Home
Class 12
MATHS
If a(1),a(2),a(3),a(4),,……, a(n-1),a(n)...

If ` a_(1),a_(2),a_(3),a_(4),,……, a_(n-1),a_(n) " are distinct non-zero real numbers such that " (a_(1)^(2) + a_(2)^(2) + a_(3)^(2) + …..+ a_(n-1)^(2))x^2 + 2 (a_(1)a_(2) + a_(2)a_(3) + a_(3)a_(4) + ……+ a_(n-1) a_(n))x + (a_(2)^(2) +a_(3)^(2) + a_(4)^(2) +......+ a_(n)^(2)) le 0 " then " a_(1), a_(2), a_(3) ,....., a_(n-1), a_(n)` are in

A

A.P.

B

G.P.

C

H.P.

D

A.G.P.

Text Solution

Verified by Experts

The correct Answer is:
B
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment (Section -C) (objective Type Questions ( more thena one options are correct )|35 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment (Section -D) Linked comprehension Type Questions|13 Videos
  • COMPLEX NUMBERS AND QUADRATIC EQUATIONS

    AAKASH INSTITUTE|Exercise Assignment (Section -A) (objective Type Questions ( one option is correct)|47 Videos
  • BINOMIAL THEOREM

    AAKASH INSTITUTE|Exercise Assignment (section-J) Objective type question (Aakash Challengers Questions)|4 Videos
  • CONIC SECTIONS

    AAKASH INSTITUTE|Exercise SECTION - J ( Aakash Challengers Questions )|14 Videos

Similar Questions

Explore conceptually related problems

a_(1),a_(2),….a_(n) be in arithmetical progression , show that a_(1)^(2)a_(2)^(2)…….a_(n)^(2) gt a_(1)^(n) a_(n)^(n)

(a_(1))/(a_(1)+a_(2))+(a_(3))/(a_(3)+a_(4))=(2a_(2))/(a_(2)+a_(3))

Knowledge Check

  • If a_(1), a_(2),…,a_(n) are n non-zero real numbers such that (a_(1)^(2) + a_(2)^(2) + ... + a_(n-1)^(2)) (a_(2)^(2)+ a_(3)^(2) + ....+ a_(n)^(2)), le (a_(1)a_(2) + a_(2) a_(3) + ....+....+ a_(n-1) a_(n))^(2) then a_(1), a_(2),…, a_(n) are in

    A
    A.P.
    B
    G.P.
    C
    H.P.
    D
    none of these
  • If a_(1),a_(2),a_(3), . . .,a_(n) are non-zero real numbers such that (a_(1)^(2)+a_(2)^(2)+ . .. +a_(n-1).^(2))(a_(2)^(2)+a_(3)^(2)+ . . .+a_(n)^(2))le(a_(1)a_(2)+a_(2)a_(3)+ . . . +a_(n-1)a_(n))^(2)" then", a_(1),a_(2), . . . .a_(n) are in

    A
    H.P.
    B
    G.P
    C
    A.P.
    D
    none of these
  • If (1 + x)^(2n) = a_(0) + a_(1) x + a_(2) x^(2) +… + a_(2n) x^(2n) , then (a_(0) - a_(2) + a_(4) - a_(6) +…- a_(2n))^(2)+(a_(1) - a_(3) + a_(5) - a_(7) +...+a_(2n-1))^(2) is equal to

    A
    `2^(n)`
    B
    `4^(n)`
    C
    0
    D
    none of these
  • Similar Questions

    Explore conceptually related problems

    If a_(1),a_(2),a_(3),.....a_(n) are in H.P.and a_(1)a_(2)+a_(2)a_(3)+a_(3)a_(4)+......a_(n-1)a_(n)=ka_(1)a_(n) then k is equal to

    (1 + x + x^(2))^(n) = a_(0) +a_(1)x + a_(2) x^(2) +...+ a_(2n )x^(2n) , then a_(0) a_(2n) - a_(1) a_(2r+1) + a_(2) a_(2r+2) - a_(3) a_(2r+3) +...+a_(2n-2r)a_(2n)= .

    If a_(1), a_(2), a_(3), a_(4),…a_(n) are in harmonic progression, then a_(1) a_(2) + a_(2) a_(3) +…+ a_(n - 1).a_(n) =

    If a_(1), a_(2), a_(3),…a_(n) are in H.P., then (a_(1))/(a_(2) + a_(3) + ...+ a_(n)) , (a_(2))/(a_(1) + a_(3) +....+ a_(n)), (a_(3))/(a_(1)+a_(2)+...+a_(n)).......... are

    If (a_(2)a_(3))/(a_(1)a_(4))=(a_(2)+a_(3))/(a_(1)+a_(4))=3((a_(2)-a_(3))/(a_(1)-a_(4))) , then a_(1),a_(2),a_(3),a_(4) are in