Download OU Pharm D Question Paper 1st Year 2014 7289 Remedial Mathematics

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Code No. 7289

FACULTY OF PHARMACY

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Pharm. D. I Year (Instant) Examination, January 2014

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 (10 x 2 = 20 Marks)

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1. If A= {1 0} write A².
2. If |2 3| = 1, Find the values of x and y. |3 0|
3. Eliminate ‘?’ from the equations x = a Sec ?, y = b tan ?.
4. Find the equation to the line passing through (2, 4) and parallel to x-axis.
5. Find the equation to the circle whose one end point is (2, 4) and mid point is (0,0).

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6. Find the integral of ?1/(vx) dx.
7. Define the order and degree of the differential equation and hence find the order and degree from the d.e. d³y/dx³ + (d²y/dx²)² + dy/dx + y = 0
8. Evaluate Lt _x?2 (x²-4)/(x-2)
9. Find the Laplace transform sinat.
10. If u = log (x²+y²) then find x(?u/?x) + y(?u/?y).

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PART - B(5x 10 = 50 Marks)

11. (a) If A=

    [1 -1] [x y]

    and B =

    [10 2] [a b]

    and (A+B)² = A²+B². Find x and y. (b) If A=

    [a b] [c d]

    and I=

    [1 0] [0 1]

    then show that A² — (a+d) A = (bc —ad) I.
12. (a) If tan 20° = K, show that (Tan 250° + Tan 340°)/(Tan200°-Tan110°) = (1-K²)/(1+K²) (b) Prove that 1/(Cos290° +v3Sin250°) + 1/v3 = 4/v3
13. (a) Show that Lt _?0 (tan a?)/(sin b?) = a/b. (b) If u=tan^-1( (x²+y²)/(x+y) ) then prove that x (?u/?x) +y(?u/?y) = ½ sin2u.
14. (a) Evaluate ? dx/(4+vx) (b) Evaluate ? (x²-x³) dx.

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15. (a) Solve e^xtan y dx + (1-e^x) sec²y dy = 0. (b) Solve (D²+1)y = x + sin x + x².
16. (a) If L[F(t)] = F(s) then prove that L[e^atF(t)] = F(s-a). (b) Find the Laplace transform of e^t + 2 + t sint.
17. (a) Verify (?²z)/(?x ?y) = (?²z)/(?y ?x) when z is equal to x³ + y³ — 3axy. (b) Solve (xy² + x) dx + (yx² +y) dy = 0.
18. (a) Find the equation to the circle which passes through the point (4,1), (6,5) and has the centre on the line 4x +y — 16 = 0. (b) Find the equation of the ellipse whose focus is (0,3), eccentricity is ½ and directrix is 3y—25=0.

*kk

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