Hemchandracharya North Gujarat University 2001 B.Sc Computer Science 102 : Advance Mathematics - Question Paper
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B-12702 Seat No.---------
1st Year Master of Science exam
May/June –2001
Advance Mathematics: Paper-102
(Computer Application & informationTechnology)
Time: three Hours] [Total Marks: 70
Instructions: (I) All ques. are compulsory
(II) Figures to the right shows marks of the corresponding ques.
1 (a) Let S=Set of all people, 3
B=Set of all IT men,
C= Set of all people who smoke cigarettes,
D= Set of all pipe smokers,
E= Set of all wine drinkers.
Express the subsequent statements in the set notations.
(I) Some IT men pipe smokers are wine drinkers.
(ii)An IT man is neither a wine drinker nor a pipe smoker.
(b) State and prove the distributive laws. 3
(C) (1) obtain the largest interval or IR on which the formula f (x)=x2 describes a one-one
Function.
(2) If f (x)=log a x and f (x)=ax then show that F (f (x)) = f (F(x)) for all suitable x.
(3) discuss the subsequent terms with suitable illustrations (A) convex function (B)
Concave function.
OR
1 (a) Examine whether the subsequent sets are finite or infinite: 2
(I) The set of points on the circumference of a circle of radius two c.m
(II) The set of all lines parallel to a provided line.
(III) The set of all real numbers ranging from zero and one.
(IV) The set of all citizens of India.
(b) (I) which of these sets are equal: 2
{n, g, u}, {n, g, n,u},{n,g,u,g},{n,u,g,u}
justify your ans.
(II) Let M={ ?, { ? }, { ?, { ? }}} Then , discuss with justification, which of the statements are accurate or incorrect.
(A) {?} ?M (B) {{ ? }} ? M
(C) { ?,{ ? }} ? M
(c) (I) Determine whether f (x)=2x3,0=x
_
2 (a) (I) Show that 3v2 is an irrational number. 3
(II) Show that the function described as follows is discontinuous at x=0.
| Earning: Approval pending. |
