Home
Class 11
MATHS
Let a,b,c,d, be any four real numbers. T...

Let a,b,c,d, be any four real numbers. Then `a^n+b^n=c^n+d^n` holds for any natural number n if

A

a+b=c+d

B

a-b=c-d

C

`a+b=c+d,a^2+b^2=c^2-d^2`

D

`a-b=c-d,a^2-b^2=c^2-d^2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • 3D-GEOMETRY

    PATHFINDER|Exercise QUESTION BANK|39 Videos
  • BINOMIAL THEOREM

    PATHFINDER|Exercise QUESTION BANK|225 Videos

Similar Questions

Explore conceptually related problems

Let a , b , c ,d ,be any four real number . Then a^(n)+b^(n)=c^(n)+d^(n) holds for any natural no . If -

The S.D of the first n natural numbers is

Check whether 6^n can end with the digit 0 for any natural number n.

If a/b and c/d be two rational numbers and if a = nc, b = nd,when n is a natural number , then what type of rational numbers are the numbers a/b and c/d and why ?

A sequence b_(0),b_(1),b_(2), . . . is defined by letting b_(0)=5 and b_(k)=4+b_(k-1) , for all natural number k. Show that b_(n)=5+4n , for all natural number n using mathematical induction.

Prove that (n !+1) is not divisible by any natural number between 2 and n

Let [x] denote the greatest integer less than or equal to x for any real number x. Then lim_(n to oo) ([n sqrt(2)])/(n) is equal to

The function f(x)=(4sin^2x−1)^n (x^2−x+1),n in N , has a local minimum at x=pi/6 . Then (a) n is any even number (b) n is an odd number (c) n is odd prime number (d) n is any natural number

Prove by mathematical induction that n^(5) and n have the same unit digit for any natural number n.

If f and g are two functions defined on N , such that f(n)= {{:(2n-1if n is even), (2n+2 if n is odd):} and g(n)=f(n)+f(n+1) Then range of g is (A) {m in N : m= multiple of 4 } (B) { set of even natural numbers } (C) {m in N : m=4k+3,k is a natural number (D) {m in N : m= multiple of 3 or multiple of 4 }

PATHFINDER-BASIC MATHEMATICS-QUESTION BANK
  1. Let alpha,beta be such that pi lt alpha-beta lt3 pi. If sin alpha+ sin...

    Text Solution

    |

  2. If alpha is a root of 25 cos^2 theta+5 cos theta-12=0, pi/2 lt alpha l...

    Text Solution

    |

  3. Let f(theta)=sin theta(sin theta+ sin 30) then f(theta)

    Text Solution

    |

  4. The general solution of the equation, 2cos 2x=3 cdot 2 cos^2 x-4 is

    Text Solution

    |

  5. Angles A and B are obtuse angles such that, tan A + tan B + tan A tan ...

    Text Solution

    |

  6. If x in [0,pi/2], the number of solutions of the equation, sin 7x + si...

    Text Solution

    |

  7. The principal solution set of the equation, 2 cos x = sqrt(2+2sin2x) i...

    Text Solution

    |

  8. The value of x and y satisfying the equations log(100)abs(x+y)=1/2, lo...

    Text Solution

    |

  9. Total number of solutions of [sin x] + cos x = 0, where [.] denotes th...

    Text Solution

    |

  10. Let f(n)=[1/2+n/100], where [.] denotes the greatest integer function,...

    Text Solution

    |

  11. If 0lt thetalt 2pi, then the intervals of values of theta for which 2...

    Text Solution

    |

  12. Number of solutions of the equation [2x] - 3{2x} = 1 is (where [/] and...

    Text Solution

    |

  13. If x ge0 and yge0, then the area bounded by the graph of [x] + [y] = 2...

    Text Solution

    |

  14. Let cos(alpha+beta)=4/5 and let sin(alpha-beta)=5/13, where 0le alpha,...

    Text Solution

    |

  15. If [x+[2x]] lt3, where [.] denotes the greatest integer function, then...

    Text Solution

    |

  16. Let a,b,c,d, be any four real numbers. Then a^n+b^n=c^n+d^n holds for ...

    Text Solution

    |

  17. Let P(x) be a polynomial, which when divided by x-3 and x-5 leaves rem...

    Text Solution

    |

  18. If log(0.2) (x-1) gt log(0.04) (x+5) then

    Text Solution

    |

  19. The number of real roots of equation loge x+ ex=0

    Text Solution

    |

  20. Let x1, x2,.......,x15 be 15 distinct numbers chosen from 1,2,3,....,1...

    Text Solution

    |