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MODERN PUBLICATION-MOCK TEST-3-EXERCISE
- Determine order and degree (if defined) of differential equation: (d^4...
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- Find |vecx|, if for a unit vector veca,(vecx-veca).(vecx+veca)=15
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- By using elementary transformations, find the inverse of the matrix A ...
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- Using determinant , find the area of triangle with verticles (1,0) ,...
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- Find dy/dx if x = a(theta +sintheta), y = a(1-cos theta)
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- Prove that the function f given by f(x) = log sin x is strictly increa...
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- Find the equation of the tangent to the curve x^2 + 3y = 3, which is p...
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- Evaluate : int [log(logx)+1/((logx)^2)]dx.
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- Solve : xyy'=1+x+y+xy.
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- If veca is any vector in space, show that : veca=(veca*hati)hati+(veca...
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- Prove that : 2tan^-1 (1/2) + tan^-1 (1/7) = tan^-1 (31/17)
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- Solve: tan^-1 2x + tan^-1 3x = frac{pi}{4}
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- If A=[[2,-1],[-1,2]],show that A^2-4A+3I=0.
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- If A=[[2,0,-1],[5,1,0],[0,1,3]], prove that : A^-1=A^2-6A+11I
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- Without expanding, prove the following |(b+c,c+a,a+b),(q+r,r+p,p+q)...
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- If the function defined by : f(x) = {:{(2x-1,x<2),(a,x=2),(x+1,x>2):...
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- Differentiate the following w.r.t.x. x^(cot x) + (sin x)^x.
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- Evalute : int(5x+3)/sqrt(x^2+4x+10)dx
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- Evaluate : int0^pi (xsinx)/(1+cos^2x)dx.
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- Evaluate : ∫0^(pi/2)frac{cos^2x}{cos^2x+4sin^2x}dx
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