B.B.A. (Sem.-1) BUSINESS MATHEMATICS Subject Code : BB-102 Paper ID : [C0202]

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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 : BB-102 Paper ID : [C0202]

Time : 3 Hrs.                                                                                                               Max. Marks : 60

                                                                     

INSTRUCTION TO CANDIDATES :

SECTION-A                          (10

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

1.    SECTION-A is COMPULSORY.                                           

2.    Attempt any FOUR questions from SECTION-B

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  (5^2logx5) = 2x, x > 0. Dx

(i) Find the values of x for which the function f (x) = |7x-3| is maximum/ minimum.

(j) Find the values of'm' for which the equation

x² - 2x (1 + 3m) + 7 (3 + 2m) = 0 has equal roots.

SECTION-B                          (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 _x2 _- — '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)

[A-12]