Download OU B.Pharma 1st Year 2015 8035 Mathematics Question Paper

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Pharmacy

B. Pharmacy I-Year (Main) Examination, June 2015

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Subject : Mathematics

Time : 3 Hours Max. Marks: 70

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

1. (a) Prove that log (a. b) = log a + logb.
   (b) If tan(x+26°) = cot(y-19°) then find the value of x.
   

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   OR
   (c) If sec A + tan A = P, then find sin A.
   (d) If a = log₂₄ 12, b = log₃₆ 24 and c = log₁₂ 36, then find 1 + abc.
2. (a) Find the lim _x?0 (1-cos4x) / (1-cos2x)
   (b) If u = sin^-1 {(x²+y²) / (x+y)} show that x ?u/?x + y ?u/?y = tanu.
   

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   OR
   (c) Find differentiation of Sinx from the first principle.
   (d) Find lim _x?0 (sinx - tanx) / x³
3. (a) Evaluate ? x⁵ dx
   (b) Find the area bounded by the ellipse x²/a² + y²/b² = 1.
   

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   OR
   (c) Evaluate ? (3x⁴ + 14x - 5) / (x⁵) dx
   (d) Show that the area of a loop of the curve y²= x² (4 - x²) is 8/3.
4. (a) If a, b, c are different and the determinant | a a² a³-1 | | b b² b³-1 | = 0 then prove that abc = 1. | c c² c³-1 |
   (b) Solve x + 4y - 2z = 3, 3x + y + 5z = 7, 2x + 3y + z = 5 by Gauss elimination method. OR
   

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   (c) Solve 3x +y -z=0, 5x + 2y - 3z =2, 15x + 6y - 9z=5 by Gauss elimination method.
   (d) Define determinant of a matrix and find A^-1 if A = | 1 2 3 | | 3 2 4 | | 4 1 3 |
5. (a) Define linear and non-linear graphs with an example to each.
   (b) Find the centre and radius of the circle x² + y² + 4x + 6y + 4 = 0.
   OR
   

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   (c) Find the focus, vertex of the parabola y² = 5x + 4y +1.

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