Download OU B.Pharma 1st Year 2012 2654 Mathematics Question Paper

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Code No. 2654

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FACULTY OF PHARMACY

B. Pharmacy I Year (Suppl.) Examination, Oct./Nov. 2012

MATHEMATICS

Time: 3 Hours] [Max. Marks: 70

Note : Answer all questions.

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All questions carry equal marks.

1. a) i) If $\frac{x}{a(b-c)} = \frac{y}{b(c-a)} = \frac{z}{c(a-b)}$, show that $x^ay^bz^c = 1$.
   ii) Prove that $\sin^{-1}(\frac{2}{3}) + \log_e 5 - \tan^{-1}(\frac{3}{4}) = 1$
   OR
   b) i) If $\tan \theta = \frac{a}{b}$, find $\frac{2asin\theta + bcos\theta}{asin\theta - bcos\theta}$

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2. a) i) Find the derivative of the function.
   ii) If f(x) = x²sin(1/x) when x? 0 and f(0) = 0, show that f is derivable for every value of x but the derivative is not continuous for x = 0.
   OR
   b) i) Find the extreme values of f(x) = 5x⁶ + 18x⁵ + 15x⁴ - 10.
   ii) If u = ax + by + cz and $\frac{\partial u}{\partial x} + \frac{\partial u}{\partial y} + \frac{\partial^2 u}{\partial z^2} = 0$, find the value of a.

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3. a) i) Evaluate $\int_1^e \frac{dx}{x(1+logx)}$
   ii) Evaluate $\int \frac{e^{ax}}{x} dx$
   OR
   b) i) Evaluate $\int \sin(log x) dx$
   ii) Evaluate $\int \frac{x^2 + 2x + 5}{(x + 2)(x - 1)(3x - 1)} dx$

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4. a) i) Define rank of the matrix. Find the rank of the matrix A = 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1
   ii) If A = 1 & 2 & 3 \\ 1 & 1 & 2 \\ 3 & 1 & 3 , find A^-1.
   OR
   b) i) Solve, with the help of matrices, the simultaneous equations x - y + z = 3; x + 2y + 3z = 4; x + 4y + 9z = 6.
   ii) By using the Gauss elimination method, solve the system of equations 2x + y + 4z = 2; x + 3y - 2z = 7; 5x + 3y - 5z = -8.

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5. a) i) Find the equation of the straight line passing through the point (-2, 1) and parallel to 4x - 7y + 3 = 0.
   ii) Derive the equations of straight line and explain the equation y = mx + c. How do you determine m. What is the importance of m and c in biological data interpretation.
   OR
   b) i) Explain about various linear and non-linear graphs and their importance in representing biological data and their comparison.
   ii) Find the equation of the circle passing through the point (3, -4) and concentric with x² + y² + 4x - 2y + 1 = 0.

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