1
MHT CET 2023 11th May Evening Shift
+2
-0

In triangle $$\mathrm{ABC}$$ with usual notations $$\mathrm{b}=\sqrt{3}, \mathrm{c}=1, \mathrm{~m} \angle \mathrm{A}=30^{\circ}$$, then the largest angle of the triangle is

A
$$135^{\circ}$$
B
$$90^{\circ}$$
C
$$60^{\circ}$$
D
$$120^{\circ}$$
2
MHT CET 2023 11th May Evening Shift
+2
-0

If the angles of a triangle are in the ratio $$4: 1: 1$$, then the ratio of the longest side to its perimeter is

A
$$\sqrt{3}:(2+\sqrt{3})$$
B
$$2:(1+\sqrt{3})$$
C
$$1:(2+\sqrt{3})$$
D
$$2: 3$$
3
MHT CET 2023 11th May Morning Shift
+2
-0

If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$$, then

A
a, b, c are in G.P.
B
a, b, c are in H.P.
C
a, b, c are in A.P.
D
a, b, c are in Arithmetico Geometric Progression
4
MHT CET 2023 11th May Morning Shift
+2
-0

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6$$ and $$\mathrm{B}=\sin ^{-1} x$$, then $$x$$ has the value

A
$$\frac{\sqrt{3}}{2}$$
B
$$\frac{2}{\sqrt{3}}$$
C
$$2 \sqrt{3}$$
D
$$\frac{1}{2 \sqrt{3}}$$
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