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

40 units of calories, 1 unit of B contains 100 units of vitamin, two units of minerals and
40 units of calories, obtain what combination of foods should be used to have the lowest cost?





S AMPLE PAPERS – 2008

part A
1. State the Euclid’s Division Lemma.
2. Find the condition that if the linear equations and have unique solution.
3. For the polynomial , what is the sum of zeros?
4. How many terms of the AP will provide the sum zero
5. If the mean of n observations is then obtain
6. One letter is opted at random from the word ‘UNNECESSARY’. obtain the probability of selecting an E
7. Evaluate
8. The lengths of 2 cylinders are in the ratio 3:1 and their diameters are in the ratio 1:2 .Calculate the ratio of their quantities
9. In the provided figure DE is parallel to BC and determine




10. A point P is 13 cm from the centre of a circle. If the radius of the circle is five cm,
then the length of the tangent drawn from P to the circle is:
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part B

11. If the zeroes of the polynomial x3 – 3x2 + x + one are a – b, a, a + b, obtain a and b.
12. The diagonals of a quadrilateral ABCD intersect every other at the point O such that . Show that ABCD is a trapezium.
13. Consider ??ACB, right-angled at C, in which AB: AC = . obtain ?ABC and also determine the values of Cos2B+Sin2B
14. Find the coordinates of the point P on y-axis, equidistant from 2 points A(-3,4) and B(3,6) on the identical plane.
15. Cards numbered 3, 4, 5, 6, ------ 17 are put in a box and mixed thoroughly. A card is drawn at random from the box. obtain the probability that the card drawn bears i)An even perfect square number, ii) A number divisible by three or 5.
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part C
16. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + one for a few integer m.
17. Solve the subsequent system of linear formula graphically
2x-3y=5
3x+4y+1=0
.Calculate the area bounded by these lines and y-axis
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

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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 )




part D
26. A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of every article (in rupees) was three more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, obtain the number of articles produced and the cost of every article.
OR
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got two marks more in Mathematics and three marks less in English, the product of their marks would have been 210. obtain her marks in the 2 subjects.

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27. If a line is drawn parallel to 1 side of a triangle, to intersect the other 2 sides in distinct points, the other 2 sides are divided in the identical ratio. Prove it.
Using the result, prove the following, In the adjoining figure, if PQRS is a trapezium in which
PQ¦SR¦XY then P Q
=
X Y


S R
28. A round balloon of radius a subtends an angle at the eye of the observer, while the angle of elevation of its centre is . Prove that the height of the centre of the balloon is ( a sin cosec( /2) )
Or
A person standing on the bank of a river observes that the angle of elevation of the top of a tree standing on the opposite bank is 60o. When he moves 40 m away from the bank, he obtains the angle of elevation to be 30o. obtain the height of the tree and the width of the river.
29. The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its quantity be of the quantity of the provided cone, at what height above the base, the part has been made?
30. Find the median marks of students from the subsequent table:

Marks Number of Students
0 and above 80
10and above 77
20and above 72
30and above 65
40and above 55
50and above 43
60and above 28
70and above 16
80and above 10
90and above 08
100and above 0

Earning:   Approval pending.