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Roll No........................ Total No. of Pages : 03
Total No. of Questions : 07
B.B.A. (Sem.1) BUSINESS MATHEMATICS Subject Code :
BB102 Paper ID : [C0202]
Time : 3
Hrs. Max.
Marks : 60
INSTRUCTION TO CANDIDATES :
SECTIONA (10

x 2
= 20 Marks)
l. (a) If five times the 5^{th} term
of an A.P. is equal to six times the 6^{th} term, show that 11^{th}
term is zero.

1.
SECTIONA is COMPULSORY.
2.
Attempt any FOUR questions from SECTIONB
show that 11^{th} term is zero.
(b)
Which term of the
series 18  12 + 8 ....... is 512/729?
(c) A sum amounts to Rs. 8820 in two years and Rs. 9261 in three
years. Find the rate of compound interest.
75 5 32
(d) Prove that log 
 2 • log  + log  = log 2.
^{16}
^{9 } ^{243}
(e)Find the value of ' r' if
the coefficients of (2r + 4)^{th} and (r  2)^{th }terms in the
expansion of (1 + x)^{18} are equal.
(f) Find the domain of the
function ________ \______
(* 1)(2 " x)
(g) Evaluate the limit, Lt (1  4x)^{x} .
x— 0
(h) Prove that (5^{2logx}5) = 2x, x > 0. Dx
(i) Find the values of x for which the function f (x) = 7x3 is maximum/ minimum.
(j) Find the values of'm'
for which the equation
x^{2}  2x (1 + 3m) + 7 (3 + 2m) = 0 has equal roots.
SECTIONB (4 x 10 = 40
Marks)
2. (a) Using Cramar's Rule/^vethe following system of
equations for x, y
1 1_{+}1=10
x y ^{z} ^^^^
xy
(b) Solve the given equations for x, y and z by Gauss Elimination method.
x + 2y  z = 6
3x  y  2z = 3
4x
+ 3y + z = 9 (5,5)
3. (a) Discuss the continuity of the function
x > 3
(b) Sum
the series 7 + 77 + 777 + ... to n terms. (5,5)
4. (a) There are 15 points in a plane, no three of which are
in a straight line excepting four, which are collinear. Find the number of (/)
straight lines (//) triangles formed by joining them.
(b) Find the term independent of 'x' in the expansion of
^{r} 3 _{x}2 _{} — '^{9}
2^{x} 3x
5. (a) Prove the logical expression ^{p}
(b) Find — where y " a^{x} + x^{a}
+ a^{a} +
x^{x}  log x. (5,5)
♦
6. (a) y = x ^{x} + (1 + x)^{x} , find .

(b) Define a set.
State and prove De Morgan's
Laws. *V^^ (5,5)
2x + 3 V<V
^{7.} ^{(a)} I^{f} ^{y} " ^{f}^{(x)}
" 7—^{,} ^{prove} ^{that} ^{f(y)} " ^{x}^{.}
(b) If xjl + y + y .ijl + x = 0,
Show
that d
"  (i + x)^{2}. (5,5)
[A12]
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