Home
Class 11
MATHS
Using binomial theorem evaluate each of ...

Using binomial theorem evaluate each of the following: `(102)^5`

Text Solution

Verified by Experts

`=(100+2)^{5}`
`=\ ^{5} C_{0} times 100^{5} times 2^{0}+\ ^{5} C_{1} times 100^{4} times 2^{1}+\ ^{5} C_{2} times 100^{3} times 2^{2}+\ ^{5} C_{3} times 100^{2} times 2^{3}+\ ^{5} C_{4} times 100^{1} times 2^{4}+\ ^{5} C_{5} times 100^{0} times 2^{5}`
`=10000000000+1000000000+40000000+800000+8000+32`
`=11040808032`
Promotional Banner

Topper's Solved these Questions

  • ARITHMETIC PROGRESSIONS

    RD SHARMA|Exercise Solved Examples And Exercises|248 Videos
  • BRIEF REVIEW OF CARTESIAN SYSTEM OF RECTANGULAR COORDINATES

    RD SHARMA|Exercise Solved Examples And Exercises|75 Videos

Similar Questions

Explore conceptually related problems

Using binomial theorem evaluate each of the following: (101)^(4)

Using binomial theorem evaluate each of the following: (98)65

Using binomial theorem evaluate each of the following: (96)^(3)

Using binomial theorem, evaluate each of the following: (i) (104)^(4) (ii) (98)^(4) (iii) (1.2)^(4)

Using binomial theorem,evaluate each of the following: (96)^(3),(102)^(5)

Using binomial theorem, expand each of the following: (1-2x)^(5)

Using binomial theorem, expand each of the following: (x-1/y)^(5)

Using binomial theorem, expand each of the following: (3x+2y)^(5)

Using binomial theorem, expand each of the following: (2x-3)^(6)

Using binomial theorem, expand each of the following: (2x-3y)^(4)

RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Find (x+1)^6+(x-1)^6. Hence evaluate (sqrt(2)+1)^6+(sqrt(2)-1)^6.

    Text Solution

    |

  2. Using binomial theorem evaluate each of the following: (96)^3

    Text Solution

    |

  3. Using binomial theorem evaluate each of the following: (102)^5

    Text Solution

    |

  4. Using binomial theorem evaluate each of the following: (101)^4

    Text Solution

    |

  5. Using binomial theorem evaluate each of the following: (98)^5

    Text Solution

    |

  6. Using binomial theorem indicate which is larger (1. 1)^(10000)or\ 1000...

    Text Solution

    |

  7. Write the general term in the expansion of (x^2-y)^6dot

    Text Solution

    |

  8. Find the 10th term in the binomial expansion of (2x^2+1/x)^(12)dot

    Text Solution

    |

  9. Find the constant term in the expansion of ((4x^2)/3+3/(2x))^9.

    Text Solution

    |

  10. Find 13th term in the expansion of (9x-1/(3sqrtx))^(18),\ x!=0.

    Text Solution

    |

  11. Find the 11th term from the end in the expansion of (2x-1/(x^2))^(25)d...

    Text Solution

    |

  12. Find n, if the ratio of the fifth term from the beginning to the fifth...

    Text Solution

    |

  13. Find a if 17th and 18th terms in the expansion of (2+a)^(50) are eq...

    Text Solution

    |

  14. Show that the middle term in the expansion of (1+x)^(2n)\ is =frac{1....

    Text Solution

    |

  15. Prove that the coefficient of the middle term in the expansion of (1+x...

    Text Solution

    |

  16. Find the coefficient of x^(10) in the binomial expansion of (2x^2-1/x)...

    Text Solution

    |

  17. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9dot

    Text Solution

    |

  18. Find the coefficient of x^(40) in the expansion of (1+2x+x^2)^(27)dot

    Text Solution

    |

  19. Find the coefficient of x^5 in the expansioin of the product (1+2x)^6(...

    Text Solution

    |

  20. Find the term independent of x in the expansion of: (x-1/x)^(14) .

    Text Solution

    |