Download PTU B.Sc-Hons 2020 March 1st Sem 77226 Maths I Question Paper

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Roll No. [ TTTTTT] Total No. of Pages : 02
Total No. of Questions : 11

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of EIGHT questions carrying TWO marks each.
2. SECTION-B contains EIGHT questions carrying FOUR marks each and students have to attempt any SIX questions.
3. SECTION-C will comprise of two compulsory questions with internal choice in both these questions. Each question carries TEN marks.

SECTION-A

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1. Attempt the following :
   1. Determine the value of k for which the following function is continuous at x = 3.
      S(x)=

      (x2-9)/(x-3)	x?3
      k	x=3

   2. State Lagrange’s Mean Value Theorem.
   3. Evaluate ? xexdx .
   4. Find the value of the integral ?_-p/2^p/2 sin² xdx .

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   5. If u=x^y find the total derivative of u.
   6. If Z=f(x+ct)+ f (x—ct), prove that ?²z/?t² = c²?²z/?x²
   7. Evaluate ?₀¹ ?₀¹(x² +3y²)dydx .
   8. If x = r cos ? and y = r sin ?, find the value of ?(x,y)/?(r,?)

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SECTION-B

2. Find the derivative of the function x^x.
3. Find the interval in which the function f(x) = 2x³ + 9x² + 12x + 20 is increasing.
4. Evaluate the integral ? (2x+1)/((x+1)(x-2)) dx.
5. Evaluate : ?₀^p/2 (vsinx)dx.

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6. Let f(x, y) be a function defined as f(x,y)= x²y/(x⁴+ y²) , (x,y)?(0,0). Show that lim_(x,y)->(0,0) f(x, y) is discontinuous at (0, 0).
7. If u=f(x,y), prove that x?u/?x+y?u/?y= u.
8. Evaluate ?₀⁸ ?_x⁸ e^-y2dydx by changing the order of integration.
9. Find the area bounded by the circle x² + y² = r² using polar coordinates.

SECTION-C

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10. Show that the surface area of a closed cuboid with square base and given volume is minimum, when it is a cube:
    Or
    Using definite integrals, find the area bounded by the curves y² = 4ax and x² = 4ay.
11. Find the dimensions of the rectangular box, open at the top, of maximum capacity whose surface is 432 cm².
    Or
    

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    Using triple integration, find the volume of the sphere x² + y² + z² = a².

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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