Download PTU B.Sc-Agriculture 2020 March 2nd Sem 72360 Mathematics ? Ii Question Paper

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Roll No. Total No. of Pages : 02
Total No. of Questions : 09

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B.Sc.(Agriculture) (2014 to 2018) (Sem.-2)
MATHEMATICS -1l
Subject Code : BSAG-205A
M.Code : 72360
Time : 3 Hrs. Max. Marks : 60

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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Q1. Write briefly :

1. Evaluate lim (tan x—sin x) / x³ as x approaches 0
2. Evaluate lim (e^x + e^-x) / (e^x — e^-x) as x approaches 0
3. Differentiate y= v(1+x) with respect to x.
4. Show that y = a sin(vx) is a solution of x(d²y/dx²) + (dy/dx) + (y/4) = 0.

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5. If y=e^cx, find y_n.
6. If the radius of a sphere is 5 cm and is increasing at 0.1 cm/sec, how fast is its volume changing?
7. Evaluate ? cotx / sin²x dx.
8. Show that ? xe^x dx = e^x(x— 1) + c.
9. Prove that ? 1/((x-1)(x-2)) dx = log((x-2)/(x-1)) + c.

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10. Evaluate ? (2 + 3sinx+5x) dx.

SECTION-B

2. Show that lim x(1 - v(1-1/x)) = 1/2 as x approaches infinity.
3. Find dy/dx for y = x^sinx
4. Find the equation of the tangent and normal to the curve y = x³ — 3x² — x + 5 at the point (3,2).

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5. Evaluate ? e^ax sin bx dx.

SECTION-C

6. Evaluate ? x / ((x-1)(x-2)) dx.
7. Evaluate ? 1 / ((x-1)(x-2)(x-3)) dx.
8. If y=tan^-1x, show that (1 +x²) y_n+2 + 2(n + 1)xy_n+1+n(n+1)y_n=0. Hence determine y_n when x = 0.

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NOTE : Disclosure of identity by writing mobile number or making passing request on any page of Answer sheet will lead to UMC case against the Student.

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