Download OU Pharm D Question Paper 1st Year 2016 6117 Remedial Mathematics

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Code No. 6117

FACULTY

Pharm D (6 – YDC) I – Year (Main / Backlog) Examination, August 2016

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Subject: Remedial Mathematics

Time: 3 Hours Max.Marks: 70

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

PART – A (10x2 = 20 Marks)

1. If A = $\left[\begin{array}{cc}-1& 3\\ 2& 3\end{array}\right]$ and B = $\left[\begin{array}{cc}3& -1\\ 3& 2\end{array}\right]$ , find AB^T.

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2. If , find x.
3. Find the slope of the line joining points (1, 2) and (-3, -4).
4. Find the centre and radius of the circle x²+y²-6x+1 = 0.
5. Evaluate ?₀¹ xe^x dx.
6. Find the order and degree of differential equation (d²y/dx²) + (dy/dx) + y = 0.

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7. Find Lim _x?1 (x²-1)/(x-1)
8. Solve y dx + x dy = 0.
9. Find the Laplace transform of 5e^2t + e^5t.
10. If z = x²+log (1+y²), find ?z/?x and ?z/?y.

PART – B (5x10 = 50 Marks)

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11. a) Show that .
12. b) If A = , B = and A + B – C = 0, then find C.
13. a) If sin A = 3/5 and sin B = 5/13, then find sin (A+B).
14. b) If x = r cos? cosa, y = r cos? sina and z = r sin?, then find x²+y²+z².

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Code No. 6117

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13. a) Find the equation of the circle passing through (3, 4), (3, 2) and (1, 4).
14. b) Find vertex and focus of x²-6x-6y+6 = 0.

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15. a) Show that Lim _x?1 sin(x-1)/(x²-1) = 1/2.
16. b) If u = sec^-1(x+y), then show that x ?u/?x + y ?u/?y = 2 cot u.
17. a) Evaluate ?₀^p/2 x sin^-1 x / v(1-x²) dx.
18. b) Evaluate ?₀^p/3 cos x / (3 + 4 sin x) dx.
19. a) Solve dy/dx + y tan x = sin x.

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20. b) Solve dy/dx = (x+y)/(x+y).
21. a) Find the Laplace transform of e^2t + 4t³ – 2 sin 3t.
22. b) Find the Laplace transform of e^t sin² t.
23. a) Solve dy/dx = (log x + 1) / (sin y + y cos y).
24. b) If Lim _x?0 x (1+a sin x) = 1, then find 'a'.

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