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Let f: NvecN be defined by f(n)={(n+1...

Let `f: NvecN` be defined by `f(n)={(n+1)/2,\ "if"\ n\ "i s\ o d d"n/2,\ \ "if\ "n\ "i s\ e v e n"\ \ for\ a l l\ n\ \ N}` Find whether the function `f` is bijective.

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Let f : N->N be defined by f(n)={(n+1)/2,"if n is odd " n/2,"if n is even " for all n in N . State whether the function f is bijective. Justify your answer.

Let f: N->N be defined0 by: f(n)={(n+1)/2, if n is odd (n-1)/2, if n is even Show that f is a bijection.

Let f:N to N be defined by f(n)={{:((n+1)/2, " if n is odd"),(n/2, "if n is even"):} for all n in N . Prove that f is many-one, onto function.

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ e v e nn-1,\ if\ n\ i s\ od d Show that f is a bijection.

Let f: N to N be defined as f(n) = (n+1)/(2) when n is odd and f(n) = (n)/(2) when n is even for all n in N . State whether the function f is bijective. Justify your answer.

check that f : N- N defined by f(n)={(n+1)/2,(if n is odd)),(n/2,(if n is even)) is one -one onto function ?

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

Let f: Nuu{0}->Nuu{0} be defined by f(n)={n+1,\ if\ n\ i s\ even\,\ \ \n-1,\ if\ n\ i s\ od d Show that f is invertible and f=f^(-1) .

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let f: Nuu{0}->Nuu{0} be defined by f={(n+1 ,, ifn \ i s \ e v e n),(n-1 ,, ifn \ i s \ od d):} Show that f is a bijection.

XII BOARD PREVIOUS YEAR PAPER ENGLISH-BOARD PAPER SOLUTIONS-All Questions
  1. On a multiple choice examination with three possible answers (out o...

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  2. If vec p is a unit vector and ( vec x-\ vec p).( vec x+\ vec p)...

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  3. Let f: NvecN be defined by f(n)={(n+1)/2,\ "if"\ n\ "i s\ o d d"n/2...

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  4. Solve the following differential equation: cos^2x(dy)/(dx)+\ y=tanx

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  5. Solve the following differential equation: x(dy)/(dx)=y-xtan(y/x)

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  6. Find the distance of the point P(6,5,9) from the plane determined b...

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  7. If matrix A=[[1,-1],[-1 ,1]] and A^2=k A , then write the value of k

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  8. Find the points on the line (x+2)/3=(y+1)/2=(z-3)/2\ at a distance ...

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  9. Evaluate: int(x^4\ dx)/((x-1)(x^2+1))

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  10. If y=cos^(-1)((3x+4\ sqrt(1-x^2))/5), find(dy)/(dx)

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  11. Evaluate the following: int1^2(5x^2)/(x^2+4x+3)\ dx

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  12. If y=e^(asin^(-1)x)\ ,\ -1\ lt=x\ lt=1, then show that (1-x^2)\ (d^...

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  13. Find the coordinates of the foot of the perpendicular and the perpen...

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  14. A bag contains 4 balls. Two balls are drawn at random, and are foun...

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  15. One kind of cake requires 300g of flour and 15g of fat, another kin...

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  16. If the length of three sides of a trapezium other than the base is 1...

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  17. Using matrix method, solve the following system of equations: 2/x+...

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  18. Using elementary transformations, find the inverse of the matrix [[1...

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  19. Solve the following differential equation: [(e^(-2\ sqrt(x)))/(sqrt(x)...

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  20. Solve the following differential equation: 3e^xtany\ dx+(2-e^x)sec^2y\...

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