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If (9^(n)xx3^(2)xx(3^(-n//2))^(-2)-(27)^...

If `(9^(n)xx3^(2)xx(3^(-n//2))^(-2)-(27)^(n))/(3^(3m)xx2^(3))=(1)/(27)`, prove that m-n=1.

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To solve the equation \[ \frac{9^n \cdot 3^2 \cdot (3^{-\frac{n}{2}})^{-2} - 27^n}{3^{3m} \cdot 2^3} = \frac{1}{27} \] we will simplify it step by step. ...
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NAGEEN PRAKASHAN-NUMBER SYSTEM-Exercise 1e
  1. Rationalise the denominator of each the following (i)(2)/(sqrt(3))" ...

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  2. Rationalise the denominator of each the of the following : (i)(1)/(3...

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  3. Simplify each of the following : (i)(sqrt(2)+1)/(sqrt(2)-1)+(sqrt(2)...

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  4. If sqrt(2)=1.414,sqrt(3)=1.732, find the value of the following : (i...

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  5. Find the value of a and b in each of the following (i)(3+sqrt(2))/(3...

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  6. If x=2+sqrt(3), then find : (i)(1)/(x)" "(ii)x+(1)/(x)" "(iii...

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  7. If x=3+2sqrt(2), then find : (i)(1)/(x)" "(ii)x+(1)/(x)" "(ii...

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  8. If x=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2)) and y=(sqrt(3)-sqrt(2))/(sqrt...

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  9. If a=1-sqrt(2),"then find the value of "(a-(1)/(a))^(3)

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  10. Evaluate 15/( sqrt10+sqrt20+sqrt40-sqrt5-sqrt80) is being given that s...

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  11. Write the following surds in decending order of their magnitudes : (...

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  12. If 25^(x-1)=5^(2x-1)-100, then find the value of x.

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  13. Which is greater sqrt(11)-sqrt(6) or sqrt(17)-sqrt(12) ?

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  14. If x=7-4sqrt3 then find the value of sqrtx+1/sqrtx

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  15. If x=2+sqrt(3), then find the value of x^(4)-4x^(3)+x^(2)+x+1.

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  16. sqrt(5+2sqrt(6))+sqrt(8-2sqrt(15))

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  17. If (9^(n)xx3^(2)xx(3^(-n//2))^(-2)-(27)^(n))/(3^(3m)xx2^(3))=(1)/(27),...

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  18. Rationalise the denominator of : (i)(5)/(3+sqrt(5)-2sqrt(2))" ...

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