Download OU Pharm D Question Paper 1st Year 2018 1105 Remedial Mathematics

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Code No. 1105

FACULTY

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Pharm D (6-YDC) I – Year (Instant) Examination, March 2018

Subject: Remedial Mathematics

Time: 3 Hours

Max.Marks: 70

Note: Answer all questions from Part – A. Any Five questions from Part – B.

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PART – A (10x2 = 20 Marks)

1. If A =

   -2	1
   -1	4

   and B =

   5	0
   4	0

   -2	3	1
   2	0	2

   then find A +2B'.
2. Find the distance between (a cosa, a sina ) and (0, 0).
3. If sin A = 3/5 then find cos A + tan A.
4. Find dy/dx if y = (ax+b)ⁿ.

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5. Find ? log x dx.
6. Find the order and degree of differential equation d²y/dx² + (dy/dx)² + y = x².
7. Find Laplace transform of e^t sin t.
8. Find the center and radius of the circle 3x² + 3y² - 6x + 12y + 3 = 0.
9. Find the lim _x->2 (x² - 4)/(vx² + 5 - 3)

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10. If Z = yx²z + xy² then find ?z/?x and ?z/?y

PART - B (5x10 = 50 Marks)

1. a) Show that

   1	a	a2
   1	b	b2
   1	c	c2

   = (a-b) (b-c) (c-a).
2. b) If

   2x+1	0
   2y + 4	0

   =

   3	0
   8	0

   then find x and y.
3. a) If tan A = 5/12 then find tan (A+B).

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4. b) If x = r cos ? cos a, y = r cos ? sin a and z = r sin ? then find x² + y² + z².
5. a) Find the equation of the circle passing through (0, 0), and having center at (-4, -3).
6. b) Find the vertex and focus of 4y² + 12x – 20y + 67 = 0.
7. a) Find lim _x->1 tan (x - 1)/(x²-1)
8. b) Using Euler's theorem show that x ?u/?x + y ?u/?y = 1/2 tan u for the function u = sin^-1 (x+y)/(vx + vy)

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9. a) Evaluate ? e^x(1+x)/cos²(xe^x) dx.
10. b) Evaluate ?₀^p/2 1/(1+ sin x) dx.
11. a) Solve dy/dx = (1+y²)/(1+x²)
12. b) Solve (x³ – 3xy²) dx + (3x²y - y³ )dy = 0.
13. a) Find the Laplace transform of e^-2t + t² + cos 3t.

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14. b) Find the Laplace transform of e^-t cos²t.
15. a) Solve cos² x dy/dx + y = tan x
16. b) If x³ + y³ = 3axy then prove that d²y/dx² = (2a²xy)/(y²-ax)³

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