punjabtechnicaluniversity.blogspot.in

**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. - 4**

**th**

**)**

**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 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, 4*k*+ 6, 3*k*– 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*

*)***Twelve persons meet in a room and each shakes hands with all the others.**

*Q2)*
Find
the number of hand-shakes.

**(a) Prove that 5Cr = 31**

*Q3)**r*=1

5Ó

.

(b)
Find

*r*, if 10Pr = 2 ⋅ 9P*r*.**Find the sum of**

*Q4)**n*terms of the series 7 + 77 + 777 + ...... upto

*n*-terms.

**Insert 5 arithmetic means between 8 and 26.**

*Q5)***If the 5th and 12th terms of an AP are 30 and 65, respectively, find the sum of**

*Q6)*
its
first 20 terms?

**If sec è = 13**

*Q7)*
5

,è lies in the fourth quadrant, find the values of other
trigonometric

functions?

**Use Cramer’s rule to solve 6**

*Q8)**x*+

*y*– 3

*z*= 5,

*x*+ 3

*y*– 2

*z*= 5, 2

*x*+

*y*+ 4

*z*= 8.

**Find the inverse of A =**

*Q9)*
2 1
3

4 –1
0

–7 2
1

.

**Prove that**

*Q10)*
1 1
1

*a b c*

*a*3

*b*3

*c*3

= (

*a*–*b*) (*b*–*c*) (*c*–*a*) (*a*+*b*+*c*).**In a group of 400 people, 250 can speak Hindi and 200 can speak English.**

*Q11)*
How
many can speak both Hindi and English?

**If U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {2, 4, 6, 8} and B = {2, 3, 5, 7}. Verify that**

*Q12)*
(A ∪ B)′ = A′∩ B′ and (A ∩ B)′ = A′∪ B′.

**Check which is tautology or contradiction?**

*Q13)*
(a) [(~

*q*) ∧*p*]∨[*p*∨ (~*p*)].
(b) [((~

*p*) ∧*q*) ∧ (*q*∧*r*)]∧ (~*q*) .
## 0 comments:

Post a Comment