Posted Date: 09 Dec 2010      Posted By:: zafar    Member Level: Gold  Points: 5 (Rs. 1)

# 2009 Gujarat Technological University General Diploma Hospital Management Diploma Engg. - Maths II, GTU Question paper

 Course: Diploma Hospital Management University/board: Gujarat Technological University

Seat No.: _____ Enrolment No.______
GUJARAT TECHNOLOGICAL UNIVERSITY
Diploma Sem-II Remedial Examination September 2009
Subject code: 320001 Subject Name: Mathematics II
Date: 18/09/2009 Time: 11:00am-1:30pm
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 y-axis divides line segment joining points (3,5) and (6,7)? Is
division internal or external? Find co-ordinates of division point.
03
(b) If two straight lines 3x+4my+8=0 and 3my-9x+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 3y-2x=1.
04
Q:2 (a) 1. Find center and radius of the circle 4x2+4y2+8x-12y-3=0. 03
2. Find equation of tangent and normal to the circle x2+y2-2x+4y-20=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 + 3e-2x 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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