Home
Class 11
MATHS
Using binomial theorem prove that 2^(3n)...

Using binomial theorem prove that `2^(3n)-7n-1` is divisible by 49, where `ninN`

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    V PUBLICATION|Exercise QUESTION BANK|80 Videos

Similar Questions

Explore conceptually related problems

Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 , where n in N

(a)Prove that 3^(2n)-1 is divisible by 8.

For all nge1 , prove that p(n):2^(3n)-1 is divisible by 7.

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

Prove 'that 10^n+3 xx 4^(n+2)+5 is divisible by 9 .

For all nge1 , prove that p(n):2.7^n+3.5^n-5 is divisible by 24.

Using mathematical induction prove that 10^(2n-1)+1 is divisible by 11 for all n in N

Using mathematical induction prove that x^(2n)-y^(2n) is divisible by x+y for all n in N

For all nge1 , prove that p(n):n(n+1)(n+5) is divisible by 3.

(b) P(n):7^n-3^n is divisible by 4,then find P(2) .

V PUBLICATION-BINOMIAL THEORM-QUESTIONBANK
  1. Using binomial theorem expand (sqrt(x/a)-sqrt(a/x))^6.

    Text Solution

    |

  2. Using binomial thẹorem, prove that 3^(3 n)-26 n-1 is divisible by 676 ...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |