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If A = R -{3} and B = R -{1}. Consider t...

If A = R -{3} and B = R -{1}. Consider the function `f:A to B` defined by `f(x)=(x-2)/(x-3)`, for all `x in A`. Then, show that f is bijective. Find `f^(-1)(x)`.

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SHARAM PUBLICATION-MODEL QUESTION PAPER-4-EXERCISE
  1. If the cartesian equation of a line is (3-x)/5=(y+4)/7=(2z-6)/4 then w...

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  2. Show that the relation S defined on set N xx N by (a, b) S(c,d) rArr a...

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  3. If A = R -{3} and B = R -{1}. Consider the function f:A to B defined b...

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  4. Prove that 2 tan^-1(1/2) + tan^-1 (1/7) = tan^-1 (31/17).

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  5. Find the feasible region of the following system. 2y- x ge 0, 6y - 3x ...

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  6. f(x)={(x^2 sin (1/x), xne0 ),(0, x=0):} at x=0

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  7. Find (dy)/(dx) when y^x = e^(x-y).

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  8. Differentiate with resi to x : Y = 2^(x^2) + tan^(-1)((cosx-sinx)/(cos...

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  9. Find the equation of the tangent to the curve x = y^2-1 at the point w...

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  10. Find the intervals in which the function y=(lnx)/(x) is increasing and...

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  11. Prove by vector method that in a Delta ABC, c^(2) = a^(2) + b^(2) - 2a...

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  12. The diagonals of a parallelogram are given by veca =2hati - 3hatj + 5h...

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  13. Find the image of the point (2, 3, 4) with respect to the plane x - y ...

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  14. Find the equation of planes passing throught the points (1,2,3),(1,-4,...

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  15. If A and B are square matrices of same order, then show by means of an...

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

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

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

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

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

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