Download OU B.Pharma 1st Year 2010 7004 Mathematics Question Paper

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Code No. 7004

FACULTY OF TECHNOLOGY

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B. Pharmacy I - Year (Supplementary) Examination, March 2010

Subject : MATHEMATICS

Time : 3 Hours) (Max. Marks: 70

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

1. (a) If x = log_ba, y = log_cb and z = log_ac then show that xyz = x + y + z + 2.
   

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   (b) If sinx + siny = 1/4 and cos x + cosy = 1/3 then show that tan((x-y)/2) = and cot((x+y)/2)
   (c) If A + B + C = 180°, prove that sin A + sin B + sin C = 4 cos(A/2) cos(B/2) cos(C/2)
   OR
   (d) If 8a is not an integral multiple of p, prove that tan a + 2tan 2a + 4tan 4a + 8cot 8a = cota
   (e) If A + B + C = 180°, prove that, sin A + sin B - sin C = 4sin(A/2) sin(B/2)cos(C/2)
   

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   (f) If a cosa + b sina = c, show that a cos 2a + b sin 2a = c.
2. (a) If u = x³ + y³ + xy², find (?²u)/(?x ?y) at x=2, y=1
   (b) Compute xⁿe^x
   (c) Find dy/dx when y = logx using first principle.
   OR
   

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   (d) Find the maximum value of 2x³ - 3x² - 36x + 10.
   (e) If x = rcos?, y = r sin?, then find (?x/?r)² + (?y/?r)² and (?x/?r)(?x/?) + (?y/?r)(?y/?)
   (f) Differentiate, log(1+x²)/x⁵
3. (a) Evaluate ? x/(1+x²) dx.
   (b) Evaluate ? (x²-2)/(vx) dx.
   

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   (c) Evaluate ? v(1+sin x) dx.
   OR
   (d) Evaluate ?₀^p/2 x sinx dx.
   (e) Evaluate ? dx/(1+sinx)
   (f) Find the area bounded between the curves y² = 4ax, x² = 4by.

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4. (a) If A = [[2, 2], [-2, -1]], then show that A² - 4A - 5I = 0
   (b) Define row matrix, column matrix. Find the rank of the matrix A = [[1, 2, -1], [2, 4, -2], [-3, -6, 3]]
   OR
   (c) Solve the following equation by Gauss-Jordon method.
   3x + 4y + 5z = 18
   

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   2x - y + 8z = 13
   5x - 2y + 7z = 20
   (d) If A = [[2, 4], [-1, 2]] and B = [[3, -2], [1, 5]], then find AB and BA.
5. (a) Define Boolean algebra. Discuss the set of postulates defining Boolean algebra.
   (b) Construct logic circuit for the following Boolean function using AND / OR / NOT gates
   

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   f = (A+B)(A¯ B¯)
   OR
   (c) Show that the points (-1, 7) (3, -5) (4, -8) are collinear.
   (d) Show that the points 2i + 3j - k, i - 2j + k, 3i + 4j - 2k are coplanar.

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