Home
Class 12
MATHS
Let N=alphaalphaalphaalphaalphaalpha be ...

Let` N=alphaalphaalphaalphaalphaalpha` be a 6 digit number (all digit repeated) and N is divisible by 924 and let `alpha,beta` the roots of the equation `x^(2)-11x+lambda=0`, if product of all possible values of `lambda` is `168K` then the value of K is

Text Solution

Verified by Experts

The correct Answer is:
D
`N = alpha (111111)` is divisible by `7xx11xx3`.
Hence for N to be a divisible by 924, `alpha=4` or 8
and `alpha` and `beta` are roots of `x^(2)-11x+lambda=0`
`impliesalpha+beta=11`
`implies (alpha,beta)-=(4,7),(8,3)`
possible value of lambda =28,24
implies product of `lambda =672`
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    ALLEN |Exercise part-2 Mathematic|17 Videos

  • TEST PAPERS

    ALLEN |Exercise part-2 Mathematics|48 Videos

  • TEST PAPERS

    ALLEN |Exercise MATHEMATICS|136 Videos

  • TEST PAPER

    ALLEN |Exercise CHEMISTRY SECTION-II|16 Videos

  • VECTOR ALGEBRA

    ALLEN |Exercise All Questions|1 Videos

Similar Questions

Explore conceptually related problems

Find all roots of the equation x^(6)-x^(5)+x^(4)-x^(2)+x-1=0.

Let alpha,beta be the roots of the equation x^2-p x+r=0 and alpha/2,2beta be the roots of the equation x^2-q x+r=0 , the value of r is

All possible values of a, so that 6 lies between the roots of the equation x^2 + 2(a-3)x +9 =0

Let alpha and beta be the roots of equation px^2 + qx + r = 0 , p != 0 .If p,q,r are in A.P. and 1/alpha+1/beta=4 , then the value of |alpha-beta| is :

Let alpha,beta be the roots of the equation (x-a)(x-b)=c ,c!=0 Then the roots of the equation (x-alpha)(x-beta)+c=0 are

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=0 where i=sqrt(-1) , the value of |alpha-beta|^(2) is

The range of values of a so that all the roots of the equations 2x^(3)-3x^(2)-12x+a=0 are real and distinct, belongs to

If alpha, beta be the roots of 4x^(2) - 16x + c = 0, c in R such that 1 lt alpha lt 2 and 2 lt beta lt 3 , then the number of integral values of c is

Let alpha and beta be roots of the equation X^(2)-2x+A=0 and let gamma and delta be the roots of the equation X^(2)-18x+B=0 . If alpha lt beta lt gamma lt delta are in arithmetic progression then find the valus of A and B.