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Let A=Set of all real numbes except 1. L...

Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab for all a, `b in A`.Show that
Every element 'a' of A has an inverse `a/(1-a) in A`.

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PRADEEP PUBLICATION-MODEL PAPER (2)-EXERCISE
  1. Let A=Set of all real numbes except 1. Let * be defined as a+b-ab for...

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  2. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  3. Let A=Set of all real numbes except 1. Let 'cdot' be defined as a+b-ab...

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  4. Prove that cot^-1 7 + cot^-1 8 + cot^-1 18 = cot^-1 3

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  5. Solve the following equations sin(sin^(-1)""(1)/(5)+cos^(-1)x)=1

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  6. Solve the following equations 5x-7y+z=11, 6x-8y-z=15, 3x+2y-6z=7 by Cr...

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  7. Find dy/dx if x^y + y^x = a^b

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  8. If f(x)={((x-5)/(|x-5|)+a" , if "xlt5),(a+b" , if "x=5),((x-...

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  9. Find the interval of increase and decrease of the function f(x)=log(1+...

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  10. Prove that the curves x=y^2 and xy=k cut at right angles* if 8k^2 =1

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  11. int (sin^-1x)/(1-x^2)^(3//2) dx

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  12. Evaluate: underset0 oversetpi int sinxdx .

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  13. Sketch the graph of the function: y=f(x)={(x, if, 0lexle1),(1/x, if, 1...

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  14. Solve the differential equation (d^2y)/(dx^2)=x+sinx given that when x...

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  15. There is a group of 50 people who are patriotic out of which 20 believ...

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  16. With the help of vector method, prove that,cosA=(b^2+c^2-a^2)/(2bc)

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  17. Experiments show that radium decomposes at a rate proportioanl to the ...

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  18. The following matrix depicts the number of students of a school who we...

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  19. The following matrix depicts the number of students of a school who we...

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  20. The following matrix depicts the number of students of a school who we...

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