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Show that f : N to N, given by f(x)= {...

Show that `f : N to N`, given by
`f(x)= {(x+1", if x is odd"),(x-1", if x is even"):}`
is bijective (both one-one and onto).

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SHARAM PUBLICATION-MODEL QUESTION PAPER-4-EXERCISE
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  2. If A and B are square matrices of same order, then show by means of an...

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  3. Prove that the following. [[1+a,1,1],[1,1+b,1],[1,1,1+c]] = abc(1+1/...

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  4. Find the value of |{:(17,58,97),(19,60,99),(18,59,98):}| without expan...

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  5. Find the inverse of [(2,-1),(1,3)].

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  6. Evaluate int tan^-1 sqrt((1-x)/(1+x))dx

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  7. Evaluate int (e^x-1)/(e^x+1) dx

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  8. Evaluate int(0)^(pi//4)log(1+tanx)dx.

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  9. Find the area of the region bounded by the curve y=6x-x^(2), the X-axi...

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  10. Solve the following differential equations x log x (dy)/(dx)+y= 2 lo...

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  11. Find the value of k so that the function f defined by f(x)={((kcos x)/...

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  12. Find (dy)/(dx) if x^y = y^x.

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  13. Show that the rectangle of maximum area that can be inscribed in a giv...

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  14. Evaluate int0^ pi x/(1+ sin x) dx

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  15. Find the area of region in the first quadrant enclosed by the X-axis, ...

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  16. Solve the following differential equation (2x + y + 1) dx + (4x + 2y —...

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  17. Show that f : N to N, given by f(x)= {(x+1", if x is odd"),(x-1", if...

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  18. If A=[{:(2,0,1),(2,1,3),(1,-1,0):}] then find the value of A^(2)-3A+2I

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  19. If a, b and c are all positive real, then prove that minimum value of ...

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  20. Three vectors veca, vecb and vecc satisfy the condition veca + vecb + ...

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