Home
Class 11
MATHS
Find the last three digits in 11^(50)...

Find the last three digits in `11^(50)`

Text Solution

AI Generated Solution

To find the last three digits of \( 11^{50} \), we can use the Binomial Theorem. Here is a step-by-step solution: ### Step 1: Rewrite \( 11^{50} \) We can express \( 11^{50} \) as \( (10 + 1)^{50} \). ### Step 2: Apply the Binomial Theorem Using the Binomial Theorem, we expand \( (a + b)^n \): \[ ...
Promotional Banner

Topper's Solved these Questions

  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE-I|28 Videos
  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise EXERCISE-II|11 Videos
  • Solutions of Triangle & Binomial Theorem

    ALLEN|Exercise Do yourself -6|4 Videos
  • SOLUTION AND PROPERTIES OF TRIANGLE

    ALLEN|Exercise All Questions|106 Videos
  • TRIGNOMETRIC RATIOS AND IDENTITIES

    ALLEN|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Find last three digits in 19^(100)

Find (i) the last digit, (ii) the last two digits, and (iii) the last three digits of 17^(256)dot

Find (i) the last digit, (ii) the last two digits, and (iii) the last three digits of 17^(256)dot

The number obtained after dividing the number formed by the last three digits of 17^(256) by 100 is

Find the last three digits of the number 27^(27)dot

Find the least three digit number which when divided by 20, 30, 40 and 50 leaves remainder 10 in each case.

Find the least number of three digits which is perfect square.

Find the last digit, last two digits and last three digits of the number (81)^(25)

Find the last two digits of the number (23)^(14)dot

Find the last two digits of the number 27^(27)dot

ALLEN-Solutions of Triangle & Binomial Theorem-Illustration
  1. Find the term independent of x in the expansion off the following ex...

    Text Solution

    |

  2. Prove that : ""^(25)C(10)+""^(24)C(10)+……..+""^(10)C(10)=""^(26)C(11)

    Text Solution

    |

  3. A student is allowed to select at most n books from a collection of (...

    Text Solution

    |

  4. Prove that (i) C(1)+2C(2)+3C(3)+……+nC(n)=n.2^(n-1) (ii) C(0)+(C(1)...

    Text Solution

    |

  5. If (1+x)^n=underset(r=0)overset(n)C(r)x^r then prove that C(1)^2+2.C(2...

    Text Solution

    |

  6. If (1 + x)^(n) = C(0) + C(1) x + C(2)x^(2) + C(3) x^(3)+ …+ C(n) x^(n...

    Text Solution

    |

  7. Prove that (""^(2n)C(0))^2-(""^(2n)C(1))^2+(""^(2n)C(2))^2-.....+(-1)^...

    Text Solution

    |

  8. Prove that : ""^(n)C(0).""^(2n)C(n)-""^(n)C(1).""^(2n-2)Cn(n)+""^(n)...

    Text Solution

    |

  9. If (1+x)^n=C(0)C1c+C(2)x^2+…..+C(n)x^n then show that the sum of the p...

    Text Solution

    |

  10. If (1+x)^n=C(0)+C(1)x+C(2)x^2+….+C(n)x^n then prove that (SigmaSigma)...

    Text Solution

    |

  11. Find the coffiecient of x^2 y^3 z^4 w in the expansion of (x-y-z+w)^(...

    Text Solution

    |

  12. Find the total number of terms in the expansion of 1(1+x+y)^(10) and c...

    Text Solution

    |

  13. Find the coffiecient of x^5 in the expansion of (2-x+ 3x ^2)^6

    Text Solution

    |

  14. If (1+x+x^2)^n = underset(2n)overset(r=0)Sigma a (r)x^r then prove th...

    Text Solution

    |

  15. If f ( x ) = [ x ] , where [ ⋅ ] denotes greatest integral function...

    Text Solution

    |

  16. Find the last three digits in 11^(50)

    Text Solution

    |

  17. Prove that 2222^(5555)+5555^(2222) is divisible by 7

    Text Solution

    |

  18. If x is so small such that its square and digher powers may be neglect...

    Text Solution

    |

  19. The value of cube root of 1001 upto five decimal places is

    Text Solution

    |

  20. If (1+x+x^2)^n = Sigma(2n)^(r=0) a (r)x^r then prove that (a) a(r...

    Text Solution

    |