**Roll No…..**

**Total No. of Questions: 07**

**PAPER ID: [BB102]**

**BBA (Sem.-1**

^{st})**BUSINESS MATHEMATICS (BB-102)**

**Time: 3 Hrs. Max. Marks: 60**

**Instruction to Candidates:**

1. Section-A
is Compulsory.

2.
Attempt any Four questions from Section-B.

**SECTION-A**

Q1.

(a) If A=[1,2,3,5], B=[4,5,7] and C=[1,6,7] then
prove that A-(B=(A-B)(A-C).

(b) Construct the truth table for [P

_{^}(p
(c) In how many ways a
committee of 3 students can be formed from 4 boys and 3 girls so that committee
contains at least one boy and one girl.

(d) State Binomial
Theorem and using it expand (1-x)

^{2}.
(e) Find the
derivative of 2

^{x }log x with respect to x.
(f) Evaluate

(g) If A= then find A

^{2}&A^{2}.
(h) Using Matrix
Inversion Method, solve the following system of linear equations.

3x+2y=1

x-y=2

(i) Define
Logarithm. List few properties of
logarithm.

(j) How much money is
needed today so that we will have Rs.2500 after 2 years if interest is 8% compounded
quarterly.

**SECTION-B**

Q2.

(a) In a
class of 35 students 17 have taken mathematics, 10 have taken mathematics but
not economics. Find the number of
students who have taken both mathematics and economics and the number of
students who have taken economics but not mathematics, if it is given that each
student has taken either mathematics or economics or both.

(b) Solve
the equation:

12x

^{2}-56x^{3}+89x^{2}-56x+12=0
Q3.

(a) State
the converse and contra positive of the following statements:

(i) If today is Holi then tomorrow is Tuesday.

(ii) If John is a poet then he is poor.

(iii) If triangle ABC is right angled then AB

^{2}+BC^{2}=AC^{2}
(iv) If P is a square then P is a rectangle.

(v) If a
triangle is not isosceles then it is not equilateral.

(b) A bit is either 0 or 1: a byte is a
sequence of 8 bits. Find

(i) the
number of bytes that can be formed.

(ii) the
number of bytes that begin with 11 and end with 11.

(iii) the
number of bytes that begin with 11 and do not end with 11,

(iv) the
number of bytes that begin with 11 or
end with 11.

Q4. (a) Find the sum of first 20 terms of an A.P
.in which 3

^{rd}terms is 7
and
the 7

^{th}terms is two more than thrice of its 3^{rd}terms.
(b) Find the extreme values of the function
given by f (x) = (x- 1) 2

(x+
1 )

^{3}.
Q5. (a) Express the matrix A as sum of a symmetric and skew

Symme..c matrix where

A=

(b) Using Cramer`s rule , solve the following
of linear equations:

x-
y +z =4

2x
+y -3 z =0

x+
y + z =2

Q6. Using
Gauss limination method solve the
following system of

Linear
equations :

2x
+ z = 3

x-
y + z = 1

4x
– 2y + 3z = 3

Q7. Define
Depreciation . Explain Straight –Line Method of

Depreciation
.A dishwasher was purchased by the Check –Inn Restaurant on october I.The purchase price was Rs.1200 and
installation cost was Rs.300. The
estimate usefull life of the dishwasher is 6 years and its salvage value
is Rs .300 What is the amount of depreciation to the nearest paisa at the end
of 4

^{th}year ?
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