FCI Assistant Grade III 2012 Paper-I

If $$\frac{2p}{p^{2}-2p+1}$$=$$\frac{1}{4}$$, $$p \neq 0$$ then the value of $$p+\frac{1}{p}$$ is

The ortho centre of a right angied triangle lies

The angles of a triangle are $$(x + 5)^\circ , (2x - 3)^\circ$$ and $$(3x + 4)^\circ$$ The value of x is

Two line segments PQ and RS intersect at X in such a way thal AP = XR. if $$\angle PSX= \angle RGX$$. then one must have

ADis trie median of a triangle ABC and O is the centroid such that AO = 10 cm. The length of OD in cm is

The external bisector of $$\angle B$$ and $$\angle C$$ of $$\angle ABC$$ (where AB and AC extended to E and F respectively) meet at point P. If $$\angle BAC = 100^\circ$$, then the measure of $$\angle BPC$$ is

If $$\tan (26 + 45^\circ) = \cot 3 \theta$$ where $$(2\theta + 45^\circ)$$ and $$3 \theta$$ are acute angles, then the value of $$\theta$$ is

One flies a kite with a thread 150 metre long. [f the thread of the kite makes an angle of $$60^\circ$$ with the horizontal line, then the height of the kite from the ground (assuming the thread to be in a straight line) is

If $$\theta$$ be acute angle and $$\cos \theta = \frac{15}{17}$$, then the value of $$\cot (90^\circ - \theta)$$ is

If $$\sec^{2} \theta + \tan^{2} \theta = \frac{7}{12}$$ then $$\sec^{2} \theta - \tan^{2} \theta =$$