Download OU B.Pharma 1st Year 2011 6504 Mathematics Question Paper

Code No.: 6504

FACULTY OF PHARMACY

B.Pharmacy I Year (Supplementary) Examination, December 2011

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MATHEMATICS

Time : 3 Hours] [Max. Marks : 70

Answer all questions.

All questions carry equal marks.

1. (a) (i) If log₂(^2b/_c) = a, log₂(^c/_5a) = b, and a³b⁵c^p = 1, find the value of P.
   

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   (ii) If tanA = 1/2 and tanB = 1/3, where A and B are acute angles then find A+B.
   Or
   (b) (i) If 2log_xa + log_axa + 3log_a²xa = 0, find x.
   (ii) sinA.sin(60+A)sin(60 - A) = ¼sin3A.
2. (a) (i) Find the derivative of the function cos ax using first principle.
   

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   (ii) Show that f(x) =
   { (cos ax - cos bx) / x², if x ? 0
   { b² - a² / 2, if x = 0
   where a and b are real constants, is continuous at 0.
   (iii) Solve 5x= sin(x + y) + cos(x +y).
   

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   Or
   (b) (i) Show that f'(x) = sin x (1+ Cos x) has a maximum value at x = p/3
   (ii) If u = Sec^-1(^{X -y}/_{X +y}) then show that
   X (?u/?x) + Y (?u/?y) = 0
3. Find the value of
   

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   (i) Evaluate ? (9 cos x - sinx) / (4+ 5 sin x) dx
   (ii) Evaluate ? (x²e^x3) dx
   (iii) Evaluate ? (sin x) / (X + cos x) dx
   (iv) Evaluate ? (sin2x) / (acos x + 1) dx
   (v) Evaluate ? (x⁵ -1) / (1+ x²) dx for x?(-1,1)

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4. (a) (i) If A = | 1 -1 1 | then show that A³ - 6A² + 5A + 11I = 0
   | 2 1 -3 |
   | 3 -3 4 |
   Or
   (b) Solve the following equations
   

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   3x+ 4y + 5z= 18
   2x-y + 8z=13
   5x-2y+ 7z=20
5. (a) (i) Find the equation of the line passing through (2, 0) (0, 3).
   (ii) If a line makes an angle of 60° with positive x - axis, what is its slope.
   

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   (iii) Discuss the set of postulates defining Boolean Algebra.
   Or
   (b) (i) Write Boolean function to realize the full adder and draw the corresponding logic diagram.
   (ii) Find the equation of the circle passing through the origin 0 (0,0) and the points (1, 2), (-1, -2)

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