Quant Boosters  Kamal Lohia  Set 7

Q20) Three circles are in a row touching each other such that all three of them have two common tangents. The radii of the largest and the smallest circle are 9 and 4 respectively. Line segment AB passes through the centres of the circles and lies on the two outer circles. What is the length of AB?
(a) 38
(b) 26 + 3rt(32)
(c) 26 + 2rt(38)
(d) 19

Q21) A regular hexagon with a perimeter of 12rt(2) units lies in the Cartesian plane in such a way that its center is on the origin, two of the vertices lie on the xaxis, and the midpoints of two of its sides lie on the yaxis. If the portion of the hexagon that lies in Quadrant I is completely revolved around the xaxis, a solid whose volume is X cubic units results. If the same portion is completely revolved around the yaxis, a solid with a volume of Y cubic units results. Evaluate (X/Y)² .
(a) 48/49
(b) 1
(c) 4/3
(d) 16/9

Q22) One angle of a regular polygon measures 179˚. How many sides does it have?
(a) 179
(b) 180
(c) 280
(d) 360

Q23) In two equilateral triangles ABC and BMN, ∠ABM = 120˚. AN & CM intersects at O. Find ∠MON.
(a) 120˚
(b) 90˚
(c) 60˚
(d) 30˚

Q24) In a parallelogram ABCD, let M be the midpoint of the side AB and N the midpoint of BC. Let P be the intersection point of the lines MC and ND. Find the ratio of area of ▲s APB : BPC : CPD : DPA.
(a) 3:1:2:4
(b) 3:2:1:4
(c) 2:1:3:4
(d) 1:2:3:4

Q25) In a quadrilateral ABCD, sides AD and BC are parallel but not equal and sides AB = DC = x. The area of the quadrilateral is 676 cm². A circle with centre O and radius 13 cm is inscribed in the quadrilateral such that it is tangent to each of the four sides of the quadrilateral. Determine the length of x.
(a) 13
(b) 24
(c) 26
(d) 12

Q26) C and D are two points on a semicircle with AB as diameter such that AC – BC = 7 and AD – BD = 13. AD and BC intersect at P. Find the difference in area of triangles ACP and BDP.
(a) 24
(b) 26
(c) 28
(d) 30

Q27) Points A, D and C lie on the circumference of a circle. The tangents to the circle at points A and C meet at the point B. If ∠DAC = 83˚ and ∠DCA = 54˚. Find ∠ABC.
(a) 88˚
(b) 94˚
(c) 100˚
(d) 104˚

Q28) The sum of all interior angles of eight polygons is 3240˚. What is the total number of sides of polygons?
(a) 16
(b) 18
(c) 32
(d) 34

Q29) Circles with centers P and Q have radii 20 and 15 cm respectively and intersect at two points A, B such that ∠PAQ = 90°. What is the difference in the area of two shaded regions?
(a) 175 Pi
(b) 150 Pi
(c) 125 Pi
(d) 90 Pi

Q30) Given f(x) = x  1/x, solve the equation f(f(x)) = x.