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?
(b) 26 + 3rt(32)
(c) 26 + 2rt(38)
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 x-axis, and the midpoints of two of its sides lie on the y-axis. If the portion of the hexagon that lies in Quadrant I is completely revolved around the x-axis, a solid whose volume is X cubic units results. If the same portion is completely revolved around the y-axis, a solid with a volume of Y cubic units results. Evaluate (X/Y)² .
Q22) One angle of a regular polygon measures 179˚. How many sides does it have?
Q23) In two equilateral triangles ABC and BMN, ∠ABM = 120˚. AN & CM intersects at O. Find ∠MON.
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.
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.
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.
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.
Q28) The sum of all interior angles of eight polygons is 3240˚. What is the total number of sides of polygons?
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
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Q30) Given f(x) = x - 1/x, solve the equation f(f(x)) = x.