FCI Assistant Grade III 2013 Evening Shift

If each interior angle of a regular polygon is $$120^\circ,$$ then the number of its sides are

G is the centroid of an equilateral $$\triangle ABC$$ each of whose sides is 12 cm. Then the length of AG is

Two tangents drawn at points A and B of a circle with centre O intersect each other at a point P. If $$\angle AOB = 120^\circ$$ then measure of $$\angle APB$$ is

The side AC of the $$\triangle ABC$$ is produced to D, such that CD = CB. If $$\angle ACB = 70^\circ,$$ then the value of $$\angle ADB$$ is

In a circle of radius 5 cm, $$\overline{AB}$$ and $$\overline{AC}$$ are two equal chords such that $$\overline{AB} = \overline{AC} = 6 cm$$. The length of $$\overline{BC} (in cm) is

If $$\tan \theta = \frac {3}{4} (\theta $$ being positive acute angle), then the value of $$\sin \theta + \cos \theta$$ is

The heights of two towers are 180 m and 60 m respectively. If the angle of elevation of the top of the first tower from the second is $$60^\circ$$, what is the angle of elevation of the top of the second from the foot of the first?

If $$\sec \theta = \cosec \phi$$ and the angle $$\theta$$ and $$\phi$$ be +ve acute angles, then the value of $$\sin(\theta + \phi)$$ is

If $$\frac{\sin\theta + \cos\theta}{\sin\theta - \cos\theta} = 3,$$ then the value of $$\sin^4 \theta - \cos^4 \theta$$ is

If $$\theta$$ be a positive acute angle and $$\cos^4 \theta - sin^4 \theta = \frac {2}{3},$$ then the value of $$1 - 2 sin^2 \theta$$ is