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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- Show that if R is an equivalence relation on X then dom R=rngR =X.
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- Prove that: cos^(-1)(12/13)+sin^(-1)(3/5)=sin^(-1)(56/65)
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- Solve sin^(-1)(1-x)-2sin^(-1)x=frac[pi][2]
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- Let f be a real function. Prove that f(x)-f(-x) is an odd function and...
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- If A=[{:(3,1),(-1,2):}] then prove that A^(2)-5A+7I=O
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- Express as a sum of a symmetric and a skew symmetric matrix: [[4,-3],[...
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- If ABC is a triangle, then prove that abs[[tanA,1,1],[1,tanB,1],[1,1,...
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- Evaluate abs[[1,a,bc],[1,b,ca],[1,c,ab]]-abs[[1,a,b^2],[1,b,b^2],[1,c,...
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- Find the inverse of the matrix [[1,2],[3,4]]
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- Find the number of critical points of f(x)=frac[abs(x-1)][x^2]
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- If f(x)={(ax^2+b if x lt1),(1 if x=1),(2ax-b if xgt1):} is continuous...
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- Find the equation of the tangent to the curve x = y^2-1 at the point w...
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- If y=sin^(-1)(x^3), then find that dy/dx
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- If y=e^(x^(e^(x^(e^x)))), then find dy/dx.
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- Evaluate int0^2abs(x^2+2x-3)dx
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- Find the area of the region bounded by the curve y=sin^(3)x and the st...
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- intdx/(1+tanx)
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- Evaluate inte^(tan-1)x((1+x+x^2)/(1+x^2))dx.
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- Find the solution of the following differential equations: (4x+6y+5)dx...
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- Let veca,vecb,vecc be three vectors such that veca+vecb+vecc=vec0 and ...
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