141. Let $$L\sin \theta = 10 + \log \sin \theta .$$ The number of triangles $$ABC$$ such that $$\log b + 10 = \log c + L\sin B$$ is
A
one
B
two
C
infinite
D
None of these
Answer :
one
142. In a $$\Delta \,ABC,$$ if $$\frac{{\cos A}}{a} = \frac{{\cos B}}{b} = \frac{{\cos C}}{c},$$ and the side $$a = 2,$$ then are $$a$$ of the triangle is
A
$$1$$
B
$$2$$
C
$$\frac{{\sqrt 3 }}{2}$$
D
$$\sqrt 3 $$
Answer :
$$\sqrt 3 $$
143. In a $$\vartriangle ABC,A = {90^ \circ }.$$ Then $${\tan^{ - 1}}\frac{b}{{a + c}} + {\tan ^{ - 1}}\frac{c}{{a + b}}$$ is equal to
A
$$\frac{\pi }{4}$$
B
$$\frac{\pi }{2}$$
C
$${\tan ^{ - 1}}\frac{a}{{b + c}}$$
D
None of these
Answer :
$$\frac{\pi }{4}$$
144. The angle of elevation of a stationary cloud from a point $$2500\,m$$ above a lake is $${15^ \circ }$$ and the angle of depression of its reflection in the lake is $${45^ \circ }.$$ The height of cloud above the lake level is
A
$$2500\sqrt 3 \,{\text{metres}}$$
B
$$2500 \,{\text{metres}}$$
C
$$500\sqrt 3 \,{\text{metres}}$$
D
None of these
Answer :
$$2500\sqrt 3 \,{\text{metres}}$$
