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Prove the following : [[1,x,x^2],[x^2,1,...

Prove the following : `[[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. If [(x+y,y-z),(5-t,7+x)]=[(t-x,z-t),(z-y,x+z+t)], then find the values...

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  2. Express as a sum of a symmetric and a skew symmetric matrix: [[1,2,3],...

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  3. Prove the following : [[1,x,x^2],[x^2,1,x],[x,x^2,1]]=(1-x^3)^2

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  4. Find the intervals where the following functions are (a) increasing an...

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  5. Find (dy)/(dx), if y=tan^(-1)((cosx)/(1+sinx)).

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  6. Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = ...

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  7. Use the function f(x) = x^(1//x), x gt 0 to show that e^(pi) gt pi^(e)...

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  8. Let f(x)={(absx/x,if xne0),(0,if x=0):} Examine the continuity of f(x)...

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  9. int(1+x^2)/(xsqrt(x^4+1))dx

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  10. Determine the area within the ellipse x^2/a^2+y^2/b^2=1.

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  11. int0^pi(xsinxdx)/(1+cos^2x)

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  12. Evaluate the following integrals int(3sinx+28cosx)/(5sinx+6cosx)dx

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  13. Find the equation of the plane passing through the line (x-8)/3=(y+19)...

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  14. Prove that the sum of the vectors directed from the vertices to the mi...

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  15. If A (1,0,-1), B (-2,4,-2) and C(1,5,10) be the vertices of a triangle...

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  16. Find the image of the point (3,-2,1) in the plane x-y+3z=2.

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  17. Prove the following by vector method. The diagonals of a rhombus are a...

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  18. Prove that intdx/((x-1)^2(x+2))=1/9ln abs((x+2)/(x-1))-1/(3(x-1))+c

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  19. int0^pi((xtanx)/(secx+tanx))dx

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  20. Solve: (1+x^2)dy/dx+2xy-x^3=0

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