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Seat No.: Enrolment
GUJARAT TECHNOLOGICAL UNIVERSITY
MCA -INTEGRATED SEMESTER-I • EXAMINATION -SUMMER 2017
Subject Code: 4410604 Date: 06-06-2017
Subject Name: Basic Mathematics for IT
Time: 10.30 am to 01.00 pm Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
Q.1 Define:
Singleton set
Empty set
Power set
Union of two sets
Complement set
Contradiction
Reflexive relation
07
If
Find X U X
X X
07
Q.2 Prove the following relation:
07
Find the equation of a circle which passes through the points 07
OR
Solve the following system of equation using Gauss Elimination method
2 3 14
3 2 11
2 3 11
x y z
x y z
x y z



07
Q.3
Show that for a matrix
1 1 1
2 3 0
18 2 10
A





A(Adj 0
07
Using Predicate, Quantifier and rule of inference determine the given argument
is valid or not
"All student in the class understand logic. Xavier is a student in this class.
Therefore, Xavier understand logic."
07
OR
Q.3
Show that
1
1 0
1
a b c
b c a
c a b



07
2

Construct the truth table for the following


07
Q.4 Define recurrence relation. Suppose that a person deposits $10,000 in a savings
account at a bank yielding 11% per year with interest compounded annually.
How much will be in the account after 30 year?
07
In a survey of 30 students, it was found that 19 take Mathematics, 17 take
Music, 11 take History, 7 take Mathematics and History, 12 take Mathematics
and Music, 5 take Music and History and 2 take all three courses. Find
The number of students that take Mathematics but do not take
history
The number that take exactly two of the three courses.
07
OR
Q.4 Suppose that the number of bacteria in a colony triples every hour.
Set up a recurrence relation for the number of bacteria after n hours
have alapsed.
If 100 bacteria are used to begin a new colony how many bacteria
will be in the colony after 10 hours?
07
Use mathematical Induction for the statement
1 2 1 1 2 2 ..... 2 2 1 n n P n for all non-negative integers n
What is the statement
Show that is true.
What is inductive hypothesis?
Prove inductive step.
07
Q.5 Find the point which divides the join of and externally in the ratio
2:3 the point lying towards the point
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(i)Define Vector and Scalar.
Find the intercept that the line 3x-4y+12=0 make with the axis. What is the
slope of the line?
02
05
OR
Q.5 Show that the points and are the vertices of a right
triangle.
07
Show that the three points with position vectors given by
a-2b+3c
-2a+3b+2c
-8a+13b are collinear.
07