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Show that f\ : NvecN ,\ given by f(x)=...

Show that `f\ : NvecN ,\ ` given by `f(x)={x+1, if\ x\ i s\ od dx-1,\ \ if\ x\ i s\ e v e n` is both one-one and onto.

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XII BOARDS PREVIOUS YEAR-BOARD PAPER SOLUTIONS-All Questions
  1. If [[1,2],[3,4]] [[3,1],[2,5]]=[[7,11],[k,23]], then write the value o...

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  2. Find the particular solution of the differential equation. (dy)/(dx...

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  3. Show that f\ : NvecN ,\ given by f(x)={x+1, if\ x\ i s\ od dx-1,\ \ ...

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  4. Evaluate : int(logx)/x\ dxdot

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  5. What is the value of the determinant |(0,2,0),(2,3,4),(4,5,6)|?

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  6. What is the degree of the following differential equation? 5x\ ((d...

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  7. What is the range of the function f(x)=(|x-1|)/((x-1))?

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  8. If A=[[cos alpha,-sin alpha],[sin alpha,cos alpha]], then for what val...

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  9. What is the principal value of sin^(-1)(-(sqrt(3))/2)\ ?

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  10. Find the equation of the plane through the points (2, 1, 1) and (1,...

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  11. Find the shortest distance between the following lines: (x+1)/7=(y+1)...

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  12. A cottage industry manufactures pedestal lamps and wooden shades, e...

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  13. A factory has two machines A and B. Past record shows that machine ...

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  14. Find the inverse of the following matrix using elementary operations: ...

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  15. Using properties of determinants, prove the following: |[x,x^2,1+px^3]...

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  16. Prove the following: tan^(-1)(1/4)+tan^(-1)(2/9)=1/2cos^(-1)(3/5)

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  17. Solve the following for x : cos^(-1)((x^2 - 1)/(x^2 + 1))+t a n^(-1...

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  18. Using matrices, solve the following system of equations: x\ -\ y+z...

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  19. If A^(-1) =[(3,-1,1),(-15,6,-5),(5,-2,2)] and B = [(1,2,-2), (-1,3,0),...

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  20. A merchant plans to sell two types of personal computers — a deskto...

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