## BBA (Sem. - 1st) BUSINESS MATHEMATICS (BB - 102) Paper ID [BB102]

• Friday, March 01, 2013
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Roll No......................... ...
Total No. of Questions : 07]                                                                              [Total No. of Pages : 02

Paper ID [BB102]

(Please fill this Paper id in OMR Sheet)
BBA (Sem. - 1st) BUSINESS MATHEMATICS (BB - 102)
Time : 03 Hours                                                                                                           Maximum Marks : 60
Instruction to Candidates:
1)       Section - A is Compulsory.
2)           Attempt any Four questions from Section - B.

Section - A
Ql)                                                                                                                                                               (10x2 = 20)
a)        For any two sets A and B show that, AnBcAcAuB
b)        Construct the truth table for -/? v ~q
 c)  lf8C,.-7q = 7C2,findr.
c)        Using Binomial theorem, evaluate (99)5.
d)        If aAc are in AP show that t+c, c+a, a+b are also in A.P.
V
^ , x2-4x + 3jC   t"
f)     A function is defined as, f(x)=-—     ' ^for x * 1
x -1
= 2               for x = 1
Test its continuity at x=1.
g)     Find the maximum value of 1 -x2.
h)     State Cramer's rule to solve simultaneous equations.
i)      If the sum of the series 2,5,8,11,........ is 60100, then find n.
j)   Which is greater ; log2 3 or log, 5 .

R-546 [2058]

P.T.O.

Section - B
(4x10 = 40)
Q2)  (a) For any two sets A and B, show that, (A nB)c=AcuBc.
(b) For any logical statementsp,q and r, show that, p v (q a r)=(p v q) a (/; v /•).

Q3)  (a) Solve jt W2x2-8x +12 =4^ + 6.
(b) How many different words can be formed out of the letters of the word ALLAHABAD? In how many of them the vowels occupy uV even positions?
Q4)  (a) Prove that the coefficient of x" in the expansion of (1+x)2" is double the coefficient of x" in the expansion of (1+x)2""7.
(b) Sum to n terms the series, .7 + .77 + .777 + ... .
Q5)  (a) If in an A.P. , the sum of p terms in equal to the sum of q terms, then prove that the sum of p + q terms is zero.

(b) If a & 0 then evaluate

Q6)  (a) If xy = yx, prove that

Lt Ja + 2x- V3je x —»a V3a + x - 2^[x

dy _y(x\ogy-y) dx   x(y\ogx-x)'

(b) Divide 64 into two parts such that the sum of the cubes of two parts is minimum.
Q7)  (a). Apply Gauss elimination method to solve the equations, x+Ay-z= -5 ; x+y-6z= -12; 3x-y-z~4.

(b) Find the value of, (.235)5 (.005)2 (208.610)"2.

R-546

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