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Integrate the following int0^1x^7/sqrt(1...

Integrate the following `int_0^1x^7/sqrt(1-x^2)dx`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Solve (x+y+1)frac[dy][dx]=1

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  2. Integrate intfrac[tanx+tanalpha][tanx-tanalpha]dx

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  3. Integrate the following int0^1x^7/sqrt(1-x^2)dx

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  4. Find the area of the circle x^2+y^2=2ax.

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  5. int0^2[x^2]dx

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  6. Show that the line passing through the points (a1,b1,c1) and (a2,b2,c2...

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  7. If the sum of two unit vectors is a unit vector, show that the magnitu...

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  8. Calculate the area of the triangle ABC (by vector method) where A(1,2,...

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  9. The plane 4x+7y+4z+81=0 is rotated through a right angle about its lin...

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  10. Find the equation of lines joining the points. (4,-6,1) and (0,3,-1)

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  11. Evaluate intln(x^2+x+2)dx

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  12. Evaluate int0^1frac[ln(1+x)][1+x^2]dx

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  13. Solve xfrac[dy][dx]+y=x^4

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  14. If f:XrightarrowY is onto, then prove that f(f^(-1)(B))=B for all Bsub...

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  15. Prove that f:X rarr Y is injective iff f^(-1) (f(A)) = "A for all" A s...

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  16. Prove that cos^(-1)(frac[b+acosx][a+bcosx])=2tan^(-1)(sqrt(frac[a-b][a...

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  17. Prove that the measure of the angle between two main diagonals of a cu...

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  18. Show that the shortest distance between the lines x+a=2y=-12z and x=y+...

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  19. If e^(y//x)=(x)/(a+bx) then show that x^(3)(d)/(dx)((dy)/(dx))=(x(dy)/...

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  20. Find the extreme values of the function f(x)=x^2e^(-x^2) and show that...

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