Home
Class 12
MATHS
If the lines lx+y+1=0,x+"my"+1=0" and "x...

If the lines `lx+y+1=0,x+"my"+1=0" and "x+y+n=0` intersect at one point then the value of
`(1)/(1-l)+(1)/(1-m)+(1)/(1-n)` is (l,m, n are unequal).

A

0

B

1

C

2

D

3

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly, `|{:(l,1,1),(1,m,1),(1,1,n):}|=0,{:(C_(2)toC_(2)-C_(1)),(C_(3)toC_(3)-C_(1)):}" "|{:(l,1-l,1-l),(1,m-1," "0),(1," "0,n-1):}|=0`
`impliesl(m-1)(n-1)+(l-1)(n-1)+(l-1)(m-1)=0" "("Expanding along "R_(1))`
`:." ""On dividing by "(l-1)(m-1)(n-1)," we get "`
So, `(1)/(1-l)+(1)/(1+m)+(1)/(1-n)=1.`Ans.
Promotional Banner

Topper's Solved these Questions

  • TEST PAPERS

    BANSAL|Exercise Mathematics SECTION-3 (PART-A) [COMPREHENSION TYPE]|3 Videos

  • TEST PAPERS

    BANSAL|Exercise Mathematics SECTION-3 (PART-A) [RESONING TYPE]|2 Videos

  • TEST PAPERS

    BANSAL|Exercise Chemistry, SECTION-2 (PART-B) [MATRIX TYPE]|1 Videos

  • PROBABILITY

    BANSAL|Exercise All Questions|1 Videos

  • THERMODYNAMICS

    BANSAL|Exercise Match the column|7 Videos

Similar Questions

Explore conceptually related problems

if the two line 11x+m1y+n1=0 and 12x+m2y+n2=0 cut axes at con-cyclic points, then :-

The lines lx+my+n=0,mx+ny+l=0 and nx+ly+m=0 are concurrent if (where l!=m!=n)

If m, n in N , then l_(m n) = int_(0)^(1) x^(m) (1-x)^(n) dx is equal to

Lines x=n, y=n^(3) intersect at the point A_(n).L_(n) is a line through A_(n) parallel to x+y=0 and make an intercept of length l_(n) on the axis of x, then the value of sum_(n=1)^(5)l_(n) is equal to K^(4)-16 , where K =

The condition that the line (x-x_(1))/(l)=(y-y_(1))/(m)=(z-z_(1))/(n) lies in the plane ax+by+cz+d=0 is

A triangle is formed by the lines x+y=0,x-y=0 and lx+my+1=0 . If l and m vary subject to the condition l^(2)+m^(2)=1 , then the locus of the circumcentre of the triangle is

The line lx+my+n=0 touches y^(2)=4x and x^(2)=4y simultaneously then l+2m+3n=

A variable line L=0 is drawn through O(0,0) to meet the lines L:x+2y-3=0 and L:x+2y+4=0 at points M and N respectively.A point P is taken on L=0 such that (1)/((OP)^(2))=(1)/((OM)^(2))+(1)/((ON)^(2)). Locus of P is