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MODERN PUBLICATION-MOCK TEST-2-EXERCISE
- Evaluate : int0^(pi/2) (sin^(3/2)x)/(sin^(3/2)x+cos^(3/2)x)dx.
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- Verify that y=cx+a/c is a solution of: y=xdy/dx+adx/dy.
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- If a line angles 90^@, 135^@, 45^@ with the positive x,y and z axis re...
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- For the matrix A=[(1,5),(6,7)], verify that (A+A') is a symmetric matr...
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- For the matrix A=[(1,5),(6,7)], verify that (A-A') is a skew symmetr...
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- Solve the following eqations, using inverse of a matrix: {:(5x+2y=3)...
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- Differentiate cos^(-1) ((1 - x^2)/(1 + x^2)) , 0 lt x lt 1. w.r.t.x
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- Find the equation of the normal to the curve ay^2 =x^3 at (am^2 ,am^3)
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- Find local minimum value of the function f given by f(x) = 3+|x|, x in...
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- Evaluate the definite integral: int0^(pi/4) (sinxcosx)/(cos^4x+sin^4x)...
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- Solve the differential equation : (x^2 + xy)dy=(x^2+y^2)dx.
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- Find the volume of the parallelopiped whose sides are given by vectors...
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- Prove that : tan^-1 x +tan^-1 2x/(1-x^2) = tan^-1 ((3x-x^3)/(1-3x^2)),...
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- Solve the following equations: tan^-1((1-x)/(1+x)) = 1/2 tan^-1 x, x...
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- If A=[[1,2,2],[2,1,2],[2,2,1]], verify that : A^2-4A-5I=O
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- Solve the following system of equations by matrix method, where xne0, ...
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- If xneynez and |[x,x^3,x^4-1],[y,y^3,y^4-1],[z,z^3,z^4-1]|=0, then pro...
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- If x^(y)=e^(x-y), then prove that (dy)/(dx)=(logx)/((1+logx)^(2))
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- If y=xlog[(ax)^-1+a^-1], prove that : x (x+1) (d^2y) / (dx^2) + xdy/dx...
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- Evaluate : int x^2/((x^2+1)(3x^2+4))dx
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