SSC CGL Tier-2 12-January-2017 Maths

$$\triangle ABC$$ is an isosceles right angled triangle having $$\angle C = 90^\circ$$. If D is any point on AB, then $$AD^2 + BD^2$$ is equal to

D and E are points on the sides AB and AC respectively of $$\triangle ABC$$ such that DE is parallel to BC and AD : DB = 4 : 5, CD and BE intersect each other at F. Then the ratio of the areas of $$\triangle DEF$$ and $$\triangle CBF$$

Diagonals of a Trapezium ABCD with AB $$\parallel$$ CD intersect each other at the point O. If AB = 2CD, then the ratio of the areas of $$\triangle AOB$$ and $$\triangle COD$$ is

If O is the orthocentre of a triangle ABC and $$\angle BOC = 100^\circ$$, the measure of $$\angle BAC$$ is

PQ and RS are common tangents to two circles intersecting at A and B. AB, when produced both sides, meet the tangents PQ and RS at X and Y,respectively. If AB = 3 cm, XY = 5 cm, then PQ (in cm) will be

If $$\sec A + \tan A = a$$, then the value of $$\cos A$$ is

If $$\sin P + \cosec P = 2$$, then the value of $$\sin^7 P + \cosec^7 P$$ is

If $$\cos x . \cos y + \sin x . \sin y = -1$$ then $$\cos x + \cos y$$ is

The value of the expression $$2(\sin^6 \theta + \cos^6 \theta) -3 (\sin^4 \theta + \cos^4 \theta)+1$$ is

If $$\cos \theta = \frac{x^2 - y^2}{x^2 + y^2}$$ then the value of $$\cot \theta$$ is equal to [If $$0 \leq \theta \leq 90^\circ$$]