Download Pharm D 1st Year 2014 April Remedial Mathematics Question Paper

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PHARM. D DEGREE EXAMS

FIRST YEAR

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PAPER VI - REMEDIAL MATHEMATICS

O.P. Code : 383806

Time : 3 hours Maximum : 70 marks

I. Elaborate on : (2x20=40)

1. If A = 5 2 7 3 and B = 2 -1 -1 1 then prove that (AB)^T = B^TA^T.

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2. If u=sin^-1 [ (x+y) / (vx + vy) ]. Using Euler’s theorem, show that x.(?u/?x) + y.(?u/?y)= 1/2 tanu.

II. Write notes on : (10x3=30)

1. Find the determinant, A = 2 5 1 1 4 1 1 1 2
2. Show that the straight lines 2x + y - 9 = 0 and 2x + y — 10 = 0 are parallel?
3. Show that cos²A - sin²A =1 - 2sin²A.

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4. Evaluate:
   1. cos 45°cos60°- sin45°sin60°.
   2. cos48°cos12° - sin48°sin12°.
5. Find the derivative of x^{sin x} by using logarithmic differentiation?
6. Find dy/dx if y = x⁵ — 6x⁴ + 7x + 6.

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7. Integrate: ? x e ^xdx.
8. Solve dy/dx =1+x +y + xy.
9. Find the Laplace transform for t^e+10.
10. Solve: (D²+7D+12) y = e^x.

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