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

A right circular cone is divided into 2 portions by a plane parallel to the base and passing through a point, which is 1/3 of the height from the top. obtain the ratio of the smaller cone to that of the remaining frustum of the cone.
30. For the subsequent frequency distribution draw the less than provide and using it obtain the median.
Marks obtained 50-60 60-70 70-80 80-90 90-100
No. of students 4 8 12 6 6





Sample Paper – 2007–
Mathematics
part - A
1. obtain the domain of the function e3logx.
2. obtain a branch of the function cos-1 other than the principal value branch.
3. If A is a 3x3 matrix such that |A|=5 then what is |adjA| ?
4. What is the minimum value of | sin4x + 3| ?
5. Write square matrices A and B of order two such that AB=0, A?0 and B?0.
6. If and are any 2 vectors such that | . | = | x | then what is the angle ranging from
and ?
7. If the lines and are perpendicular then obtain the value of k.

9. If and are unit vectors such that | + | =1 then what is | - |?
10. If A is a square matrix of order three such that |A| = four then obtain A(adjA).


SECTION_- B
11.Solve for x:

Or
Simplify:


13. Using properties of determinants, prove that



OR
Using elementary transformations obtain the inverse of


14. obtain the values of a and b such that the function described


.

OR


17. Using differentials, obtain the approximate value of (255)1/4 upto 4 places of decimals.


19. obtain the shortest distance ranging from the lines

20. Using properties of definite integrals, evaluate

21. Using vectors obtain the area of the triangle whose vertices are A(1,1,2), B(2,3,5) and C(1,5,5).
22. The probability that a bomb dropped from a plane will strike the target is 1/5. If 6 bombs are
dropped, obtain probability that (i) exactly 2 will strike the target.
(ii) atleast 2 will strike the target.

Earning:   Approval pending.