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Let `f: N -> S` be a function defined as `f(x)=9x^2+6x-5`. Show that `f:N -> S,` where `S` is the range of `f` , is invertible. Find the inverse of `f` and hence `f^(-1)(43) and f^(-1)(163)`

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XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. An urn contains 3 white and 6 red balls. Four balls are drawn one by o...

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  2. Find the coordinate of the point P where the line through A(3,-4,-5) a...

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  3. Let f: N -> S be a function defined as f(x)=9x^2+6x-5. Show that f:N -...

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  4. A manufacturer produces two products A and B. Both the products are ...

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  5. If x=asin2t(1+cos2t) and y=bcos2t(1-cos2t), find the values of (dy)/(d...

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  6. Find the position vector of a point which divides the join of points w...

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  7. Matrix A=[0 2b-2 3 1 3 3a3-1] is given to be symmetric, find values of...

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  8. If y=x^x , prove that (d^2y)/(dx^2)-1/y((dy)/(dx))^2-y/x=0

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  9. Show that the equation of normal at any point t on the curve x=3cost-c...

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  10. If A is a square matrix such that A^2=I , then find the simplified val...

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  11. Find the maximum value of |[1, 1, 1],[ 1, 1+sintheta,1],[ 1, 1, 1+cost...

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  12. Find the vector equation of a plane which is at a distance of 5 units ...

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  13. Find : int(sqrt(x))/(sqrt(a^3-x^3))dxdot

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  14. Find the intervals in which f(x) = sin 3x – Cos 3x, 0 < x < pi, is str...

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  15. Show that the altitude of the right circular cone of maximum volume th...

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  16. A and B throw a pair of dice alternately. A wins the game if he gets a...

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  17. Prove that |[yz-x^2,zx-y^2,xy-z^2],[zx-y^2,xy-z^2,yz-x^2],[xy-z^2,yz-x...

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  18. Using elementary transformations, find the inverse of the matrix A = [...

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  19. Three persons A, B and C apply for a job of Manager in a Private Compa...

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  20. Solve for : 2\ tan^(-1)(cosx)=tan^(-1)(2\ cos e c\ x) .

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