Institute of Chartered Financial Analysts of India (ICFAI) University 2003 B.Sc Mathematics semestar - Question Paper
Monday, 17 June 2013 10:20Web
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9. If ‘a’ is the length of 1 of the sides of an equilateral triangle ABC base BC lies on x-axis and vertex B is at the origin, obtain the coordinates of the vertices of the triangle ABC.
10. The coordinates of the mid-point of the line joining the points (2p+1, 4) and (5, q – 1) are (2p, q). obtain the value of p and q.
11. Find the value of K for which the points with coordinates (3, 2), (4, K) and (5, 3) are collinear.
12. A is a point on the y-axis whose ordinate is five and B is the point (-3, 1). compute the length of AB.
13. The distance ranging from A (1, 3) and B(x, 7) is 5. obtain the possible values of x
14. Show that the points (3, 3), (9, 0) and (12, 21) are the vertices of a right angled triangle.
15. The center of a circle is (1, -2) and 1 end of a diameter is (-3, 2), obtain the co-ordinates of the other end.
16. Find the area of the quadrilateral whose vertices , taken in order are (-6,-2), (-3,-5) ,(4,-2) and (2,4)
17. Find area of the square whose points are A(5,6) B( 1,5) C(2,1) D( 6,2).
18. Determine the ratio in which the points P (m, 6) divides the join of A (-4, 3) and B (2, 8). Also obtain the value of m.
19. Find the value of p for which the points (-1, 3), (2, p) and (5,-1) are collinear.
20. Calculate the ratio in which the line joining A (6, 5) and B (4,-3) is divided by the line y=2. Also obtain the point of division.
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21. If the 2 opposite sides of the square are (5, 4) and (-1, 6). obtain the other two.
22. If the points (x,y) is equidistant from the points (2,1) and (1,-2). Show that x+3y=0.
23. Show that the points (1, 1), (-1,-1) and ( form an isosceles triangle.
24. Find the coordinates of 3rd side of the triangle if its 2 vertices are (-1, 4) and (5, 2) and mid point of 1 side is (0, 3).
25. Find area of triangle formed by (5, 6), (8, 9) and (2, 1).
26. Show that the points (0, -1), (-2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.
27. The points A (0, 3), B (-2, a) and C (-1, 4) are the vertices of a right angled triangle at A, obtain the value of a.
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