Download OU B.Pharma 1st Year 2016 6035 Mathematics Question Paper

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Code No. 6035

FACULTY

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B. Pharmacy I Year (Main) Examination, April / May 2016

Subject : Mathematics

Time : 3 Hrs Max. Marks: 70

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

1. (a)
   1. Solve the equation for x: e^x - e^-x - 6 = 0.

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   2. In a triangle ABC, prove that sin²A + sin²B - sin²C = 4cosAcosBcosC
   OR (b)
   1. If x = 1 + log_ba; y = 1 + log_cb; and z = 1 + log_ac. Prove that xyz = xy + yz + zx.
   2. If Tan 35° + cot 37° + tan 325° = xtan 53° + tan 127° then find the value of x.
2. (a)
   1. Find the derivative of secx using first principle.

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   2. If f(x) =
      5x ; 0 < x < 1
      4x² + 3bx; 1 < x < 2
      Is continuous at every point of its domain then find the value of b.
   OR (b)
   1. Find the maximum and minimum values of the polynomial f(x) = x³ - 3x² - 6x + 6.

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   2. If u=e^mx sin(y/x) + e^nx cos(y/x) then show that x²(?²u/?x²) + 2xy(?²u/?x?y) + y²(?²u/?y²) = 0.
3. (a)
   1. Evaluate ? e^x/(1+e^x) dx.
   2. Evaluate ? v(1-ksin²x) dx.
   OR (b)
   1. Evaluate ? 1/(4+5cosx) dx.

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   2. Evaluate ? e^v(4x+12) dx.
4. (a)
   1. If A = { 5 4; 1 0; 2 2} satisfies the equation x² + 4x - p = 0 then find ‘P’.
   2. Solve the equation 2x + 4y + 5z = 18; 2x - y + 8z = 13 and 5x - 2y + 7z = 20 by matrix inversion method.
   OR (b)
   1. Find the rank of the matrix A = {4 2 4; 0 1 2; 2 1 8}.

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   2. If A = {1 2; 2 3}, B = {4 1; 3 4} and C = {0 1; 1 2} then prove that A(B + C) = AB + AC.
5. (a)
   1. Explain linear and non-linear graphs with examples.
   2. Find the equation of circle whose centre is (1, 2) and the end of diameter is (4, 6).
   OR (b)
   1. What are the basic mathematical principles are used in Biological Testing.

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   2. Find the equation of the line perpendicular to the line 2x + 3y - 5 = 0 and passing through (3, 4).