## B.Sc. IT (402) (S05) / 102 (New) (Sem. - 4th) BASIC MATHEMATICS – I, Punjab Technical University, PTU, Question paper

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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 A B and A∩ B.
e) Let p: I like tennis, q: I like foot ball, then find for what ~ p ^ ~ q stands for.
f) Prove that sin2 θ + cos2 θ = 1.
g) Find sin(765°).
h) Define a scalar and lower triangular matrix.
i) If A = ½ ¾   , 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 +………..∞.
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?

Q2) Twelve persons meet in a room and each shakes hands with all the others. Find the number of hand-shakes.
5
Q3) (a) Prove that    Σ     5Cr = 31.
r=1
(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 θ = 13/5, θ lies in the fourth quadrant, find the values of other trigonometric functions?

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′∩ B′ and (A ∩ B)′ = A′ B′.
Q13)Check which is tautology or contradiction?
(a) [(~ q) p][p (~ p)].
(b) [((~ p) q) (q r)] (~ q) .

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