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

18. Divide 3x2 – x3 – 3x + five by x – one – x2, and verify the division algorithm.
19. Find the sum of all 3 digit numbers every of which leave the remainder three when divided by 5
OR
How many terms of the AP 78,71, 64 …… are needed to provide the sum 468? Also obtain the last term of this AP
20. In the fig AB and CD are 2 parallel tangents touching the circle at Q. Show that ? SOT=900
21. Draw a circle of radius 3.5 cm. Take a point outside the circle. Construct the pair of tangents from this point to the circle without using its centre. Measure the length of tangents.
22. Prove the subsequent identity:
cot? + cosec? - one = one + cos?
cot? – cosec? + one sin ?
OR
Evaluate without using tables

23. Show that the points (0, 1), (2, 3), (6, 7) and (8, 3) are the vertices of a rectangle.
24. Find the co-ordinates of the points of trisection of the line segment joining the points (3, -3) and (6, 9).
25. A square ABCD is inscribed in a circle of radius 10 units .Find the area of the circle, not included in the square (use )






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part D
26. Abdul traveled 300 Km by train and 200 Km by taxi, it took him five hous 30 minutes. But if he travels 260 Km by train and 240 Km by taxi, he takes six minutes longer. obtain the speed of the train and that of the taxi.
OR
Two pipes running together can fill a cistern in two 8/11 minutes. If 1 pipe takes
one minute more than the other to fill the cistern, obtain the time in which every pipe
would fill the cistern.
27. If the radii of the ends of a bucket,45 cm high, are 28 cm and seven cm, obtain the capacity and surface area.
28. The ratio of areas of similar triangles is equal to the ratio of the squares on the corresponding sides. Prove.
Using the above theorem, prove that the area of the equilateral triangle defined on the side of a square is half the area of the equilateral triangle defined on the diagonal.
29.Prove that in a right triangle , the square of the hypotenuse is equal to the sum of the squares of the other 2 sides
Using the above solve the subsequent
L and M are the mid points of AB and BC respectively of , right angled at B prove
that
30.A building is in the form of a cylinder surmounted by a hemispherical vaulted dome ,the building contains 17.7 m3 of air and its internal diameter is equal to the height of the cylindrical part obtain the height of the building (use )

Earning:   Approval pending.