## BASIC MATHEMATICS – I, Punjab Technical University, PTU, Question Papers

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Roll No. .................
Total No. of Questions : 13]                                                                            [Total No. of Pages : 02

Paper ID [A0314]

(Please fill this Paper ID in OMR Sheet)

B.Sc. IT (402) (S05) / 102 (New) (Sem. - 4th)
BASIC MATHEMATICS – I

Time : 03 Hours                                                                                           Maximum Marks : 75

Instruction to Candidates:
1) Section - A is Compulsory.
2) Attempt any Nine questions from Section - B.

Section - A
(15 x 2 = 30)

Q1)
a) List all the elements of the set B = {x : x is an integer,
1
2
< x < 9
2
}.

b) Define a set and a subset.

c) If A = {2, 4, 6, 8} and B = {6, 8, 10, 12}. Find AB and AB.

e) Let p: I like tennis, q: I like foot ball, then find for what ~ p ^ ~ q stands
for.

f) Prove that sin2 è + cos2 è = 1.

g) Find sin(765°).

h) Define a scalar and lower triangular matrix.
i) If A = 1 2
3 4
 
 
, write all minors and cofactors of A?

j) Define transpose of a matrix. If A= A then point out whether A is
symmetric or skew symmetric.

k) Write sum and n th term of a G.P. with common ratio r and first term a.

l) Find the sum of the progression
1+
1
2
+ 1
22 + 1
23 +L.

m) Find k if k + 2, 4k + 6, 3k – 2 form an AP.

n) State fundamental principle of counting.

o) In how many ways 5 person draw water from 5 taps, assuming no tap
remains unused?

Section - B
(9 x 5 = 45

)
Q2) Twelve persons meet in a room and each shakes hands with all the others.
Find the number of hand-shakes.

Q3) (a) Prove that 5Cr = 31
r=1
5Ó
.
(b) Find r, if 10Pr = 2 9Pr .

Q4) Find the sum of n terms of the series 7 + 77 + 777 + ...... upto n-terms.

Q5) Insert 5 arithmetic means between 8 and 26.

Q6) If the 5th and 12th terms of an AP are 30 and 65, respectively, find the sum of
its first 20 terms?

Q7) If sec è = 13
5
,è lies in the fourth quadrant, find the values of other trigonometric
functions?

Q8) Use Cramer’s rule to solve 6x + y – 3z = 5, x + 3y – 2z = 5, 2x + y + 4z = 8.

Q9) Find the inverse of A =
2 1 3
4 –1 0
–7 2 1


.

Q10)Prove that
1 1 1
a b c
a3 b3 c3
= (a b) (b c) (c a) (a + b + c).

Q11)In a group of 400 people, 250 can speak Hindi and 200 can speak English.
How many can speak both Hindi and English?

Q12)If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that
(A B)= A′∩ Band (A B)= A′∪ B.

Q13)Check which is tautology or contradiction?
(a) [(~ q) p][p (~ p)].
(b) [((~ p) q) (q r)](~ q) .