Diploma paper
2nd Semester Applied Mathematics2
PartA
Fill in the blanks
1.Centroid divides the median in the ratio of………….
2.yintercept of the line 6x5y+2=0 is……….
3.A function is said to be odd if f(x)=…………
4.d/dx(cos1x)=……………
PartB
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 xy+1=0 with xaxis?
3.Find the centre of the circle x2+y26x+4y+3=0?
4.Differentiate e2x+3/x w.r.t x?
5.The equation of the motion is given by s=2t23t+1. Find the velocity after 3 second?
6.Write the order and degree of the differential equation?
PartC
1.Show that the points (2,5),(3,4),and (7,10) are the vertices of a rightangled 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 xintercept is twice the yintercept?
4.Two diameters of a circle are 3x+4y=17,4x3y=6 and its radius is Find the equation of the circle?
5.Show that the circles x2y22x2y+9=0 and 3x2+3y212x+18y33=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=3x26x+1 at (2,1)?
9.If y=tan1 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 xaxis?
11.Solve the differential equation dy/dx=3x+4 if y= 2 when x=1?
PartD
1.In what ratio does the yaxis 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)?
