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If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove ...

If `a^x=b ,\ b^y=c\ a n d\ c^z=a ,` prove that `x y z=1`

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MTG IIT JEE FOUNDATION-NUMBER SYSTEMS-Olympiad/HOTS Corner
  1. If a^x=b ,\ b^y=c\ a n d\ c^z=a , prove that x y z=1

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  2. Which of the following statements is incorrect ?

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  3. Find the value of (9^(3//2)-3xx5^(0)-[(1)/(81)]^(-1//2))/(((64)/(125))...

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  4. If x=(sqrt(a+2b)+sqrt(a-2b))/(sqrt(a+2b)-sqrt(a-2b)) then bx^(2)+b =

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  5. The value of sqrt(6+2sqrt(3)+2sqrt(2)+2sqrt(6))-(1)/(sqrt(5-2sqrt(6)))...

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  6. If a=2+sqrt(3)+sqrt(5) and b=3+sqrt(3)-sqrt(5), then a^(2)+b^(2)-4a-6b...

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  7. Find the values of the integers a and b respectively, for which the so...

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  8. The value of expression ((0.6)^(0)-(0.1)^(-1))/(((3)/(2^(3)))^(-1).((3...

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  9. Expressing 0.bar23+0.2bar3 as a single decimal, we get

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  10. If (4sqrt(3)+5sqrt(2))/(sqrt(48)+sqrt(18))=(a+bsqrt(6))/(15) and ((a)/...

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  11. If\ \ sqrt(2^n)=1024 ,\ \ then 3^(2(n/4-4))= 3 (b) 9 (c) 27 (d...

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  12. Express 1-(1)/(1+sqrt(3))+(1)/(1-sqrt(3)) in the form a+bsqrt(3), wher...

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  13. If (3+2sqrt(3))/(3-sqrt(3))=a+sqrt(3)b , then the value of sqrt(a+b) ,...

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  14. Simplify: 2/(sqrt(5)+\ sqrt(3))+1/(sqrt(3)+\ sqrt(2))-3/(sqrt(5)+\ sq...

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  15. What is the value of 2.bar(6)-1.bar(9) ?

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  16. The sum of 0.bar(6) and 0.bar(7) is

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  17. If 2^(x)=4^(y)=8^(z) and ((1)/(2x)+(1)/(4y)+(1)/(6z))=(24)/(7), then f...

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  18. If 3sqrt(3)xx3^(3)-:3^(-3//2)=3^(a+2) , then a =

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  19. Find the value of a and b respectively, if (5+sqrt(3))/(7-4sqrt(3))=47...

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  20. If 2^(x+3)=32 , then what is the value of 3^(6-x) ?

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  21. The numbers 7.478478…. and 1.101001000100001 ….. are

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