Download OU Pharm D Question Paper 1st Year 2018 1242 Remedial Mathematics

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FACULTY

Pharm D (6 – YDC) I – Year (Main & Backlog) Examination, July 2018

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Subject: Remedial Mathematics

Time: 3 Hours Max.Marks: 70

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

PART – A (10x2 = 20 Marks)

1. If A =

   1	-1
   0	3

   and I =

   1	0
   0	1

   , find AI.

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2. If

   0	2a
   3b	0

   =

   0	6
   9	0

   then find a and b.
3. Find the slope of the joining points (x₁, y₁) and (x₂, y₂).
4. Find the center and radius of (x-a)² + (y-b)² = r².
5. Evaluate ?₀^p/2 sin x dx.
6. Find the order and degree of differential eqn. y" + (y')² + 5y = x².

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7. Solve x²dx + (1/y)dy = 0.
8. Find lim_x?1 (x²-2x+1)/(x-1)
9. Find the Laplace transform of f(t) = t² + e^3t.
10. Find ?u/?x and ?u/?y and ?u/?z if u(x, y, z) = x² + xyz.

PART – B (5x10 = 50 Marks)

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11. a) If A =

    1	0
    0	1

    and B =

    1	1
    0	-1

    then find (sin ?)A + (cos ?)B.
    b) Show that

    a2 + 2a	2a +1	1
    2a +1	a+2	1
    3	3	1

    = (a-1)³.
12. a) If (A+B) = p/4 then prove that (1+tan A) (1+ tan B) = 2.
    b) If sin A = 12/13 and cos B = 3/5 then find sin² A + cos² A and sin² B + cos² B.
13. a) Find the radius and center of the circle x² + y² + 2ax – 2by + b² = 0.
    

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    b) Find the coordinates of vertex and focus and directors of the parabola y² = 25x.
14. a) If lim_x?1 (ax² + x + 5)/(x² + x - 2) = 3 then find value of a.
    b) If u = sin^-1 (x³ - y³)/(x + y) then find x ?u/?x + y ?u/?y
15. a) Evaluate ? log x dx.
    b) Evaluate ?₀^p/4 (x tan^-1 x)/(1+x²) dx.

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16. a) Solve dy/dx = (1+y²)/(1+x²).
    b) Solve dy/dx = e^ax+by.
17. a) Find the Laplace transform of e cos² t.
    b) Show that L[af(t)+bg(t)] = aL[f(t)] + bL[g(t)].
18. a) Show that lim_x?2 (tan(x - 2))/(x² - 4) = 1/4
    

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    b) Evaluate ? x² e^x dx.

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