FCI Assistant Grade III 2012

If P and Q are the middle points of the sides AB and AC respectively of a triangle ABC,X is any point on BC and AX meets PQ at O, then the length AO is equal to

ABCD is a parallelogram with AB = 10cm, AD = 6 cm. The bisector of $$\angle A$$ meets DC in E, and is extended to meet BC produced at F. CF is

The radius of a circle is 13 cm and AB is a chord whichis at a distance of 12 cm from the centre. Then the length of the chord is

Radius of the in circle of an equilateral $$\triangle$$ ABC of sides $$\sqrt{3}$$ units is

Radii of two circles are 7 cm and 137, 3 cm. If one of these lies wholly inside the other, then the distance between their centresis

The sum of two angles is $$135^\circ $$ and their diffrence is $$\frac{\pi}{2}$$ the value of greater angle in radian is

A guard observes an enemy boat, from an observation tower at a height of 186 metre above sea level, to be at an angle of depression of $$60^\circ$$.The diastance of boat from the foot of observation is

If tan 22 $$\frac{1}{2}^\circ$$ =x,then the value of cos 67 $$\frac{1}{2}^\circ$$ is

If cos x = sin y and $$cot (x — 40^\circ)$$ = tan $$(50^\circ —y)$$, then the values of x and y are

If $$f(x) = \cos^{2}x + \sec^{2}x$$, then the minimum value of f(x) is