FCI Assistant Grade III 2012 Paper-I Second Sitting

The area of an equilateral triangle is $$4\sqrt{3}$$ sq.cm .Its perimeter is

I is the incentre of $$\triangle$$ ABC.If $$\angle ABC=60^\circ$$,$$\angle BCA=80^\circ$$, then the $$\angle BIC$$ is

If two equal circles whose centres are O and O’, intersect each other at the points A and B, OO’ = 12 cm and AB = 16 cm, then the radius of the circles is

In $$\triangle$$ ABC, draw BE AC and CF AB and the perpendicular BE and CF intersect at the point O. If $$\angle BAC=70^\circ$$, then the value of $$\angle BOC $$is

Two circles of radii 9 cm and 2 cm respectively have centres X and Y and XY = 17 cm. Circle of radius r cm, with centre Z touches two given circles externally. If $$\angle XZY=90^\circ$$, find r

Three interior angles of a quadrilateral are $$60^\circ$$, $$120^\circ$$, $$90^\circ$$. The remaining angle in circular measure is given by

A man 6 ft tall casts a shadow 4 ft long at the same time when a flag pole casts a shadow 50 ft long. The height of the flag pole is

If 2 $$(cos^{2} \theta - sin^{2} \theta )$$ = 1, $$\theta$$ is a positive acute angle, then the value of $$\theta$$ is

The value of $$(2 \cos^2 \theta - 1)$$

If $$\angle A and \angle B$$ are complementary to each other, then the value of $$sec^{2}A + sec^{2}B - sec^{2}A sec^{2}B$$ is