Goa Board Class 12 Question Paper June 2018 Mathematics _Vocational_

*V311(N04)* 2018 III 23 1000 Seat No. : Time : 2 Hours MATHEMATICS (Vocational) Subject Code V 3 1 1 Total No. of Questions : 5 (Printed Pages : 2) Maximum Marks : 50 INSTRUCTIONS : 1) Answer each question on a fresh page. 2) Write the numbers of the question and sub-question clearly. 3) All questions are compulsory. 4) Figures to the right indicate full marks. 5) Use of logarithm table is allowed. 6) Graph paper will be supplied on request. 1. A) Find the matrix A if A = [a ij ]3×2 and aij = i – 2j when i = j =i+j when i < j = 2i + j when i > j [1] B) Construct a backward difference table for the following data : [2] X 1 2 3 4 5 6 Y 12 15 20 27 39 69. Hence identify ∇ y 34 and ∇ y 25 . x 3 − 5x − 12 C) Evaluate xlim , if it exists. [3] →3 2x 2 − 9 − 3 D) Solve the following linear programming problem using graphical method : Maximize Z = 2x + 5y subject to 2x + 4y ≤ 8, 3x + y ≤ 6, and x ≥ 0, y ≥ 0. [4] V-311 (N-04) -1- P.T.O.

*V311N04* 2. A) Differentiate Cot (xy) with respect to x. [1] ⎡3 − 2 ⎤ 2 B) If B = ⎢ ⎥ , find s, so that B + 2I = s.B. [2] ⎣ 4 − 2 ⎦ C) Evaluate ∫ x 2Sin x dx . [3] dy x D) If xmyn = (x + y)m+n, show that = . [4] dx y Cos x 3. A) Evaluate ∫ dx . [1] 5 + Sinx B) A bag contains 7 white, 5 black and 4 red balls. If two balls are drawn at random from the bag, find the probability that one is black and the other is red. [2] 4 C) Evaluate ∫ x(4 x 2 + 9x + 6)dx . [3] 0 D) Find the regression line of Y on X for the following data : X 3 2 –2 –1 –2 0 Y 0 3 –2 –2 2 –1 [4] ⎡4 x ⎤ 4. A) Find x, if C = ⎢ ⎥ is a singular matrix. [1] ⎣ 3 − 6⎦ ⎡ 1 ⎤ B) Evaluate ∫ ⎢ ⎥ dx . [2] ⎣ 2x + 3 − 2 x ⎦ 6 C) Evaluate ∫ (2 x + 5)dx , using Trapezoidal rule with 6 strips. [3] 0 D) Solve the following equations using matrix method. [4] x + 3z = 5, 2x +2y + z = 5, –4y – 4z = – 4. 5. A) Evaluate ∫ [(3 x + 7)4 − (7 − 3 x)−4 ] dx . [1] dy B) Find , if yex + 2x = Cos y. [2] dx C) Form a differential equation given y = Ae–5x + Be5x. [3] D) Using Lagrange’s Interpolation formula, find f(2) given that f(0) = 3, f(1) = 4, f(3) = 12. [4] ____________ V-311 (N-04) -2-