Download PTU B.Sc-Hons 2020 March 1st Sem 76930 Elementary Mathematics Question Paper

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Roll No. EEEEEEEEEEN Total No. of Pages : 02

Total No. of Questions : 09

B.Sc. (Hons)Agriculture (2019 Batch) (Sem.-1)

ELEMENTARY MATHEMATICS

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Subject Code : BSAG-106-19(B)

M.Code : 76930

Time : 3 Hrs. Max. Marks : 60

INSTRUCTIONS TO CANDIDATES :

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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

1. Write briefly :
   1. If the angle between two lines is ? and slope of one of the lines is m, find the slope of the other line.

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   2. Find the equation of a line perpendicular to the line x — 2y — 3 = 0 and passing through the point (1, —1).
   3. Find centre and radius of the circle with equation x² + y² + 8x + 10y — 8 = 0.
   4. Evaluate lim_x?0 (1+x -1)/x.
   5. Find dy/dx for y=(x+1)/(x-1)
   6. If A=[2 3; 1 4] and B=[1 -2; 1 3], then verify that (AB)^T=B^TA^T.

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   7. Evaluate ? sinx/cos²x dx
   8. For A=[1; 2; 3] and B=[2 3 4], find AB and BA.
   9. Differentiate y = xe^x with respect to x.
   10. Evaluate ? (e^x - e^-x)/(e^x + e^-x) dx

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SECTION-B

1. Find the area of a triangle with vertices (4, 4), (3, —2) and (-3, 16).
2. Find the derivative of f'(x) using the first principle where f (x) = sin x.
3. Evaluate ? e^x sin x dx.
4. Find ½(A+A^T) and ½(A-A^T) when A=[0 a b; -a 0 c; -b -c 0].

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5. Prove that |b+c a a; b c+a b; c c a+b| = 4abc.

SECTION-C

1. Find the condition that the line y = mx + c is tangent to the circle x² + y² = a².
2. If y = sin^-1 x, show that (1 — x²) d²y/dx² — x dy/dx = 0.
3. Find inverse of the matrix A = [3 2 3; 2 1 -1; 4 -3 2].

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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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