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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- Find A^-1 if A=[(4,-1),(2,3)]
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- Express[(3,-1,0),(2,2,5),(1,3,2)]as sum of a symmetric and a skew symm...
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- Find the point on the curve x^2 + y^2 - 4xy + 2 = 0 where the normal...
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- If sin (x + y) = y cos (x + y) then prove that dy/dx =-(1 + y^2)/y^2
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- Find the interval where f(x)=sinx,x in[0,2pi] increasing.
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- If siny=xcos(a+y),show that dy/dx=cos^2(a+y)/cosaand find the value of...
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- Determine the area of the region bounded by y^2=x^3 and the double ord...
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- int(xe^x)/(1+x^2)dx
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- Evaluate int0^1frac[ln(1+x)][1+x^2]dx
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- Find the solution of the following differential equations: xdy/dx+sqrt...
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- int(pi//6)^(pi//3)dx/(1+sqrtcotx)
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- Prove the following by vector method. The diagonals of a rhombus are a...
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- Show that the vector area of the triangle whosse vertices have positio...
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- Find the perpendicular distance of the point (-1,3,9) from the line (x...
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- If the sum of two unit vectors is a unit vector, show that the magnitu...
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- Find the image of the point (3,5,7) with respect to the plane 2x+y+z=6...
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- Prove that intxlog(1+1/x)dx =x^2/2log((x+1)/x)-x^2/2 logx-1/2log(x+1)+...
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- Prove that int(dx)/(2+sinx)=2/sqrt(3)tan^-1((2tanx//2+1)/sqrt3)+c.
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- Solve dy/dx-y/x=xy^2.
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- Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...
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