Download OU Pharm D Question Paper 1st Year 2020 6179 Remedial Mathematics

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Code No. 6179

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FACULTY

Pharm. D. (6 YDC) I-Year (Instant) Examination, February 2020

Subject: Remedial Mathematics

Time: 3 Hours Max. Marks: 70

Note: Answer all questions from Part A, Answer any five questions from Part B.

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PART-A (10x2 = 20 Marks)

1. If A = 1 4 5 1 and B = 6 1 2 5 , find 2A - 3B.
2. If 1 2 2 x = 0, find x.
3. Find the distance between the points (0,-2) and (-1,0).
4. Find the centre and the radius of the circle x² + y² - 4x - 2y - 5 = 0.

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5. Evaluate ? Tan x dx.
6. Find the order and degree of the differential equation d²y/dx² = 1 + (dy/dx)³.
7. Find lim_x?3 (7x³ + 4x² + 3x).
8. Solve dy/dx = Sec (x + y).
9. Find the Laplace transform of {cos at}.

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10. If u = 2x²y - y³ - 4, find ?u/?x and ?u/?y.

PART-B (5x10=50)

11. (a) If A = 1 2 4 2 2 1 1 2 1 show that A³ - 4A - 5I = 0.
    (b) Show that 1 1 1 a b c a3 b3 c3 = (a-b)(b-c)(c-a)(a+b+c)
12. (a) If sin a = 4/5 and sin ß = 5/13 then find the value of sin (a + ß), Cos (a + ß)
    

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    (b) Eliminate ? from x = a Sec ?, y = b Tan ? , Prove that x²/a² - y²/b² = 1
13. (a) Find the equation of the circle passing through the points (0,2) (3,0) (3,2)
    (b) Find the equation of the parabola whose Focus is (-1, 1) and directrix is x+y+7=0
14. (a) If u = sin^-1(x²+y²)/(x+y), then show that x(?u/?x) + y(?u/?y) = Tan u.
    (b) Find dy/dx if y = x²/(1 + log x)

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15. Evaluate ? x²sin 3x dx.
16. (a) Solve (e^x + 1)ydy = (y + 1) e^x dx.
    (b) Solve dy/dx = x + y/xy
17. (a) Find the Laplace transforms of (2t² - 3t + 4).
    (b) Find the Laplace transforms of cos 3t.sin² 2t .

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18. (a) Find the equation of the circle whose centre is (-2, 3) and passing through the centre of the circle x² + y² - 6x + 4y + 9 = 0
    (b) Show that lim_x?2 (x² - 4)/(x - 2) = 4

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