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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- int0^2[x^2]dx
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- Show that the line passing through the points (a1,b1,c1) and (a2,b2,c2...
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- If the sum of two unit vectors is a unit vector, show that the magnitu...
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- Calculate the area of the triangle ABC (by vector method) where A(1,2,...
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- The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...
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- Find the equation of lines joining the points. (4,-6,1) and (0,3,-1)
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- Evaluate intln(x^2+x+2)dx
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- Evaluate int0^1frac[ln(1+x)][1+x^2]dx
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- Solve xfrac[dy][dx]+y=x^4
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- If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all Bsub...
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- Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...
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- Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...
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- Prove that the measure of the angle between two main diagonals of a cu...
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- Show that the shortest distance between the lines x+a=2y=-12z and x=y+...
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- If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...
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- Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...
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- Shows that the triangle of greatest area that can be inscribed in a ci...
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- Find the inverse of [(1,1,2),(0,1,2),(1,2,1)] using elementary operati...
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- If [[x,x^2,x^3-1],[y,y^2,y^3-1],[z,z^2,z^3-1]]=0 then prove that xyz...
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- If A [[1,2,0],[1,1,0],[-1,4,0]],B=[[1,2,3],[1,1,-1],[1,1,1]]"and"C=[[1...
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