In a triangle $$ABC$$, $$\angle B = {\pi \over 3}$$ and $$\angle C = {\pi \over 4}$$. Let $$D$$ divide $$BC$$ internally in the ratio $$1:3$$ then $${{\sin \angle BAD} \over {\sin \angle CAD}}$$ is equal to
A
$${1 \over {\sqrt 6 }}$$
B
$${1 \over 3}$$
C
$${1 \over {\sqrt 3 }}$$
D
$$\sqrt {{2 \over 3}} $$
2
IIT-JEE 1994
MCQ (Single Correct Answer)
If the lengths of the sides of triangle are $$3, 5, 7$$ then the largest angle of the triangle is
A
$${\pi \over 2}$$
B
$${5\pi \over 6}$$
C
$${2\pi \over 3}$$
D
$${3\pi \over 4}$$
3
IIT-JEE 1990
MCQ (Single Correct Answer)
In a triangle $$ABC$$, angle $$A$$ is greater than angle $$B$$. If the measures of angles $$A$$ and $$B$$ satify the equation $$3{\mathop{\rm sinx}\nolimits} - 4si{n^3}x - k = 0,$$ $$0 < k < 1$$, then the measure of angle $$C$$ is
A
$${\pi \over 3}$$
B
$${\pi \over 2}$$
C
$${2\pi \over 3}$$
D
$${5\pi \over 6}$$
4
IIT-JEE 1983
MCQ (Single Correct Answer)
From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^ \circ }$$. The distance of the boat from the foot of the light house is
