Download PTU B.Tech 2020 March Biotechnology 2nd Sem BTAM 207 Basic Mathematics Ii Question Paper

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Roll No. Total No. of Pages : 03
Total No. of Questions : 09

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B.Tech. (Bio Tech) (2018 & Onwards) (Sem.-2)
BASIC MATHEMATICS-II
Subject Code : BTAM-207-18
M.code : 76258
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 & C have FOUR questions each. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
3. Select atleast TWO questions from SECTION - B & C.

SECTION-A

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1. Answer the following :

1. Define an onto function, also give an example of an onto function.
2. Find the domain of the function f(x) = log(sinx), € 0 < x < 2p.
3. Give an example of a function which is continuous but not differentiable.
4. Find the derivative of xⁿ with respect to x.

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5. Find partial derivative of f w.r.t. x, if f (x, y) = xy / (xy+cosx).
6. Solve ? log x dx.
7. Evaluate the integral ? e^x sin x dx.
8. Form a differential equation representing the family of curves y = mx where, m is arbitrary constant.
9. Form a differential equation whose order is 2 and degree is 3.

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10. Define a homogeneous function of degree n also give one example of a homogeneous function of degree 2.

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SECTION-B

2. a) Find all points of discontinuity of the function defined by f(x) = x, if x?0
   0, if x=0
   

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   b) Differentiate tan^-1(sinx / (1+cosx)) w.r.t x.
3. Differentiate the function x^sinx + (sin x)^x w.r.t. x.
4. a) Find the interval in which the function f (x) = x³ - 4x² is increasing and decreasing.
   b) Find maxima and minima, if any, of the function f(x) =sinx + cos x, 0 <x < p/2.
5. a) Show that the function f(x,y) = x²y / (x⁴+ y²) if (x,y)?(0,0) and 0 if (x,y)=(0,0) is not continuous at (0, 0), also check whether its partial derivatives f_x and f_y exist at (0, 0).
   

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   b) Find the local extreme values of the function F(x, y) = 4x² - 6xy + 5y² - 20x + 26y

SECTION-C

6. a) Find the area lying above x-axis and included between the circle x² + y² = 8x and inside of the parabola y² =4x.
   b) Solve the integral ? x / (1-x⁶) dx.
7. a) Evaluate ? (xsinx) / (1+cos² x) dx.
   

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   b) Evaluate ? (3sin?-2)cos? / (5-cos²?-4sin?) d?.
8. Solve the differential equation (x dy-ydx)ysin(y/x) =(ydx +xdy)x cos(y/x).
9. a) Find general solution of the following differential equation cos²x dy/dx +y=tanx (0<x<p/2).
   b) Form the differential equation representing the family of curves y = ae^2x + be^-x, where a and b are arbitrary constants.

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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