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No....................... ^{n }Total
No. of Questions : 07]^{}
[Total No.
of Pages: 03
Paper ID [BB102]
(Please fill this paper ID in OMR Sheet)
BBA (Sem.  1^{st}) BUSINESS MATHEMATICS
(BB102)
Time: 03 Hours Instruction to
Candidates:
1)
Section  A is Compulsory.
2)
Attempt any Four questions from Section  B.
Maximum Marks: 60
QD
Section  A
(10x2 = 20)
a)
If A = {1, 2, 3, 5}, B = {4, 5, 7} and C = (1, 6, 7}
then prove that A  (B nC) = (A  B) u(A  C).
b)
Construct the truth table for [pA(p —> q) ] »q.
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  jc)^{4}.
e) Find the
derivative of T log
jc with respect to ,v.
cosG 0 sinG

0

1

g) If A

0

then find A^{2} &

sine 0
cose
h) Using Matrix Inversion
Method, solve the following system of linear
equations:
3x + 2y =
xy = 2
i) Define Logarithm. List few
properties of logarithm.
p.t.o.

j). How much money is needed
today so that we will have Rs. 2500 after 2 years if interest is 8% compounded
quarterly.
J9161
Section  B
~ (4 x 10 = 40)
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:
12.x^{4}
 56jc^{3} + 89jc^{2}  56* + 12 = 0
Q3) (a) State the converse and contrapositive 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} term is 7 and the 7^{th} term
is two more than thrice of its 3^{rd} term, (b) Find the extreme values
of the function given by f(x) = (x  l)^{2 }(x + l)^{3}.
Q5) (a) Express the matrix A as sum
of a symmetric and skew symmei.x matrix where
"21 3" . A
1 4
1 0 22
(b) Using Cramer's rule, solve the following system of
linear equations:
xy+z=4
2x + y  3z
= 0 x + y + z = 2 ,
2
Q6) Using Gaiis: 'imination method, solve the following
system of linear equations: ^ 2x + z = 3 x  y + z = 1 ' 4x  2y + 3z = 3
Q7) Define Depreciation. Explain
StraightLine Method of depreciation. A dishwasher was purchased by the
CheckInn Restaurant on October 1. The purchase price was Rs. 1200 and
installation cost was Rs. 300. The estimate useful life of the dishwasher
isj3j^ears 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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