Download OU B.Pharma 1st Year 2010 4404 Mathematics Question Paper

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Code No. : 4404

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1. a) If log2 [1+log3 [½+log?x]] =0, find x.
   b) If sin a= ? and a , ß are acute then find a.
   OR
   c) Prove that sin A sin(60-A) sin(60+A) = ¼ sin 3A . Hence show that sin 2p/9 sin 7p/9 sin 4p/9 = v3/8
   d) If x = 1+log_bc, y = 1+log_ca, and z=1+log_ab, prove that xyz = xy+yz+zx

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2. a) Show that (x^-1)^x-1 = 1
   b) Find the maximum and minimum values of f(x) = x³+1/x
   OR
   c) If u= x³+y³+z³ - 3xyz show that x ?u/?x + y ?u/?y + z ?u/?z = 0.
   d) Prove that x³-3x²+3x+7=0, has neither maximum nor minima.

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3. a) Evaluate ? x(1+logx) dx
   b) Evaluate ? x²/(1+x) dx
   OR
   c) Evaluate ? sin x/(x + cosx) dx
   d) Evaluate ? sin x cos x/(1+ sin x) dx

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4. a) Define Rank of the matrix and hence find the rank of the matrix,
   A =

   1	2	3	4
   2	4	6	8
   3	6	9	12

   
   b) Solve the system of equations
   2x -y + 8z=13; 3x +4y +5z =18 and 5x -2y + 7z = 20 by Gaussian elimination method.
   OR
   

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   c) Solve the system of equations
   x+2y+3z=4, 2x+3y+5z=15, 3x + 4y + 6z = 12 by matrix inversion method.
5. a) Define linear and non-linear correlation.
   b) From the data given below find the coefficient of correlation. n=8, Sx=12, Sy=20, Sx²=90, Sy²=120, Sxy=65 where x y are deviations from arithmetic average.
   OR
   

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   c) If A =

   1	2	3
   -1	4	2
   1	0	2

   and B =

   2	3
   -1	1
   4	2

   , then find AB.
   d) Fit the curve of the form y = ab^x to the following data:

   x	0	1	2	3	4	5	6	7
   y	30	25	19	16	13	10	8	7

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