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Determine order and degree (if defined) of differential equation: `(d^4y)/dx^4 + sin(y'' ') = 0`

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MODERN PUBLICATION-MOCK TEST-3-EXERCISE
  1. Write the element a(12) of the matrix A=[a(ij)](2xx2), whose elements ...

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  2. Given : int e^x(tanx+1)secxdx=e^xf(x)+c, write f(x) satisfying the abo...

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  3. Determine order and degree (if defined) of differential equation: (d^4...

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  4. Find |vecx|, if for a unit vector veca,(vecx-veca).(vecx+veca)=15

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  5. By using elementary transformations, find the inverse of the matrix A ...

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  6. Using determinant , find the area of triangle with verticles (1,0) ,...

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  7. Find dy/dx if x = a(theta +sintheta), y = a(1-cos theta)

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  8. Prove that the function f given by f(x) = log sin x is strictly increa...

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  9. Find the equation of the tangent to the curve x^2 + 3y = 3, which is p...

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  10. Evaluate : int [log(logx)+1/((logx)^2)]dx.

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  11. Solve : xyy'=1+x+y+xy.

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  12. If veca is any vector in space, show that : veca=(veca*hati)hati+(veca...

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  13. Prove that : 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)

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  14. Solve: tan^-1 2x + tan^-1 3x = frac{pi}{4}

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  15. If A=[[2,-1],[-1,2]],show that A^2-4A+3I=0.

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  16. If A=[[2,0,-1],[5,1,0],[0,1,3]], prove that : A^-1=A^2-6A+11I

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  17. Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q)...

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  18. If the function defined by : f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):...

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  19. Differentiate the following w.r.t.x. x^(cot x) + (sin x)^x.

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  20. Evalute : int(5x+3)/sqrt(x^2+4x+10)dx

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