\mathrm{a}^2-\mathrm{b}^2$$
2
MHT CET 2023 14th May Morning Shift
+2
-0

If the angles $$\mathrm{A}, \mathrm{B}$$, and $$\mathrm{C}$$ of a triangle are in an Arithmetic Progression and if $$\mathrm{a}, \mathrm{b}$$ and $$\mathrm{c}$$ denote the lengths of the sides opposite to A, B and C respectively, then the value of the expression $$\frac{\mathrm{a}}{\mathrm{c}} \sin 2 \mathrm{C}+\frac{\mathrm{c}}{\mathrm{a}} \sin 2 \mathrm{~A}$$ is

A
$$\frac{1}{2}$$
B
$$\frac{\sqrt{3}}{2}$$
C
1
D
$$\sqrt{3}$$
3
MHT CET 2023 13th May Evening Shift
+2
-0

In $$\triangle A B C$$, with usual notations, if $$\frac{b+c}{11}=\frac{c+a}{12}=\frac{a+b}{13}$$, then the value of $$\cos A+\cos B+\cos C$$ is

A
$$17 / 35$$
B
$$51 / 35$$
C
$$5 / 7$$
D
$$19 / 35$$
4
MHT CET 2023 13th May Morning Shift
+2
-0

The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one, then the sides of the triangle (in units) are

A
3, 4, 5
B
4, 5, 6
C
5, 6, 7
D
2, 3, 4
EXAM MAP
Medical
NEET