SSC CGL Tier-2-17-February-2018 Maths

If $$3x + 5y + 7z = 49$$ and $$9x + 8y + 21z = 126,$$ then what is the value of y?

Cost of 4 pens, 6 note books and 9 files is Rs 305. Cost of 3 pens, 4 notebooks and 2 files is Rs 145. What is the cost (in Rs) of 5 pens, 8 notebooks and 16 files?

$$ABC$$ is a right angled triangle. $$\angle BAC = 90$$° and $$\angle ACB = 60$$°. What is the ratio of the circum radius of the triangle to the side $$AB?$$

In the given figure, $$ABCD$$ is a square whose side is 4 cm. $$P$$ is a point on the side $$AD$$. What is the minimum value (in cm) of $$BP + CP?$$

Triangle $$ABC$$ is similar to triangle $$PQR$$ and $$AB : PQ = 2 : 3. AD$$ is the median to the side $$BC$$ in triangle $$ABC$$ and $$PS$$ is the median to the side $$QR$$ in triangle $$PQR.$$ What is the value of $$(\frac{BD}{QS})^2$$?

In the given figure, $$B$$ and $$C$$ are the centres of the two circles. $$ADE$$ is the common tangent to the two circles. If the ratio of the radius of both the circles is $$3 : 5$$ and $$AC = 40$$, then what is the value of $$DE$$ 

In the given figure, Ab = 30 cm and CD = 24 cm. What is the value (in cm) of MN?

$$AB$$ and $$AC$$ are the two tangents to a circle whose radius is 6 cm. If $$\angle BAC = 60^\circ$$ then what is the value (in cm) of $$\surd(AB^2 + AC^2)?$$

In the given figure, ABC is a right angled triangle. $$\angle ABC = 90^\circ$$ and $$\angle ACB = 60^\circ$$. If the radius of the smaller circle is 2 cm, then what is the radius (in cm) of the larger circle ?

In the given figure, O is centre of the circle. Circle has 3 tangents. If $$\angle QPR = 45^\circ$$, then what is the value (in degrees) of $$\angle QOR?$$