Download SGBAU B-Pharma 2019 Summer 1st Year Mathematics n Statistics New Question Paper

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B.Pharm. - I (New)

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35007 : Mathematics & Statistics : I-T-7

AW -2262

Max. Marks : 80

Pages: 2

Time : Three Hours

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Notes:

1. All questions carry equal marks.
2. Answer any eight questions.
3. Use of slide rule logarithmic tables, Steam tables, Mollier's Chart, Drawing instrument, Thermodynamic table for moist air, Psychrometric Charts and Refrigeration charts is permitted. Use of simple calculator is permitted.
4. Use of pen Blue/Black ink/refill only for writing the answer book.

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1. Solve the following any two.
   1. Evaluate lim (x² + 5) / (x² + 3) as x approaches 0.
   2. Evaluate lim (5^x - 3^x) / x as x approaches 0.
   3. Evaluate lim (1 - sin(x)) / (2 - csc(x)) as x approaches p/6.
2. Solve the following.
   1. If f(x) = (1 - cos(Kx)) / x for x ? 0 and f(x) = 8 for x = 0. Is continuous at x = 0 then find K.

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   2. If f(x) = (3 / (x tan x)) for x ? 0 and f(x) = t for x = 0. Then discuss the continuity at x = 0.
3. Solve the following
   1. Find derivative of cos x w. r. t. x by first principle of derivatives.
   2. If y = x⁴ + a⁴ + x² + a² find dy/dx.

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4. Solve the following
   1. If y = (sinx)^x find dy/dx.
   2. If x = a sin t, y = a cos t find d²y/dx².
5. Solve the following any two parts.
6. Solve the following any two.
   1. Evaluate ? (sec²(log x)) / x dx

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   2. Evaluate ? x e^x dx from 0 to 1.
7. Prove that ? (1 / (1 + cotx)) dx from 0 to p/2 = p/4
8. Solve the following.
   1. Find the order & degree of (d³y/dx³) = v(4 + (dy/dx)).
   2. Form a differential equation by eliminating the arbitrary constants A & B from y = Ae^mx + Be^-mx.

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9. Solve the following.
   1. Find L[e^t]
   2. Find L[t cos3t]
10. Solve the following
    1. Find mean, mode & median from the following data.

       Class:	0-10	10-20	20-30	30-40	40-50
       Frequency:	8	12	20	8	2

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    2. Write short note on following.
       1. Histogram
       2. Pi diagram
11. Find the coefficient of correlation between X & Y from the following data.

    X	Y
    6	8
    10	11
    12	12
    13	14

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