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Diploma paper

2nd Semester

Applied Mathematics-2

Part-A

Fill in the blanks

1.Centroid divides the median in the ratio of………….

2.y-intercept of the line 6x-5y+2=0 is……….

3.A function is said to be odd if f(-x)=…………

4.d/dx(cos-1x)=……………



Part-B

1. Find k if (2,3) is the centroid of the triangle formed by the points (2,3),(-5,4) and (k,8)?

2.Find the inclination of the line x-y+1=0 with x-axis?

3.Find the centre of the circle x2+y2-6x+4y+3=0?

4.Differentiate e-2x+3/x w.r.t x?

5.The equation of the motion is given by s=2t2-3t+1. Find the velocity after 3 second?

6.Write the order and degree of the differential equation?

 

Part-C

1.Show that the points (-2,5),(3,-4),and (7,10) are the vertices of a right-angled isosceles triangle?

2.Find the equation of straight line passing throught (-2,5) and parallel to the line joining the points(-3,-1) and (2,-4)?

3.Find the equation of the straight line passing through (4,-1) and whose x-intercept is twice the y-intercept?

4.Two diameters of a circle are 3x+4y=17,4x-3y=6 and its radius is Find the equation of the circle?

5.Show that the circles x2-y2-2x-2y+9=0 and 3x2+3y2-12x+18y-33=0 cut orthogonally?

6.Find dy/dx if x2+y2+2x+2y=2xy?

7.The area of a circular plate is increasing at a constant rate of 3cm2 / miniute. Find the rate at which the radius is increasing when the radius is 5cm?

8.Find the equation of tangent to the curve y=3x2-6x+1 at (2,1)?

9.If y=tan-1 x, Show that (1+x2) d2y/dx2 +2x.dy/dx=0?

10.Find the volume of solid generated by revolving y2=x2+5x between x=1,x=2 about x-axis?

11.Solve the differential equation dy/dx=3x+4 if y= 2 when x=1?

Part-D

1.In what ratio does the y-axis divide the line joining the points (-6,-8) and (4,5). Also find the point of division?

2.Find the equation of the median throught the point A in a triangle whose vertices are A(-1,3),B(-3,5) and C(7,-9)?

3.Differentiate sin x w.r.t x from the first principle?

4.Find the RMS value of cos x over the range (0,pi)?