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Show that the set G={a+bsqrt2//a,binQ} i...

Show that the set `G={a+bsqrt2//a,binQ}` is an infinite abelian group with respect to Binary operation addition. Satisfies closure, associative, identity and inverse properties.

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FULL MARKS-SAMPLE PAPER -12 (UNSOLVED)-PART-III
  1. Find the value of cos(cos^(-1)((4)/(5))+sin^(-1)((4)/(5)))

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  2. Determine whether the points ( -2,1) ,(0,0) and ( -4,-3) lie outside, ...

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  3. Prove that [vecaxxvecb,vecbxxvecc,veccxxveca]=[veca,vecb,vecc]^(2)

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  4. Find the intervals of monotonicity and local extrema of the function f...

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  5. If u(x,y) = (x^(2) + y^(2))/sqrt(x+y), prove that x(del u)/(del x) + y...

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  6. Four defective oranges are accidentally mixed with sixteen good ones. ...

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  7. Show that not(p^^q)equiv((notp)vv(notq))

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  8. Find the rank of each of the following matrices: (i) [{:(3,2,5),(1,1,2...

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  9. In a T20 match, Chennai Super Kings needed just 6 runs to win with 1 b...

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  10. Prove that (1+costheta+isintheta)^(n)+(1+costheta-isintheta)^(n)=2^(n+...

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  11. Solve (x-4)(x+2)(x+3)(x-3)+8=0

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  12. Prove thate tan^(-1)((2)/(11))+tan^(-1)((7)/(24))=tan^(-1)((1)/(2))

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  13. A road bridge over an irrigation canal have two semi circular vents ea...

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  14. Show that the set G={a+bsqrt2//a,binQ} is an infinite abelian group wi...

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  15. Find the parametric form of vector equation, and Cartesian equations o...

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  16. The mean and standard deviation of a binomial variate X are respectiv...

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  17. Find the intervals of concavity and the points of inflection of the fu...

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  18. For each of the functions find the f (x), f (y), and show that f (xy) ...

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  19. (dy)/(dx)+(y)/(x)=sinx

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  20. Evaluate: int(pi//6)^(pi//3)(dx)/(1+sqrtcotx)

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