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Total No. of Questions : 071 [Total No. of Pages : 03
J1375[6373 A] [2957]
BBA (Semester  1^{st})
BUSINESS MATHEMATICS (BB 102)
Time : 03 Hours Maximum Marks : 60
Time : 03 Hours Maximum Marks : 60
Instruction to Candidates:
1)
Section  A is compulsory
2)
Attempt any Four questions from Section  B.
Section  A (10x2 = 20)
QD
a)
Two finite sets have x and y number of elements. The total
number of subsets of the first set is four times the total number of subsets of
the second set. Find the value of x  v.
b)
Determine whether the proposition [p a (p—»<?)]—><? is a
tautology.
c)
How many committees of five people can be chosen from
20 men and 12 women if at least four women must be on each committee?
d)
Expand (3a^{2}+2 y)^{5} using the Binomial Theorem.
x^{2}7x+\2
e) Evaluate _{t}_>_{4} ;
a'~3x4
f) Find the domain and range off(x) =

2 1
3
1 1
4
1 6 2

g) Express the matrix A =

as the sum of symmetric and a
skew
imetnc matrix.
the following system of
equations have a solution? Is it unique? Give reasons.
4.v+2v = 10 2.y+ v=5.
P.T.O.
i) What will be the interest on
Rs. 1,500 after 1 year if interest is
compounded quarterly at 9%.
j) If office furniture purchased on
January 5 for Rs. 7,500 has an estimated useful life of 6 years and a trade 
in value Rs. 650, what is the book value at the end of the fifth year?
Section  B (4x10 = 40)
\2) Define the converse, inverse
and contrapositive of a statement. By writing I Infollowing argument in
symbolic form, determine its validity: If Ruchi gels the supervisor's position
and works hard, then she will get a raise.
If she gets the raise, then she
will buy a new car. She has not purchased a new car.
Therefore either Ruchi did not get the supervisor's
position or she did not work hard.
Q3) In how many ways can 6 students
out of a class of 12 be chosen to attend class on a late Thursday afternoon
(and take notes for others) if
(a)
Pawan refuses to go to class?
(b)
Mohan insists on going?
(c)
Jimmi and Mohan insist on going?
(d)
Just one of Jimmi and Mohan attend?
(e)
Pawan and Mohan refuse to attend class together?
( 1
ifx<3
Q4) If ^^{3<X<5} ^{DetermmC} ^{thC}
^{ValUCS}.°^{f}" ^{a,Ml} " ^{S}° ^{llUU}
'
7, if5>x
is
continuous. Also discuss the differentiability g(x)=alj+.v2 graphically.
Q5) Define an increasing and decreasing function. Write the
criteria of testing the increasing and decreasing function. Find all the points
of local maxima and minima of the function as well as the corresponding maximum
and minimum value for the function f(x)=r'6x^{2}+9x'&.
J1375[6373 A]
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Q6) Describe the Cramers Rule for
solving the system of simultaneous linear equations and hence solve the
following system of linear equations:
3x+y + 2z=3, 2x3yz = 3, jr + 2y + z = 4.
Q7) Using the dpuble declining
balance method of depreciation* calculate the book value to theaearest rupee
TiHrfc end of the second year for the following:
(a)
Cost Rs. 120,000 Trade  in value Rs.5,700 Estimated life 25yr Purchased May 3
(b)
Cost Rs.3,000 Trade  in value Rs.O Estimated life 8yr
Purchased August 16
[1375(6373 AJ
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