Home
Class 11
MATHS
Prove that sqrt(10)[(sqrt(10)+1)^(100)-(...

Prove that `sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)]` is an even integer .

Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    CENGAGE PUBLICATION|Exercise All Questions|877 Videos

Similar Questions

Explore conceptually related problems

Prove that tan(pi/(16))=sqrt(4+2sqrt(2))-(sqrt(2)+1)

Solve, sqrt(x-6)-sqrt(10-x) ge 1 .

Prove that ((i-sqrt3)/(i+sqrt3))^200+((i+sqrt3)/(-i+sqrt3))^200= -1

Prove that : tan 11^(@) 15' = sqrt(4+2sqrt(2))-sqrt(2)-1

Prove that, int_(2)^(3)(sqrt(x)dx)/(sqrt(x)+sqrt(5-x))=(1)/(2)

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),sin^(-1)alpha are the angles of a triangle is (-1)/(sqrt(2)) (b) 1/2 (c) 1/(sqrt(3)) (d) 1/(sqrt(2))

The value of alpha such that sin^(-1)(2/(sqrt(5))),sin^(-1)(3/(sqrt(10))),sin^(-1)alpha are the angles of a triangle is

Prove that sin [2 tan^(-1) {sqrt((1 -x)/(1 + x))}] = sqrt(1 - x^(2))

Three positive numbers a, b, c are in A.P. Prove that (1)/(sqrt(b)+sqrt(c )), (1)/(sqrt(c )+sqrt(a)) , (1)/(sqrt(a) + sqrt(b)) are also in A.P.

CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. Find the degree of the polynomial 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^7-...

    Text Solution

    |

  2. If 9^7+7^9 is divisible b 2^n , then find the greatest value of n ,w...

    Text Solution

    |

  3. Prove that sqrt(10)[(sqrt(10)+1)^(100)-(sqrt(10)-1)^(100)] is an even ...

    Text Solution

    |

  4. Find the remainder when x=5^(5^(5^(5...))) (24 times 5) is divided by ...

    Text Solution

    |

  5. Find the remainder when 1690^(2608)+2608^(1690) is divided by 7.

    Text Solution

    |

  6. Find the value of {3^(2003)//28}, w h e r e{dot} denotes the fractiona...

    Text Solution

    |

  7. Find the remainder when 5^(99) is divided by 13.

    Text Solution

    |

  8. Find remainder when 7^(103) is divided by 25.

    Text Solution

    |

  9. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

    Text Solution

    |

  10. If the coefficient of the middle term in the expansion of (1+x)^(2n+2)...

    Text Solution

    |

  11. If the coefficients of three consecutive terms in the expansion of (1+...

    Text Solution

    |

  12. In the coefficients of rth, (r+1)t h ,a n d(r+2)t h terms in the binom...

    Text Solution

    |

  13. Prove that (C0+C1)(C1+C2)(C2+C3)(C3+C4)...........(C(n-1)+Cn) = (C0...

    Text Solution

    |

  14. If the coefficients of four consecutive terms in the expansion of (1+x...

    Text Solution

    |

  15. Find the sum of sum(r=1)^n r* (nCr)/(nC(r-1)

    Text Solution

    |

  16. Find the positive integer just greater than (1+0. 0001)^(10000)dot

    Text Solution

    |

  17. Find the last digit of 17^(256)dot

    Text Solution

    |

  18. If 10^m divides the number 101^(100)-1 then, find the greatest value o...

    Text Solution

    |

  19. Using the principle of mathematical induction, prove that (2^(3n)-1) i...

    Text Solution

    |

  20. If x is very large as compare to y , then prove that sqrt(x/(x+y))dot...

    Text Solution

    |