Download OU B.Pharma 1st Year 2012 6504 Mathematics Question Paper

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Code no.: 6504/M

FACULTY OF PHARMACY

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B.Pharmacy 1 Year (Main) Examination, June 2012

MATHEMATICS

Time : 3 Hours] [Max. Marks : 70

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

1. a) 1) If ax = by = cz and y² = zx, prove that log_ba = log_ch.
   

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   2) Prove that A + B = 45° <=> (1 + tan A) (1+ tan B) = 2. Hence show that tan 22.5° = v2 - 1
   OR
   b) 1) If (3.4)^x = (0.034)^y = 10000 find the value of (1/x) - (1/y).
   2) In a triangle ABC, prove that Sin 2A + Sin 2B - Sin 2C = 4 Cos A Cos B Sin C.
2. a) 1) Prove that (x²+8x+15) / (x²+3x-10) * (2x² - 3x + 1) / (2x² + 7x + 3) = (x-1) / (x-2)
   

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   2) Find dy/dx if x=acos?, y=bsin?.
   OR
   b) 1) Using first principle find the derivative of sinx.
   2) Find the maximum and minimum values of f(x) = x³ - 6x² + 9x + 15.
3. a) 1) Evaluate ? (1 / (3+5x-2x²)) dx
   

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   2) Evaluate ? (2x+3) / (3x²+14x -5) dx
   OR
   b) 1) Evaluate ? (1 / (5+4cosx)) dx
   2) Evaluate ? (1 / ((2x + 3)v(x + 2))) dx
4. a) 1) If A=

   6	2	-2
   -2	2	-2
   2	2	2

   show that (A-2I) (A-4I)=0.
   

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   2) Find the rank of

   1	2	3
   1	2	3
   3	2	1

   
   OR
   b) 1) Show that

   b+c	c+a	a+b
   a+b	b+c	c+a
   a	b	c

   = a³+b³+c³ - 3abc
   2) If A=

   2	-2
   -3	5

   show that A²+ 3A-10I=0.
5. a) 1) Find the equation of line passing through the point (2, -3) and having intercepts whose ratio is 3 : 2.
   

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   2) Show that the points (- 6, 0) (-2, 2), (-2, - 8) and (1, 1) are concyclic.
   OR
   b) 1) Find the equation of line dividing the line segment joining (2, 3), (4, - 5) in the ratio 2 : 3 and having slope - 3.
   2) Find the circle which passes through (-1, 2), (- 4, 5) and has its centre on the line x + 2y = 0.

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