# Special Quant Quiz (Advance math) SSC CGL Tier-II 2016

Q1. A quadrilateral ABCD circumscribes a circle and AB = 6 cm, CD = 5 cm and AD = 7 cm. The length of side BC is
(a) 4 cm
(b) 5 cm
(c) 3 cm
(d) 6 cm

Q2. Two chords AB and CD of circle whose centre is O, meet at the point P and ∠AOC = 50°, ∠BOD = 40°. Then the value of ∠BPD is:
(a) 60°
(b) 40°
(c) 45°
(d) 75°

Q3. If the length of a chord of a circle, which makes an angle 45°, with the tangent drawn at one end point of the chord, is 6 cm, then the radius of the circle is:
(a) 6√2 cm
(b) 5 cm
(c) 3√2 cm
(d) 6 cm

Q4. In a circle of radius 17 cm two parallel chords are present on the opposite side of the diameter. If the distance between them is 23 cm and the length of one chord is 16 cm then the length of other chord is:
(a) 15 cm
(b) 20 cm
(c) 18 cm
(d) 30 cm

Q5.The radius of a circle is 6 cm. An external point is at a distance of 10 cm from the centre. Then the length of the tangent drawn to the circle from the external point upto the point of contact is:
(a) 8 cm
(b) 10 cm
(c) 6 cm
(d) 12 cm

Q6. The number of common tangents that can be drawn to two given circles intersect each other is:
(a) One
(b) Two
(c) Three
(d) Four

Q7. P and Q are centre of two circles with radii 9 cm and 2 cm respectively, where PQ = 17 cm. R is the centre of another circle of radius x cm, which touches each of the above two circles externally. If ∠PRQ = 90°, then the value of x is
(a) 4 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm

Q8. The radii of two concentric circles are 17 cm and 25 cm. a straight line PQRS intersects the larger circle at the points P and S and intersects the smaller circle at the points Q and R. If QR = 16 cm, then the length (in cm.) of PS is
(a) 41
(b) 33
(c) 32
(d)40

Q9. The radius of a circle is 8 cm. The distance of a point lying outside the circle from the centre is 17 cm. The length of the tangent drawn from the outside point to the circle is
(a) 15 cm
(b) 16 cm
(c)1 7 cm
(d) 18 cm

Q10. In a circle, AB is the diameter of the circle, and CD is a chord such that CD ∥ AB. P is any point on the circle such that ∠BPC = 48°, then ∠BCD = ?
(a) 48°
(b) 42°
(c) 24°
(d) 96°

Q11. Find the value of ‘A’ if the distance between the points (8, A) and (4, 3) is 5.
(a) 6
(b) 0
(c) Both (a) and (b)
(d) Not

Q12. Find the area of triangle of lines x/6+y/7=1,-x/4+y/7=1 and x – axis.
(a) 30 sq. units
(b) 35 sq. units
(c) 70 sq. units
(d) 60 sq. units

Q13. The co-ordinates of a point below x-axis at a distance of 8 units from x-axis but lying on y-axis is:
(a) (0, 8)
(b) (−8, 0)
(c) (0, −8)
(d) (8, −8)
S13. Ans.(c)
Sol. Clearly, the point is (0, −8).

Q14. If a straight line ax + by = c meets x-axis at P and y-axis at Q. Then area of the triangle OPQ where O is the point of intersection of co-ordinate axes is:

Q15. The value of ‘a’ so that the lines x + 3y – 8 = 0 and ax + 12y + 5 = 0 are parallel is:
(a) 0
(b) 1
(c) 4
(d) −4
S15. Ans.(c)
Sol. Condition of parallelism
a_1/a_2 =b_1/b_2
∴ 1/a=3/12 ⇒ a = 4

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