Download OU B.Pharma 1st Year 2018 13030 Mathematics Question Paper

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Code No. 13030/Non CBCS

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FACULTY

B. Pharmacy I Year (Non CBCS)(Backlog) Examination, December 2018

Subject : Mathematics

Time : 3 Hrs Max. Marks: 70

Note: Answer all questions. All questions carry equal marks.

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1. (a)
   1. Show that sin (45° + A) sin (45° — A) = ½ cos 2A.
   2. If A + B + C = 180° prove that sin(A/2) + cos(B/2) - cos(C/2) = 2cos(A/4)cos(B/4).
   OR (b)
   1. If log_abc = x+1, log_b abc = y+1 and log_c abc = z+1 show that xyz=x+y + z.
   2. Prove that Tan9° — Tan27° — Tan 63° + Tan 81° = 4.

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2. (a)
   1. Find the derivative of f(x, y) = x² + y² + x, using first principal.
   2. Discuss the continuity of the function
      f(x, y) =
      x⁴+ y² / (x⁴+ y²) , (x,y) ? (0,0)
      0 , (x,y) = (0,0)

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   OR (b)
   1. Find the maximum and minimum values of the function f(x, y) = 4x² + 9y² — 8x — 12y + 4.
   2. If u = sin^-1( (x²-y²) / (x+y) ), prove that x(?u/?x) + y(?u/?y) = Tanu.
3. (a)
   1. Evaluate ?x⁸ dx.
   2. Evaluate ? x / (a² + x²) dx.

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   OR (b)
   1. Evaluate ? (3x+4) / (x²+2x+3) dx.
   2. Evaluate ? 1 / (2+3sinx) dx.
4. (a)
   1. If A = [4 2; 4 2] prove that A²— 5A = 14 I, where I is the unit matrix of second order.
   2. Solve the equation x + 3y + 6z =2, 3x —y + 4z =9, x — 4y + 2z = 7 by matrix Inversion method.

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   OR (b)
   1. Find the rank of the matrix A = [3 0 1 2; 0 6 2 4; 0 3 1 2].
   2. If A = [1 2; 0 2], B= [2 1; 3 2] and C= [3 1; 3 0] verify that A (B+C)=AB + AC.
5. (a)
   1. Explain Linear and non Linear graphs with examples.
   2. Find the equation of the circle passing through the points (1, 0), (2, 1) (5, 3).

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   OR (b)
   1. What are the basic mathematical principles are used in biological Testing.
   2. Find the equation of the Line passing through (3, 2) with slope 2/3.

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