Home
Class 12
MATHS
If (4+sqrt(15))^n=I+f,w h r en is an odd...

If `(4+sqrt(15))^n=I+f,w h r en` is an odd natural number, `I` is an integer and `0

Promotional Banner

Topper's Solved these Questions

  • INVERSE TRIGONOMETRIC FUNCTIONS

    RESONANCE DPP|Exercise All Questions|15 Videos

  • MATRICES

    RESONANCE DPP|Exercise All Questions|7 Videos

Similar Questions

Explore conceptually related problems

Find the sum of first 15 odd natural numbers.

If (2+sqrt(3))^n=I+f, whare I and n are positive integers and 0

If (9 + 4 sqrt(5))^(n) = I + f ,n and l being positive integers and f is a proper fraction , show that (I-1 ) f + f^(2) is an even integer.

If x , y >0,(log)_y x+(log)_x y=(10)/3 a n d x y=144 , t h e n(x+y)/2=sqrt("N")" w h e r e N" is a natural number, find the value of Ndot

Let N=(log_(3)135)/(log_(15)3)-(log_(3)5)/(log_(405)3). Then N is a natural number (b) a prime number an even integer (d) an odd integer

If n is a positive integer,then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is (1) an irrational number (2) an odd positive integer (3) an even positive integer (4) a a rational number other than positive integers

If following form the above example that (-1) an odd natural number quad =-1 and (-1) An even natural number =1 i.e.(-1)^(n)={1 if n is an even natural number and -1 if n is odd natural number

RESONANCE DPP-JEE MAINS-All Questions
  1. Consider the points P(2,-4):Q(4,-2) and R(7,1). The points P,Q,R

    Text Solution

    |

  2. If plambda^4+qlambda^3+rlambda^2+slambda+t=|lambda^2+3lambdalambda-1la...

    Text Solution

    |

  3. If (4+sqrt(15))^n=I+f,w h r en is an odd natural number, I is an integ...

    Text Solution

    |

  4. If vec a= hat i+ hat j+ hat k= hat i-2 hat j+ hat k and the vector v...

    Text Solution

    |

  5. If lines (x-3)/1=(y-[k])/2=(z-1)/1 and (x-1)/2=(y+1)/3=(z-1)/4 inter...

    Text Solution

    |

  6. If S=1+4/3+9/9+(16)/(27)+oo, then find the value of [S] (where [.] is ...

    Text Solution

    |

  7. If A=[a b c b c a c a b],a b c=1,A^T A=I , then the value of a^3+b^3+...

    Text Solution

    |

  8. Number of divisors of 2^5. 3^2 .5^3 which are divisible by 2 but not d...

    Text Solution

    |

  9. If alpha and beta are the roots of quadratic equationx^2+ px + q=0 and...

    Text Solution

    |

  10. f(x)=cos^(-1)(x-x^2)+sqrt(1-1/(|x|))+1/[[x^2-1]) then domain of f(x...

    Text Solution

    |

  11. The value of lim(n->oo)sum(r=0)^(n)(sum(t=0)^(r-1)1/(5^n)*"^n Cr*"^...

    Text Solution

    |

  12. If 25C0 25C2 +2. 25C1 25C3 +3. 25C2 .25C4+....+ 24. 25C23.25C25=k. 4...

    Text Solution

    |

  13. The graph of function f contains the point P(1, 2) and Q(s, r). The e...

    Text Solution

    |

  14. Given that the 4th term in the expansion of [2+(3//8x)]^(10) has the m...

    Text Solution

    |

  15. Let A,B,C be 2xx2 matrices with entries from the set of real numbers. ...

    Text Solution

    |

  16. Let f (n) denote the n^(th) term of the sequence 2, 5, 10, 17, 26,.......

    Text Solution

    |

  17. For |z-1|=1, i tan(("arg"(z-1))/(2))+(2)/(z) is equal to

    Text Solution

    |

  18. Number of ways in which 8 people can be arranged in a line if A and B ...

    Text Solution

    |

  19. For all real numbers x, let the mapping f (x) = 1/(x-i). where i =sqrt...

    Text Solution

    |

  20. Let A,B,C,D be real matrices such that A^(T)=BCD,B^(T)=CDA,C^(T)=DAB a...

    Text Solution

    |