Solapur University Question Paper,B.Com. I , BUSINESS MATHEMATICS (Old) ,2014 Question Paper

Solapur University Question Paper B.Com. I (Semester – II) Examination, 2014 BUSINESS MATHEMATICS (Old) Day and Date : Thursday, 3-4-2014 Max. Marks : 50 Time : 11.00 a.m. to 1.00 p.m. Instructions : 1) Graph papers will be supplied on request. 2) Use of soundless calculator is allowed. 3) All questions are compulsory. 4) Figures to the right indicate full marks. 5) Assume suitable data if necessary. 1. Select the most suitable answer for the following : 10 i) The function f (x) = 2x + 3x3 is an a) even function b) odd function c) even as well as odd d) none of these ii) The value of f…(x) at x = a is denoted by a) f…(a) b) dx df c) dx dy d) all of the above iii) The rule dx du du dy dx dy is known as a) parametric function b) inverse function c) chain rule d) none of the above iv) When both the variables are expressed in terms of a same third variable then the function is known as a) inverse function b) implicit function c) first principle d) parametric function v) Whenever x is in the index, we take ________ on both sides in the first instance then differentiate. a) square root b) logarithm c) constant d) coefficient P.T.O. Seat No. SLR-B – 22 -2- vi) > @ ‘ x 2x 5 lim 2 x 5 a) 25 b) 35 c) 40 d) 32 vii) The process of integration of the product of two functions is known as a) integration by subtraction b) integration by substitution c) integration by part d) integration through partial fractions viii) The integration of 2 with respect to x is a) 2x2 + c b) c 2 x2 c) 0 d) 2x + c ix) The integration of emx with respect to x is a) emx b) m emx c) mx ex d) memx x) If y is expressed in terms of x explicitly, then the function y = f (x) is called as a) implicit function b) explicit function c) identity function d) none of these 2. Answer the following : A) If y = f (x) = x2 find dx dy by using first principles. 5 B) Draw the graph of f (x) = x2 + 3 by taking x = – 3, – 2, – 1, 0, 1, 2, 3. 5 3. A) Evaluate i) Ý Þ Ü Í Î Ì ‘ x 3x 2 lim x 4x 3 2 2 x 1 . ii) Ý Þ Ü Í Î Ì ‘ x 2x 2 x 2 lim 1 x 2 2 . 5 B) Evaluate i) Ý Ý Þ Ü Í Í Î Ì ‘ x 2 lim x 1 5 2 x 2 ii) Ý Þ Ü Í Î Ì ‘ˆ 5x 3 lim x x 4 2 2 x . 5 -3- SLR-B – 22 4. Attempt (A) or (B) : 10 A) i) Prove that Õ Õ a 0 a 0 f (a x) dx f (x) dx ii) Evaluate dx x 1 x 3 2 2 Õ . iii) If y = 2e–3x + 3e2x find the value of 6y dx dy 5 dx d y 2 2 . B) i) Find the cost function and the average cost function if the marginal cost function is given by MC = 3x2 – 2x + 7 and the fixed cost in Rs. 200. ii) If the demand law is p = 48 – x2 find the maximum revenue. 5. Attempt (A) or (B) : 10 A) i) If u and v are differentiable functions of x, then show that dx dv dx du u v dx d . ii) Find dx dy for y 3x 2x 5 2 . iii) Find dx x log x 1 Õ . B) i) Find the maxima of y = x3 – 3x2 – 9x + 12. ii) Evaluate dx x 3 x x 3 0 Õ . _______________

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