Download OU Pharm D Question Paper 1st Year 2017 4255 Remedial Mathematics

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FACULTY OF PHARMACY

Pharm. D (6 YDC) I-Year (Main) Examination, July 2017

Subject: Remedial Mathematics Max. Marks: 70

Time: 3 Hours

Note: Answer all questions from Part - A and answer any five questions from Part-B.

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PART – A (10 x 2 = 20 Marks)

1. If A = $\left[\begin{array}{cc}1& 2& 0& -1\end{array}\right]$ and B = $\left[\begin{array}{cc}0& -1& 2& 3\end{array}\right]$ then find AB'.
2. Find the slope of the line joining points (2, 5) and (- 4, 6).
3. If cos A = ¹²/₁₃ then find cot A.
4. If y = (3x² + 2x + 1)^1/3 find ^dy/_dx.

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5. Find ?₀^p/2 cos² x dx.
6. Find order and degree of the differential equation ^d³y/_dx³ + (^d²y/_dx²)² + (^dy/_dx) + y = 0.
7. Find the Laplace transform of cos²t.
8. Find the center and radius of the circle x² + y² + 2x - 4y + 5 = 0.
9. Find lim _x?-7 ^2x²-98/_x+7.

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10. If u = 3xy - y³ + (y² - 2x)^1/2 then find ^?u/_?x.

PART-B (5 x 10 = 50 Marks)

1. (a) Show that $\left|\begin{array}{ccc}a& a²& bc& b& b²& ca& c& c²& ab\end{array}\right|$ = 0.
2. (b) If A = $\left[\begin{array}{cc}2& 1& -6& -1\end{array}\right]$ and B = $\left[\begin{array}{cc}1& 2& 0& -1\end{array}\right]$ Then find C such that A + B – C = 0.
3. (a) sin A = 8/17 then find cos (A + B).

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4. (b) Simplify v(1+ tan² A) / v(1+ cot² A)
5. (a) Find the equation of the circle passing through (1, 1), (2, 1) and (3, 2).
6. (b) Find the value of k if the line 2y = 5x + k is a tangent the parabola y² = 6x.

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14. (a) lim _x?2 (2x² + 3a + 5) = 3 then find 'a'.
15. (b) If z = log (tan x + tany) then show that sin 2x ^?z/_?x + sin 2x ^?z/_?y = 2
16. (a) Evaluate ? cot x / log(sin x) dx.
17. (b) Evaluate ? x² / 1+x dx.
18. (a) Solve (x² + y³)dx = 2xydy

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19. (b) Solve ^dy/_dx = ^2y/_1+x
20. (a) Find the Laplace transform of e^tsin²t .
21. (b) Find the Laplace transform of t² + e^tsint + e^t cost
22. (a) If u = tan^-1(^x/_y) then find x ^?u/_?x + y ^?u/_?y
23. (b) Solve ^dy/_dx = ^y²/_x²

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