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Question Bank : Age Group 1415 : XII1. Find X and Y if . 2. Show that A^{2}  5A + 7I_{2} = 0 if . 3. Find the variance of the following data: Variable 10 6 18 14 22 2 Frequency 10 7 7 15 6 5 4. The probability that a student passes English test is , the probability that he passes both English and French tests is ; the probability that he passes atleast one test is . What is the probability that he passes the French test? 5. Determine 'a' so that the points (a,a), (2,3), and (4,1) are collinear. 6. The vertices of a triangle ABC are A(1,2), B(4,5), and C(0,1). Find the slope of the altitudes. 7. Find the length of the segment joining the point (3,4) and the point of intersectionof the lines 5x+y6 = 0 and 2xy3 = 0. 8. In triangle ABC, the equation of AB is x2y+8 = 0, that of BC is x3y+10 = 0 and the equation of AC is xy+2 = 0. Find the centroid. 9. Show that . 10. Find the length of a side of a regualr polygon in centimeters inscribed in a circle of radius 1 meter if it has 24 sides. Character is who you are when no one is looking. 