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Question Bank : Age group 1415 : VI1. Two circles touch each other externally at a point P and a direct common tangent touches the circles at A and B. Prove that (i) the common tangent at P bisects AB and (ii) AB subtends a right angle at P. 5. If , find the matrix X such that 3A + 5B + 2X = 0. 6. The number of ice cream cones bought by men, women, boys, girls, and children on a day at the Trade fair was 40, 42, 46, 48, and 44 respectively. Find the Standard Deviation. 7. A number is selected at random from the first 100 natural numbers. what is the probability that the number is either a multiple of 11 or a multiple of 13? 8. Show that . 9. Find the values of angles and sides not given in the right triangle ABC in which angle C = 90°, angle A = 30° and AB = 8 centimeters. 10. Find the length of a side of a regular polygon inscribed in a circle of radius 1 meter if it has 24 sides. State the answer in centimeters. 11. Find the area of the quadrilateral formed by the points A (3,4), B(1,6), C(3,4), and D(6,1). 12. If the line joining the points (4,6) and (1,3) is perpendicular to the line joining the points (0,4) and (3,a), find a. 13. Show that x + y  2 = 0 is perpendicular bisector of the line joining the origin and (2,2). 14. Find the equation of the line which is concurrent with the lines y=x and y = 2  x and perpendicular to the line y = 4x + 5. Character is who you are when no one is looking. 