Institute of Chartered Financial Analysts of India (ICFAI) University 2003 B.Sc Mathematics semestar - Question Paper

18. obtain the vertices of the triangle, the mid-points of whose sides are (3,1), (5,6) and (-3,2).
19. Mizna is walking along the path joining (-2,3) and (2,-2) while Fathima is walking along the path joining (0,5) and (4,0). Represent and explain this situation graphically.OR
A 90% acid solution is mixed with a 97% acid solution to find 21 litres of a 95 % solution. obtain the volume of every of the solution to get the resulting mixture.
20. If seven Sin2? + three Cos2?=4, obtain the value of Sec? + Cosec?.
21. obtain the lengths of the medians of the triangle whose vertices are (1,-1), (0,4) and (-5,3).
22. The vertices of a ?ABC are (3,0), B(0,6) and C (6,9) and DE divides AB and AC in the identical ratio 1:2. Prove that area of ?ABC = 9(area of ?ADE).
23. In fig. ABC, points P and Q lies on AB and AC respectively. If PQ || BC, Prove that the median AD bisect PQ.

24. 2 circles with radii a and b (a > b) touch every other externally. obtain the length of the common angent AB.
25. The area of an equilateral triangle is 17300 cm2. With every vertex of the triangle as centre, a circle is drawn with a radius equal to half the length of the side of the triangle. obtain the area of the triangle not included in the circles. ( p = 3.14 and v3 =1.73 ) OR
A solid composed of a cylinder with hemi spherical ends . The whole height of the solid is 19cm and the radius of the cylinder is 3.5cm. obtain the weight of the solid if 1cm3 of the metal weighs 4.5g.
SECTION- D
26. In Birla auditorium the number of rows was equal to the number of seats in every row. When the number of rows was doubled and the number of seats in every row was decreased by 10, the total no. of seats increased by 300. How many rows were there?
27 2 pillars of equal height stand on either side of a roadway which is180 m wide From a point on the roadway ranging from the pillars, the angles of elevations of the top of the pillars are 60° and 30°. obtain the height of the pillars and the position of the point.
28. BL and CM are the medians of ? ABC, right angled at A.
Prove that 4(BL2 + CM2) = five BC2 OR
State and prove the converse of Pythagoras theorem. Using it prove that triangle PQR is right angled if QS2 =PS×SR and QS?PR.
29. Water is flowing at the rate of 15 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 50 m long and 44 m wide. obtain the time in which the level will rise by 21cm. OR

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