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Using binomial theorem, prove that 6^n-5...

Using binomial theorem, prove that `6^n-5 n` always leavęs remainder 1 when divided by `25 .`

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  1. Using binomial theorem prove that 2^(3n)-7n-1 is divisible by 49, wher...

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  2. Find the 11^( th) term from the end in the expansion of (2 x-1/(x^2))...

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  3. Find the coefficient of x^10 in the expansion of (2x^2-3/x)^11

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  4. Consider the expansion of (3x^2-1/(2x^3))^10 Find the term independent...

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  5. Find the middle term in the expansion of (a/x+b x)^(12).

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  6. If the first three terms in the expansion of (1+ax)^n are 1,6x and 16x...

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  7. In the expansion of (1+x)^(43), the coefficients of (2 r+1)^(t h) and ...

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  8. Expand (1-x+x^2)^4

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  9. Show that the coefficient of middle term in the expansion of (1+a)^8 i...

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  10. i) Which is the general term in the expansion of (a+b)^n ii) Find the...

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  11. i) Which is the (r+1)^ (th) term in the expansion of (a+b)^n ii) Whi...

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  12. Let cr denote the binomial coefficient "^nCr Hence, show that C1/C0+2C...

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  13. Using the expansion in simplify (a+b)^6+(a-b)^6

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  14. Expand the following by using binomial theorem (i) (-3 x-1/(3 x))^3 ...

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  15. Find the positive value of m for which the coefficient of x^2 in the e...

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  16. The first three terms in the expansion of (1+a x)^n are 1,12 x,64 x^2....

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  17. Expand (a+b)^6-(a-b)^6. Hence find the value of (sqrt2+1)^6-(sqrt2-1)^...

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  18. Write the middle term in the expansion of the following, (x-1/(2y))^...

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  19. Show that the middle term in the (1+x)^2n expansion os is (1.3.5.....(...

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  20. Using binomial theorem, prove that 6^n-5 n always leavęs remainder 1 w...

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