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

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FACULTY OF PHARMACY

B. Pharmacy I-Year (Main & Backlog) Examination, June 2011

MATHEMATICS

Time : Three Hours] [Maximum Marks : 70

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

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1. (A) (i) If sin a = 1/3, sin ß = 1/5 and a, ß are acute then show that a+ß = p/2.
   (ii) If tan A = 1/2 and tan B = 1/3 where A and B are acute angles then find A + B.

   OR

   (B) (i) If sin A - sin (60 + A) sin (60 — A)= 1/4 sin 3A.
   (ii) Prove that 4 sin 20° sin 40°sin 60° sin 80° = 3/16
2. (A) (i) Find the derivatives of the following function tan 2x using first principle.
   

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   (ii) If U = sec^-1((x⁵+y⁵)/(x+y)) then show that x ?u/?x + y ?u/?y = 4 cotu.

   OR

   (B) (i) If f(x) is given by f(x) = { Kx² if x = 2; 3 if x > 2 } is a continuous function on R, then find the value of K.
   (ii) Prove that x⁵ + 3x³ + 3x + 7 = 0, has neither maxima nor minima. (iii) Show that f(x) = sin x (1 + cos x) has a maximum value at x = p/3.
3. (A) (i) Find the value of ? (cos x + 3 sin x + 7) / (cos x + sin x + 1) dx.
   (ii) Evaluate ? (2 sin x + 3 cos x) / (3 sin x + 4 cos x) dx.
   

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   (iii) Evaluate ?₀^p/2 x cos x dx

   OR

   (B) (i) Evaluate ? v(1+sinx)/(x+cosx) dx
   (ii) Evaluate ? (2x+3) / (x² +x -2) dx
   (iii) Evaluate ? sec^-1x cosec^-1x dx .
4. (A) Show that | a² a b c |
   

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   | b² b c a | = (a—b) (b-c) (c — a) (ab + bc + ca)
   | c² c a b |
   
   (B) Show that | a+b+2c a b |
   | c b+c+2a b | = 2(a+b+c)³
   

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   | c a c+a+2b |

   OR

   (B) (i) Solve the following equations by Gauss-Jordan method :
   3x+4y+5z=18, 2x — y + 8z =13, 5x — 2y + 7z =20.
   (ii) If A = | 2 1 2 |
   | 0 -1 0 | then find A⁴ - 3A³ - A + 3I.
   

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   | 3 -1 1 |
5. (A) (i) Discuss the set of Postulates defining Boolean Algebra.
   (ii) Find the eccentricity, co-ordinates of foci, length of latus rectum and equations of directrices of the ellipse.
   9x² + 16y² - 36x + 32y - 92 = 0.

   OR

   (B) (i) Find the intercepts of the plane 4x + 3y + 2z + 2 = 0 on the co-ordinate axes.
   

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   (ii) Write Boolean function to realize the full adder and draw the corresponding logic diagram.

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