Home
Class 12
MATHS
Integral part of (7 + 5sqrt2)^(2n+1) is...

Integral part of `(7 + 5sqrt2)^(2n+1) ` is `(n in N)`

A

an even number

B

an odd number

C

an even or an odd number depending upon the value of n

D

nothing can be said

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise PRACTICE EXERCISE|95 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - 1.1 (Level - 1) |52 Videos

  • BINOMIAL THEOREM

    AAKASH SERIES|Exercise EXERCISE - I|27 Videos

  • AREAS

    AAKASH SERIES|Exercise Exercise-3.2|21 Videos

  • CIRCLE

    AAKASH SERIES|Exercise EXERCISE -1.4|38 Videos

Similar Questions

Explore conceptually related problems

Integral part of (8 + 3sqrt7)^n is

Integral part of 7 + 4sqrt3)^n is (n in N)

Prove that : Suppose that n is a natural number and I, F are respectively the integral part and fractional part of (7+4sqrt(3))^(n) . Then show that (i) I is an odd integer (ii) (I+F)(I-F)=1

If the greatest divisor 30*5^(2n)+4*2^(3n) is p, AA n in N and that of 2^(2n+1)-6n-2 is q, AA n in N , then p+q=

Evalute the following integrals int sqrt(1 + sec x ) dx on ((2n - (1)/(2)) pi, (2n + (1)/(2)) pi, (n in z ))

The least positive integral value of n for which ((1-i)/(1+i))^(2n) = 1 is

Evaluate the integerals. int sqrt(1-cos 2x) dx on I sub [2n pi, (2n +1) pi], n in Z.

Evaluate the following define integrals as limit of sums : lim_(n rarroo) [(1+1/n) (1+2/n)......(1+n/n)]^(1//n)

Show that the middle term in the expansion of (1+x)^(2n)" is "(1.3.5. ..(2n-1))/(n!)(2x)^(n).

AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - II
  1. The remainder left out when 8^(2n) - 6(2)^( 2n+1) is divided by 9 is

    Text Solution

    |

  2. Integral part of 7 + 4sqrt3)^n is (n in N)

    Text Solution

    |

  3. Integral part of (7 + 5sqrt2)^(2n+1) is (n in N)

    Text Solution

    |

  4. If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest int...

    Text Solution

    |

  5. The integral part of (sqrt2+1)^6 is

    Text Solution

    |

  6. ""^(n) C(r+1)+2""^(n)C(r) +""^(n)C(r-1)=

    Text Solution

    |

  7. If Ck is the coefficient of x^k in the expansion of (1 + x)^2005 and i...

    Text Solution

    |

  8. The sum of the series ""^20C0 - ""^20C1 + ""^20C2 - ""^20C3 +…….""^20C...

    Text Solution

    |

  9. If S(n) = underset (r=0) overset( n) sum (1) /(""^(n) C(r)) and T...

    Text Solution

    |

  10. C0 - [C1 -2.C2+ 3.C3-……..+(-1)^(n-1).n.Cn] =

    Text Solution

    |

  11. C0+4. C1 + 7. C2+…...(n+1) terms =

    Text Solution

    |

  12. 2. C2 + 6. C3 + 12. C4 +….. + n (n-1) . Cn=

    Text Solution

    |

  13. Sum of last 8 coefficients in (1 + x)^16 is

    Text Solution

    |

  14. C0 + (C1)/(2) (4) + (C2)/(3) (16) + …………..+(Cn)/(n + 1) (2^(2n))

    Text Solution

    |

  15. (1 +x)^15 = a0 + a1x +…..+a15 x^15 rArr sum(r = 1)^15 r (ar)/(a(r - 1)...

    Text Solution

    |

  16. The value of sum(r = 1)^15 r^2 ((""^15Cr)/(""^15C(r - 1)) ) of is equa...

    Text Solution

    |

  17. If ak is the coefficient of x^k in the expansion of (1 +x+x^2)^n for k...

    Text Solution

    |

  18. Find the sum of the following (""^(15)C(1))/(""^(15)C(0))+2(""^(15)C...

    Text Solution

    |

  19. If a0, a1 , a2 …..an are binomial coefficients then (1 + a1/a0)(1 +a2/...

    Text Solution

    |

  20. ((C0 + C1)(C1 + C2)(C2 + C3)………(C(n-1) + Cn) )/(C0C1C2…Cn)

    Text Solution

    |