B Student Regd. No COURSE CODE: DMTH201 COURSE TITLE: Basic Mathematics-1 Date of Exam:- 14 Oct Session:- 1:30-4:30 Time Allowed : 3 hours Max. Marks: 80 1. This paper contains 10 questions divided in two parts on 2 page. 2. Part A is compulsory. 3. In Part B (Questions 2 to 10), attempt any 6 questions out of 9. Attempt all parts of the questions chosen. 4. The marks assigned to each question are shown at the end of each question in square brackets. 5. Answer all questions in serial order. Part-A 1. a) Find the value of (2x10=20) b) Define the column matrix c) Give the example of two matrices A and B of order such that AB is not equal to BA. d) Find the adjoint of the matrix e) Define slope of the straight line. f) If the angle between two lines is and slope of one of the lines is 1/2 ,find the slope of the other line g) Equation of a line is 3x+4y + 10 = 0. Find its (i) slope, (ii) x - and y-intercepts h) Find the numbers which map to zero under the function i) Define implicit and explicit functions. j) Find the domain and range of Part-B 2. Find the general solution of equation i. 3. If ii. (5+5) then show that (10) 4. By using Cramer’s rule find the solution of following equations (10) 5. The Fahrenheit temperature F and absolute temperature K satisfy a linear equation. Given that K = 273 when F = 32 and that K = 373 when F = 212. Express K in terms of Fand find the value of F, when K = 0. (10) 6. Find the angle between the lines and . (10) 7. a. b. Let f(x) = 3x + 1 and g(x) = x2 + 2Then show that f o g(x) = f(g(x)) Which of the following functions are onto function if f : R R. (i) ii. f(x) = |x| 8. 9. 10. (5) f(x) = 115x + 49 (5) Find i. where ii. where (5+5) i. Define the continuity of function defined on (a,b) (2) ii. Show that (8) Find the derivative of i. is continuous at x = 2. ii. iii. iv. (10)

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