Home
Class 12
MATHS
If 2f(xy) =(f(x))^(y) + (f(y))^(x) for a...

If `2f(xy) =(f(x))^(y) + (f(y))^(x)` for all `x, y in R` and `f(1) =3`, then the value of `sum_(t=1)^(10) f(r)` is equal to

A

`3/2 (3^(10)-1)`

B

`3/2(3^(9)-1)`

C

`(3^(10)-1)/2`

D

`1/2 (3^(10)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • JEE MOCK TEST 4

    NTA MOCK TESTS|Exercise MATHEMETIC - SUBJECTIVE NUMERICAL|5 Videos

  • JEE MOCK TEST 6

    NTA MOCK TESTS|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

If f(x+f(y))=f(x)+y for all x,y in R and f(1)=1, then find the value of f(10)/5,f(x) is not constant function.

If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,y in R and f(1)=7, then sum_(r=1)^(n) f(r) , is

If f:R to R satisfies f(x+y)=f(x)+f(y), for all x, y in R and f(1)=7, then sum_(r=1)^(n)f( r) is

If f(x+y)=f(x)+f(y) -xy -1 for all x, y in R and f(1)=1 then f(n)=n, n in N is true if

Let f be a function satisfying f(x+y)=f(x) *f(y) for all x,y, in R. If f (1) =3 then sum_(r=1)^(n) f (r) is equal to

If f:R rarr R satisfies f(x+y)=f(x)+f(y), for all x,y in R and f(1)=2 then sum_(r=1)^(7)f(1)

If f((x)/(y))=(f(x))/(f(y)) for all x,y in R,y!=0 and f(t)!=0, if t!=0 and f'(1)=3 then f(x) is

Consider a real-valued function f(x) satisfying 2f(xy)=(f(x))^(y)+(f(y))^(x)AA x,y in R and (1)=a, where a!=1 Prove that (a-1)sum_(i=1)^(n)f(i)=a^(n+1)-a

If (x).f(y)=f(x)+f(y)+f(xy)-2AA x,y in R and if f(x) is not a constant function,the value of f(1) is equal to

NTA MOCK TESTS-JEE MOCK TEST 5-MATHEMATICS
  1. If the value of (1+tan 1^(@))(1+ tan 2^(@)) (1+tan 3^(@))………. Is 2^(...

    Text Solution

    |

  2. If (5+9+13+...... n terms)/( 7 + 9 + 11 +....(n+1) terms) = 17/16, th...

    Text Solution

    |

  3. If 2f(xy) =(f(x))^(y) + (f(y))^(x) for all x, y in R and f(1) =3, then...

    Text Solution

    |

  4. If 1/6sintheta,costheta,tantheta are in G.P. then theta is equal to (n...

    Text Solution

    |

  5. The value of integral int(0)^(1)sqrt((1-x)/(1+x))dx is

    Text Solution

    |

  6. If p , r , s gt 0 then lim(x rarr oo)((p^(1/x)+q^(1/x)+r^(1/x)+s^(1/x)...

    Text Solution

    |

  7. If (27)^999 is divided by 7, then the remainder is .

    Text Solution

    |

  8. If A=[(1,-3), (2,k)] and A^(2) - 4A + 10I = A, then k is equal to

    Text Solution

    |

  9. A piece of cheese is located at (12, 10) in a coordinate plane. A mous...

    Text Solution

    |

  10. Two medians drawn from the acute angles of a right angled triangle i...

    Text Solution

    |

  11. If Z is a non-real complex number, then find the minimum value of (Imz...

    Text Solution

    |

  12. If the coefficient of x^7 in (ax^2+1/(bx))^11 is equal to the coeffici...

    Text Solution

    |

  13. The average of five consecutive odd number is 61. Then the difference ...

    Text Solution

    |

  14. The abscissa of A and B are the roots of the equation x^(2) + 2ax -b^(...

    Text Solution

    |

  15. A tower T(1) of height 60 m is located exactly opposite to a tower T(2...

    Text Solution

    |

  16. The area between the curve y=2x^(4)-x^(2), the x-axis, and the ordinat...

    Text Solution

    |

  17. If a plane, intercepts on the coordinates axes at 8,4,4 then the lengt...

    Text Solution

    |

  18. If f(x) = {{:((sqrt(4+ax)-sqrt(4-ax))/x,-1 le x lt 0),((3x+2)/(x-8), 0...

    Text Solution

    |

  19. Check whether the relation R defined on the set A={1,\ 2,\ 3,\ 4,\ 5,\...

    Text Solution

    |

  20. int(sin^8x-cos^8x)/(1-2sin^2xcos^2x)dx=

    Text Solution

    |