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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
- Express as a sum of a symmetric and a skew symmetric matrix: [[1,2,3],...
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- Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2
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- Find the intervals where the following functions are (a) increasing an...
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- Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).
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- Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...
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- Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...
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- Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x)...
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- int(1+x^2)/(xsqrt(x^4+1))dx
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- Determine the area within the ellipse x^2/a^2+y^2/b^2=1.
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- int0^pi(xsinxdx)/(1+cos^2x)
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- Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx
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- Find the equation of the plane passing through the line (x-8)/3=(y+19)...
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- Prove that the sum of the vectors directed from the vertices to the mi...
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- If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...
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- Find the image of the point (3,-2,1) in the plane x-y+3z=2.
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- Prove the following by vector method. The diagonals of a rhombus are a...
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- Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c
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- int0^pi((xtanx)/(secx+tanx))dx
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- Solve: (1+x^2)dy/dx+2xy-x^3=0
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- Find (dy)/(dx) if x=(3at)/(1+t^3), y=(3at^2)/(1+t^3) at t=1/2
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