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Let f: X rarr Y If there exists a map ...

Let f: `X rarr Y`
If there exists a map g:Y `rarr` X such that gof = `id_(X)` and fog = `id_(y)`, then show that
f is bijective and (ii) `g =f^(-1)`

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USHA PUBLICATION-MODEL QUESTION SET-MODEL QUESTION SET
  1. Prove that int(dx)/(2+sinx)=2/sqrt(3)tan^-1((2tanx//2+1)/sqrt3)+c.

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  2. Solve dy/dx-y/x=xy^2.

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  3. Let f: X rarr Y If there exists a map g:Y rarr X such that gof = id...

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  4. If "cos"^(-1)(x/y) +"cos"^-1(y/3)= theta, "prove that" 9x^2- 12xy "co...

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  5. Maximize:Z=10x1+12x2+8x3 "Subject to": x1+2x2 le 30 5x1 -7x3 ge 12 x1+...

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  6. Prove by vector method that the medians of a triangle are concurrent.

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  7. If l1,m1,n1andl2,m2,n2 are the direction cosines of two mutually perpe...

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  8. If 2s=a+b+c show that [[a^2,(s-a)^2,(s-a)^2],[(s-b)^2,b^2,(s-b)^2],[...

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  9. If A=[{:(1,-2,2),(3,1,-1):}]andB=[{:(2,4),(1,2),(3,-1):}] , then veri...

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  10. Let A={1,2,3}, which of the following functions on A is invertible?

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  11. Let A={1,2,3}, which of the following functions on A is invertible?

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  12. Let A={1,2,3}, which of the following functions on A is invertible?

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  13. Let A={1,2,3}, which of the following functions on A is invertible?

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  14. Find sin[frac[pi][2]-sin^(-1)(-frac[1][2])]

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  15. Find the number of all possible matrices of order 3xx3 with each of ...

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  16. Find the value of x if abs[[2,3],[4,5]]=abs[[x,3],[2x,5]]

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  17. If A is a square matrix of order 2, then find det(adjA).

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  18. Evaluate inte^(x)(sinx+cosx)dx.

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  19. Write the differential equation having y=C1e^x+C2e^x as its general so...

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  20. If veca is a non zero vector of magnitude abs(veca) and lambda is a no...

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