Download SGBAU B-Pharma 2019 Summer 2nd Sem Sem II Mathematics Old Question Paper

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B.Pharm. Second Semester (Old)

35148 : Mathematics : 2.6

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Pages : 3

Max. Marks : 60

Time : Three Hours

Notes:

1. All questions carry equal marks.

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2. Answer any five questions from given 7 questions.
3. Use of slide rule logarithmic tables, Steam tables, Moller's Chart, Drawing instrument, Thermodynamic table for moist air, Psychrometric Charts and Refrigeration charts is permitted. Use of calculator is permissible.
4. Use of pen Blue/Black ink/refill only for writing the answer book.

1. Attempt any three of following.
   1. Prove that sec² ?(1 — sin² ?) — 2tan²? = 1
   2. Area of circular sector of radius 12cm is 43.2 sq. cm find it's perimeter.

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   3. Evaluate lim _x?0 (e^x - 1 - x) / x
   4. Evaluate lim _x?p/2 (sin x - 1) / (p - 2x)²
2. A) Evaluate any two of following.
   1. Find d/dx if y = x⁴ + 3^x + x³ + 33
   2. Find dy/dx if y = (sin x)^logx

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   3. Find dy/dx if x = acos³?, y = asin³?
   B) Attempt any one of following.
   1. If f(x) = (1 - cos Kx) / x when x ? 0 = 1/2 when x = 0 is continuous at x = 0 then find K.
   2. Examine the function for maxima & minima where f(x) = x³ - 6x² + 12x - 8.
3. Evaluate any three of following.
   1. If f(x) = (vx + 9 - 5) / (x - 4) for x = 4 = 2/40 for x = 4 is continuous or discontinuous at x = 4 check.

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   2. Find derivative of e^x by first principle w.r.t x.
   3. y = sinvx find dy/dx
   4. Evaluate ? e^4xdx / (e^4x + 5)
4. Evaluate any two of following.
   1. Evaluate ?₀^p/2 dx / (1 + tanx)

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   2. Find area of circle x² + y² = a² using definite integration.
   3. Solve the D. E. dy/dx = (x - e^x) / (y + e^y)
5. A) Attempt any two of following.
   1. Form the differential equation by removing arbitrary constants from y = Ae^x + Be^x
   2. Three coins are tossed simultaneously find probability that of getting
      1. at most two tails.

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      2. at least two tails.
   3. If P(A) = 1/4, P(B') = 1/3 find P(AnB) when A & B are independent events.
   B) Evaluate any one of following.
   1. If P(A) = 0.7, P(B) = 0.7, P(A/B) = 1 find P(A/B) & P(AUB).
   2. If A & B are any two events from sample space S then prove that
      1. P(AUB) = P(A) + P(B) - P(AnB)

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      2. P(A) + P(A') = 1 where A & A’ are complements of each other.
6. Write short notes on :
   1. Bar diagram.
   2. Pie diagram.

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   B) Attempt any one of following.
   1. Find mean, S. D. & coeff. of variation from data.

      Class	0-10	10-20	20-30	30-40	40-50
      Frequency	8	15	22	15	8

   2. Find mean, mode & median from data.

      Class	0-10	10-20	20-30	30-40	40-50	50-60
      Frequency	5	10	20	9	6	2

7. Attempt any one of following.
   1. Calculate the coeff. of correlation between X & Y from the following data.

      X	12	9	8	10	11	13	7
      Y	14	8	6	9	11	12	3

   2. Find standard error S_y i.e. error of estimation on y from following data.

      X	54	58	52	46	49	51	57	53	40	50
      Y	34	36	40	50	52	48	46	44	56	64

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