Part-A: I. Answer ALL the Multiple Choice Questions 1. The equation of xy- plane is (A) ? = 0 (B) ? = 0 (C) ? = 0 and ? = 0 (D) ? = 0
2. The corner points of the feasible region determined by the following system of linear inequalities: 2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5). Let Z = ax + by, where a, b > 0. Condition on a and b so that the maximum of Z occurs at both (3, 4) and (0, 5) is (A) a = b (B) a = 2b (C) a = 3b (D) b = 3a
II. Fill in the blanks by choosing the appropriate answer from those given in the bracket. 1.For a square matrix A in matrix equation AX = B. If |A| = 0 and (adj A) B ≠ 0, then there exists …… solution. 2. Sum of the intercepts cut off by the plane 2x + y – z = 5 is ……… 3. The slope of the normal to the curve y = 2 ?- 3 sin x at x = 0 is …… 4. The probability of obtaining an even prime number on each die, when a pair of dice is rolled is…..
III. Answer all the following questions 1. Define a bijective function. 2. Find the derivative of the function sec( tan√? ) with respect to x. 3. Define feasible solutions in a linear programming problem. 4. Find ∫1−????/???2? ??. 5. Define Negative of a Vector.
Instructions : 1) The question paper has five parts namely A, B, C, D and E. Answer all the parts. 2) Part A has 10 Multiple choice questions, 5 Fill in the blanks and 5 Very Short Answer questions of 1 mark each. 3) Part A should be answered continuously at one or two pages of Answer sheet and Only first answer is considered for the marks in subsection I and II of Part A. 4) Use the graph sheet for question on linear programming in PART E
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