Download PTU B-Tech Bio Technology 2020 Dec 2nd Sem 76258 Basic Mathematics Ii Question Paper

Roll No. ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ ‘ Total No. of Pages : 03

Total No. of Questions : 18

B.Tech. (Bio Tech) (2018 & Onwards) (Sem.-2)

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BASIC MATHEMATICS-II

Subject Code : BTAM-207-18

M.Code : 76258

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 & C have FOUR questions each.
3. Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4. Select atleast TWO questions from SECTION - B & C.

SECTION-A

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Answer the following :

1. Find domain and range of the relation R = {(x, y) : y=x+5,x <4,x,y ? N}.
2. Examine, if the relation R = {(2, 1), (3, 1), (4, 2)} is a function or not?
3. Draw the graph of exponential function f(x) = e^x.
4. Find the limit lim ^3x2-24/_x?2 x³—4x²+4x

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5. Find ?z/?x given that z = x³ +y³ —3axy.
6. Evaluate the integral ? ¹/_x² dx.
7. Evaluate the integral ? cosec x (cosec x + cot x) dx.
8. Evaluate ?₁²?₁³ xyz dxdy.
9. Define order and degree of a differential equation.

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10. Solve dy/dx = ^2x/_4xy.

SECTION-B

1. a) Find the value of k, so that the function f(x) =
   

   2x+k	if x<2
   kx2	if x=2
   3	if x>2

   is continuous at x = 2.
   b) Differentiate x^sinx + (sin x)^cosx.

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2. a) Differentiate sin (tan^-1 v((1-x)/(1+x))).
   b) Find dy/dx given that y=cos^-1((x-x^-1)/(x+x^-1)), 0<x<1.
3. a) Find local maximum and minimum values of f (x) = 3x⁴ + 4x³ — 12x² + 12.
   b) Find absolute maximum and minimum values of f (x) = 2x³— 15x² +36x+ 1, x ? [1, 5].
4. a) Show that x?u/?x + y?u/?y =2u log u where logu = (x³+y³)/ (3x + 4y).
   

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   b) If u=xⁿtan^-1(y/x) - yⁿtan^-1(x/y), then find the value of ?²u/?x?y.

SECTION-C

1. a) Integrate ? x⁴/v(x⁵) dx.
   b) Integrate ? 1/(5—cos²x—4sin²x) dx.
2. Using double integration, find area of plate in the form of a quadrant of the ellipse x²/a²+y²/b²=1.

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3. a) Evaluate ?_-1¹ 5x⁴v(x⁵ +1) dx.
   b) Form a differential equation by eliminating the arbitrary constants a and b from y = a sin (x + b).
4. a) Find the general solution of the differential equation dy/dx = 2+v(x-y+2).
   b) Rate of interest in a bank is 5% per year. An amount of Rs. 1000 is deposited with this bank, how much it worth after 10 years. Solve using differential equations. Given that e^0.5 = 1.648).

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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