M2 Diploma Important Question

M2 Diploma Important Question



1.Find the Equation to the straight line cutting off y-intercept 5 units and making inclination 130°?

2.Find the focus and equation to directrix of the parabola y^2=40X?

3.Find the equation of parabola with focus at(3,0) and x-axis is theaxis of the parabola?

4.If y=(x^2+5x).logx find dy/dx?

5.Differeantaiye 10x^2+3e^2x-cos^-1(x) w.r.t x?

6.If y=logx/(1+sinx) dind dy/dx?

7.If x=a tanθ , y=a secθ.find dy/dx at θ=π/4?

8.Evaluate all problems?

9.Find the equation to the straight line passing through the point(4,3) and parallel to the line 3x+5y-3=0?

10.If y=1-x^2/1+x^2 find dy/dx?

11.If y=tan^-1x ,show that (1+x^2)y^2+2xy1=0?

12.Tha radius of a spheare is increasing at the rate of 2cm/sec. Find the rate of increase of the volume when the radius is 6cm?

13.Find the volume generated by rotating the curve y=x+2 about xaxis between x=0 & y  x=2?

14.Diffreantiate sinx w.r.t to x from first princile?

15.Find the maximum and minimum value of the function?

16.solve the diffreantial euation dy/dx+y tan x=sec x?


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