Download OU Pharm D Question Paper 1st Year 2019 13279 Remedial Mathematics

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Code No. 13279

FACULTY

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Pharm. D. (6 YDC) I-Year (Main & Backlog) Examination, July 2019

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)

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1. If A = $\left[\begin{array}{c}1\\ 3\end{array}\right]$ and B = $\left[\begin{array}{ccc}1& 6& 7\end{array}\right]$ find AS
2. Find the value of $\frac{\mathrm{Tanx}}{\mathrm{Secx}}/\frac{\mathrm{Secx}}{\mathrm{Tanx}}$
3. Find the value of 'a' if the distance between the points (a, 2) and (3, 4) is v8 units.
4. Find the centre and the radius of the circle 2x² + 2y² - 8x - 12y - 3 = 0
5. Evaluate ?Secx dx

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6. Find the order and degree of the differential equation $1+{\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)}^2=7\frac{d^{2}y}{d{x}^2}$
7. Find lim (3x³ + 2x² + x) as x approaches 2
8. Solve dy/dx = (x + y)²
9. Find the Laplace transform of e^t/t
10. If z = 2xy + y² - 3, find ?z/?x and ?z/?y

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PART-B (5x10=50)

11. (a) If A = $\left[\begin{array}{cc}3& -5\\ -4& 2\end{array}\right]$ show that A² - 5A = 14I
    (b) Show that $\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^2& b^2& c^2\end{array}\right|$ = (a - b)(b - c)(c - a) 10M
12. (a) Sin? = 3/5 and ? is acute, find the value of 2Tan? + 3Sec? + 4Sec?.Cosec?
    (b) Eliminate ? from x = a cos?, y = a sin ? show that x² + y² = a² 10M

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13. (a) Find the equation of the circle passing through the points (1,1) (-2,2) (-6,0)
    (b) Find the equation of the parabola whose Focus is (-1,1) and directrix is x + y + 1 = 0 10M
14. (a) If u = (x³ + y³)/(x - y) then x(?u/?x) + y(?u/?y) = Sin2u
    (b) Find dy/dx if y = (x² - 3x + 5)/(x² + 3x + 5) 10M
15. (a) Evaluate ? 1/(1+cot x) dx
    

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    (b) Evaluate ?x³e^2xdx 10M
16. (a) Solve (x+1)dy/dx + 1 = 2e^-y
    (b) x² dy/dx = x² + xy + y² 10M
17. (a) Find the Laplace transforms of e^-3t (2 cos 5t – 3 sin 5t)
    (b) Find the Laplace transforms of e^-4t + 3e^-2t 10M

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18. (a) Find the equation of the circle whose centre is (-3, 1) and passing through the centre of the circle x² + y² + 2x – 4y + 4 = 0
    (b) Show that lim (Tan (x-2))/(x²-4) as x approaches 2 = 1/4 10M

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