Home
Class 11
MATHS
For integer n gt 1, the digit at units p...

For integer `n gt 1`, the digit at units place in the number `sum_(r=0)^(100)r!+2^(2^n)` is

A

0

B

1

C

2

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BASIC MATHEMATICS

    PATHFINDER|Exercise QUESTION BANK |266 Videos

  • BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION

    PATHFINDER|Exercise QUESTION BANK|68 Videos

Similar Questions

Explore conceptually related problems

Find the sum sum_(r=0) .^(n+r)C_r .

Find the sum sum_(r=1)^n r(r+1)(r+2)(r+3)

Find the sum sum_(i=0)^r.^(n_1)C_(r-i) .^(n_2)C_i .

The value of sum_(r=1)^n (^nP_r)/(r!) is

If n be a positive integer, then the digit in the unit's place of 3^(2n-1)+2^(2n-1) is -

Find the value of sum_(r=1)^(n) (r)/(1+r^(2)+r^(4))

Find the sum sum_(r=1)^n r^n (^nC_r)/(^nC_(r-1)) .

The value of sum_(r=0)^(3n-1)(-1)^r .^(6n)C_(2r+1)3^r is

If the sum of the series sum_(n=0)^oor^n ,|r|<1 is s , then find the sum of the series sum_(n=0)^oor^(2n) .

The value of lim_(n to oo) sum_(r=1)^(n)(r^(2))/(r^(3)+n^(3)) is -

PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. The coefficient of x^ny^n in the expansion of {(1+x)(1+y)(x+y)}^n is

    Text Solution

    |

  2. The remainder when x=5^(5^(5^(......))) (23 times 5) is divided by 24 ...

    Text Solution

    |

  3. For integer n gt 1, the digit at units place in the number sum(r=0)^(1...

    Text Solution

    |

  4. In the expansion of (1+x+x^2+x^3)^6, the coefficient of x^(14) is

    Text Solution

    |

  5. The coefficient of x^(3l+2) in the expression (a+x)^l(b+x)^(l+1)(c+x)^...

    Text Solution

    |

  6. The interval in which x must lie so that greatest term in the expansio...

    Text Solution

    |

  7. The digit in the unit place in the number (19)^(2005)+(11)^(2005)-(9)^...

    Text Solution

    |

  8. If n lt p lt 2n and p is prime and N = .^(2n)Cn, then

    Text Solution

    |

  9. If absx lt 2/3 then the 4^(th) term in the expansion of (1+3/2x)^(1/2)...

    Text Solution

    |

  10. The sum of rational in (sqrt2+root(3)(3)+root(6)(5))^10 is equal to

    Text Solution

    |

  11. Let f(x)=a0+a1x+a2x^2+.....+anx^n+....and f(x)/(1-x)=b0+b1x+b2x^2+.......

    Text Solution

    |

  12. If (1-x^2)^n=sum(r=0)^narx^r(1-x)^(2n-r), then ar is equal to

    Text Solution

    |

  13. The largest term in the expansion of (3+2x)^50, where x=1/5, is

    Text Solution

    |

  14. The sixth term in the expansion of {2^(log2root(5)(9^(x-1)+7))+1/2^(1/...

    Text Solution

    |

  15. The value of sum(r=0)^(20)r(20-r)(^(20)Cr)^2 is equal to ?

    Text Solution

    |

  16. The value of sum(r=1)^(n+1)(sum(k=1)^n^kC(r-1)) (where r, k, n in N) i...

    Text Solution

    |

  17. sum(r=0)^(300)arx^r=(1+x+x^2+x^3)^(100). If a=sum(r=0)^(300)ar, then s...

    Text Solution

    |

  18. Coefficient of x^50 in (1+x)^(1000)+2x(1+x)^(999)+3x^2(1+x)^(998)+.......

    Text Solution

    |

  19. C0/2-C1/3+C2/4-C3/5+.... is equal to

    Text Solution

    |

  20. The coefficient of x^7 in the expansion of (1-x-x^2+x^3)^6 is

    Text Solution

    |