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2009 Gujarat Technological University Diploma Hospital Management Diploma Engg.  Maths II, GTU Question paper
Seat No.: _____ Enrolment No.______ GUJARAT TECHNOLOGICAL UNIVERSITY Diploma SemII Remedial Examination September 2009 Subject code: 320001 Subject Name: Mathematics II Date: 18/09/2009 Time: 11:00am1:30pm Total Marks: 70 Instructions: 1. Attempt all questions. 2. Make suitable assumptions wherever necessary. 3. Figures to the right indicate full marks. 4. Use of programmable calculator is prohibited. 5. English version Authentic Q:1 (a) 1. Show that the points (a, b+c), (b, c+a) & (c, a+b) are collinear. 2. A variable point P moves in such a way that PA2+PB2=100, where A(3,4) and B(3,4) are given points. Find the equation of locus of point P. 02 02 3. In which ratio yaxis divides line segment joining points (3,5) and (6,7)? Is division internal or external? Find coordinates of division point. 03 (b) If two straight lines 3x+4my+8=0 and 3my9x+10=0 are perpendicular to each other then find m. 03 (c) Find equation of line passing through the point (3,4) and (i) Parallel (ii) Perpendicular to the line 3y2x=1. 04 Q:2 (a) 1. Find center and radius of the circle 4x2+4y2+8x12y3=0. 03 2. Find equation of tangent and normal to the circle x2+y22x+4y20=0 at the point (2,2). 04 (b) (1) If f(x) = then prove that f(x) + f ( ) = 0. 02 (2) Find 02 (3) Find 0 3 OR (b) (1) If f(x) = tanx then prove that f(x + y) = 02 (2) Find 02 (3) Find 0 3 Q:3 (a) Differentiate using definition. 04 (b) (1) If y = x3sin(logx) then find . 0 3 (2) If y = a(??+ sin?), x = a(1 + cos?), then find . 0 3
(c) If y = Acospt + Bsinpt then prove that + p2y = 0. 04 OR Q:3 (a) I f y = t h e n f i n d 04 (b) (1) If x + y = sin(xy) then find 0 3 (2) If y = log(sinx) + etanx then find 03 (c) If y = 2e3x + 3e2x then prove that  – 6y = 0. 04 Q:4 (a) The equation of motion of a particle is S = t3 + 3t, t > 0. (i) Find the velocity and acceleration at t = 3. (ii) When do velocity and acceleration become equal? 04 (b) Find the maxima and minima of the function f(x) = x3 – 3x + 11. 03 (c) (1) Evaluate dx 03 (2) Evaluate dx (3) Fill in the blank: dx = _____. 03 01 OR Q:4 (a) If the equation of motion of a particle is S = t3 – 6t2 + 9t + 6. Find its velocity When t = 0. Also find its acceleration when v = 0. 04 (b) Find the maximum and minimum value of the function f(x)=2x3 15x2+36x+10 03 (c) (1) Evaluate dx 03 (2) Evaluate dx (3) Fill in the blank: dx = _____. 03 01 Q:5 (a) Evaluate 03 (b) Evaluate the following: (1) dx (2) dx 08 (c) Find the area of the region bounded by the curve y = x2 and line y = x+2. 03 OR Q:5 (a) Evaluate dx 03 (b) Evaluate the following: (1) dx (2) dx 08 (c) Find the area of the circle x2 + y2 = a2. 03 **********
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