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If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\...

If `(9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27)` , prove that `m-n=1`

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If 9^(n)= 27^(n+1) , then 2^(n)=

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If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - (C_(1))/(2) + (C_(2))/(3) -…+ (-1)^(n) (C_(n))/(n+1) = (1)/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n)," prove that " 1^(2)*C_(1) + 2^(2) *C_(2) + 3^(2) *C_(3) + …+ n^(2) *C_(n) = n(n+1)* 2^(n-2) .

If (x^(3) + 3xy^(2))/(3x^(2)y + y^(3)) = (m^(3) + 3mn^(2))/(3m^(2)n + n^(3)) , show that : nx = my .

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NAGEEN PRAKASHAN ENGLISH-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 descending 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. Simplify sqrt(5+2sqrt(6))+sqrt(8-2sqrt(15))

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  17. If (9^n\ x\ 3^2\ x\ 3^n-\ 27^n)/(3^(3m)\ x\ 2^3)=1/(27) , prove that m...

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

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