SSC CGL Tier-2 18-February-2018 Maths

If $$x ­- 4y = 0$$ and $$x + 2y = 24$$, then what is the value of $$\frac{(2x + 3y)}{(2x - 3y)}$$?

If $$(\frac{x}{a}) + (\frac{y}{b}) = 3$$ and $$(\frac{x}{b}) - (\frac{y}{a}) = 9$$, then what is the value of $$\frac{x}{y}$$?

In the given figure, $$OX, OY$$ and $$OZ$$ are perpendicular bisectors of the three sides of the triangle. If $$\angle QPR = 65^\circ$$ and $$\angle PQR = 60^\circ$$, then what is the value (in degrees) of $$\angle QOR + \angle POR$$? 

In a triangle $$PQR$$, $$\angle PQR = 90$$°, $$PQ$$ = 10 cm and $$PR$$ = 26 cm, then what is the value (in cm) of inradius of incircle?

In the given figure, if $$\frac{QR}{XY} = \frac{14}{9}$$ and $$PY = 18$$ cm, then what is the value (in cm) of $$PQ$$ ? 

In a triangle $$PQR, PX, QY$$ and $$RZ$$ be altitudes intersecting at $$O$$. If $$PO$$ = 6 cm, $$PX$$ = 8 cm and $$QO$$ = 4 cm, then what is the value (in cm) of $$QY$$?

A line cuts two concentric circles. The lengths of chords formed by that line on the two circles are 4 cm and 16 cm. What is the difference (in $$cm^2$$) in squares of radii of two circles?

In the given figure, a circle touches the sides of the quadrilateral $$PQRS$$. The radius of the circle is 9 cm. $$\angle RSP = \angle SRQ = 60^\circ$$ and $$\angle PQR = \angle QPS = 120^\circ$$. What is the perimeter (in cm) of the quadrilateral ?

In the given figure, from the point $$P$$ two tangents $$PA$$ and $$PB$$ are drawn to a circle with centre $$O$$ and radius 5 cm. From the point $$O, OC$$ and $$OD$$ are drawn parallel to $$PA$$ and $$PB$$ respectively. If the length of the chord $$AB$$ is 5 cm. then what is the value (in degrees) of $$\angle COD$$?

In the given figure, $$AB$$ is a diameter of the circle with centre $$O$$ and $$XY$$ is the tangent at a point $$C$$. If $$\angle ACX = 35^\circ$$. then what is the value (in degrees) of $$\angle CAB$$?