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.

d) Define tautology and contradiction.

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     ⁵C_r = 31.

          r=1

(b) Find r, if ¹⁰P_r = 2 ⋅ ⁹P_r .

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) .

.