Home
Class 12
MATHS
Q. if x1,x2......xn are in H.P., then su...

Q. if `x_1,x_2......x_n` are in `H.P`., then `sum_(r=1)^n x_r x_(r+1)` is equal to `:` (A) `(n-1)x_1 x_n` (B) `n x_1 x_n` (C) `(n+1)x_1 x_n` (D) `(n+2)x_1 x_n`

A

`(n-1)x_(1).x_(n)`

B

`n.x_(1).x_(n)`

C

`(n+1)x_(1).x_(n)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • TIPS

    FIITJEE|Exercise OBJECTIVE|84 Videos

  • TIPS

    FIITJEE|Exercise ASSERTION REASONING|8 Videos

  • TIPS

    FIITJEE|Exercise NUERICAL DECIMAL BASED QUATIONS|20 Videos

  • TEST PAPERS

    FIITJEE|Exercise MATHEMATICS|328 Videos

  • TRIGNOMETRIC RATIOS AND IDENTITIES

    FIITJEE|Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Q.if x_(1),x_(2)......x_(n) are in H.P. then sum_(r=1)^(n)x_(r)x_(r+1) is equal to :(A)(n-1)x_(1)x_(n)(B)nx_(1)x_(n)(C)(n+1)x_(1)x_(n)(D)(n+2)x_(1)x_(n)

If x_(1),x_(2),x_(3),......x2_(n) are in A.P, then sum_(r=1)^(2n)(-1)^(r+1)x_(r)^(2) is equal to

If Sigma_(r=1)^(2n) sin^(-1) x^(r )=n pi, then Sigma__(r=1)^(2n) x_(r ) is equal to

lim_(xrarr1) (sum_(x=1)^(n)x^(r)-n)/(x-1) is equal to

If x_(1),x_(2),x_(3)...x_(n) are in H.P,then prove that x_(1)x_(2)+x_(2)x_(3)+xx x-3x_(4)+...+x_(n-1)x_(n)=(n-1)x_(1)x_(n)

If 1+x^(2)=sqrt(3)x, then sum_(n=1)^(24)(x^(n)-(1)/(x^(n))) is equal to

n + (n-1) x + (n-2) x ^ (2) + ....... + 2x ^ (n-2) + x ^ (n-1)

(1 + x)^(n) = C_(0) + C_(1)x + C_(2) x^(2) + ...+ C_(n) x^(n) , show that sum_(r=0)^(n) C_(r)^(3) is equal to the coefficient of x^(n) y^(n) in the expansion of {(1+ x)(1 + y) (x + y)}^(n) .

If Sigma_(r=1)^(n) cos^(-1)x_(r)=0, then Sigma_(r=1)^(n) x_(r) equals

FIITJEE-TIPS-ASSIGNMENT (SECTION (I): MCQ (SINGLE CORRECT)
  1. If a ,b ,c in R^+, t h e n(b c)/(b+c)+(a c)/(a+c)+(a b)/(a+b) is alwa...

    Text Solution

    |

  2. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  3. Q. if x1,x2......xn are in H.P., then sum(r=1)^n xr x(r+1) is equal to...

    Text Solution

    |

  4. Given(1+x^2)^2 (1+x)^n = sum ar x^r. If a0,a1 and a2 are in A.P. then ...

    Text Solution

    |

  5. If a, b, c are distinct real numbers such that a, b, c are in A.P. and...

    Text Solution

    |

  6. Value of (1^2)/1+(1^2+2^2)/(1+2)+(1^2+2^2+3^2)/(1+2+3)+.... 'n' terms...

    Text Solution

    |

  7. If f(x)=x^9-6x-2x^7+12 x^6+x^4-7x^3+6x^2+x-3, find f(6)dot

    Text Solution

    |

  8. Let f(x)=(1)/(1+x) and let g(x,n)=f(f(f(….(x)))), then lim(nrarroo)g(x...

    Text Solution

    |

  9. lim(xrarr0^(+)){ln((x^(7)+2x^(6)e+x^(5)e^(2)))-ln(x^(2)sin^(3)x)} is e...

    Text Solution

    |

  10. A continuous, even periodic function f with period 8 is such that f(0)...

    Text Solution

    |

  11. The value of int(0)^(1)(Pi(i=1)^(n)(x+i))(Sigma(j=1)^(n)(1)/(x+j))dx i...

    Text Solution

    |

  12. If f is a continuous and differentiable funciton in x in (0, 1) such t...

    Text Solution

    |

  13. int(0)^(1)[(x)/(sinx)]dx equals to, ([.] denotes greatest integers fun...

    Text Solution

    |

  14. If area bounded by the curve x^(2)y+y^(2)x=alpha y is 2 units, then po...

    Text Solution

    |

  15. Let f(x)={{:(2^([x]),, x lt0),(2^([-x]),,x ge0):}, then the area bound...

    Text Solution

    |

  16. The degree and order of differntial equation of family of circle touch...

    Text Solution

    |

  17. If k sin^(2)x+(1)/(k) cosec^(2) x=2, x in (0,(pi)/(2)), then cos^(2...

    Text Solution

    |

  18. Domain of the function f(x)=(1)/([sinx-1]) (where [.] denotes the grea...

    Text Solution

    |

  19. For f:N rarr R f(x)=(x^(3)-11^(3))^(1//3), the number of positive inte...

    Text Solution

    |

  20. If f(x)=={{:((sin(x))/({x})",",{x} ne 0),(k",",{x}0):}, where {x} deno...

    Text Solution

    |