JEE Main & Advanced Mathematics Straight Line Question Bank

done Concurrency of three lines Total Questions - 20

• question_answer1)
  If the lines  \[ax+by+c=0\], \[bx+cy+a=0\] and \[cx+ay+b=0\] be concurrent, then             [IIT 1985; DCE 2000, 02]
  A)
             \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}+3abc=0\]                                     done clear
  B)
             \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-abc=0\] done clear
  C)
             \[{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc=0\]                                      done clear
  D)
             None of these done clear
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• question_answer2)
  The points \[(at_{1}^{2},2a{{t}_{1}}),(at_{2}^{2},2a{{t}_{2}})\]and \[(a,0)\]will be collinear, if
  A)
             \[{{t}_{1}}{{t}_{2}}=1\]              done clear
  B)
             \[{{t}_{1}}{{t}_{2}}=-1\] done clear
  C)
             \[{{t}_{1}}+{{t}_{2}}=1\]            done clear
  D)
             \[{{t}_{1}}+{{t}_{2}}=-1\] done clear
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• question_answer3)
  If the given lines \[y={{m}_{1}}x+{{c}_{1}},y={{m}_{2}}x+{{c}_{2}}\] and \[y={{m}_{3}}x+{{c}_{3}}\] be concurrent, then
  A)
             \[{{m}_{1}}({{c}_{2}}-{{c}_{3}})+{{m}_{2}}({{c}_{3}}-{{c}_{1}})+{{m}_{3}}({{c}_{1}}-{{c}_{2}})=0\] done clear
  B)
             \[{{m}_{1}}({{c}_{2}}-{{c}_{1}})+{{m}_{2}}({{c}_{3}}-{{c}_{2}})+{{m}_{3}}({{c}_{1}}-{{c}_{3}})=0\] done clear
  C)
             \[{{c}_{1}}({{m}_{2}}-{{m}_{3}})+{{c}_{2}}({{m}_{3}}-{{m}_{1}})+{{c}_{3}}({{m}_{1}}-{{m}_{2}})=0\]      done clear
  D)
             None of these done clear
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• question_answer4)
  The lines             \[(p-q)x+(q-r)y+(r-p)=0\]                              \[(q-r)x+(r-p)y+(p-q)=0\]            \[(r-p)x+(p-q)y+(q-r)=0\]are
  A)
             Parallel                                       done clear
  B)
             Perpendicular done clear
  C)
             Concurrent                                 done clear
  D)
             None of these done clear
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• question_answer5)
  Which of the following lines is concurrent with the lines \[3x+4y+6=0\]and \[6x+5y+9=0\]
  A)
             \[2x+3y+5=0\]                            done clear
  B)
             \[3x+3y+5=0\] done clear
  C)
             \[7x+9y+3=0\]                            done clear
  D)
             None of these done clear
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• question_answer6)
  The value of k for which the lines \[7x-8y+5=0\], \[3x-4y+5=0\] and \[4x+5y+k=0\] are concurrent is given by [MP PET 1993]
  A)
             - 45 done clear
  B)
             44 done clear
  C)
             54    done clear
  D)
             - 54 done clear
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• question_answer7)
  For what value of 'a' the lines \[x=3,y=4\] and \[4x-3y+a=0\] are concurrent                     [RPET 1984]
  A)
  0      done clear
  B)
  -1 done clear
  C)
  2      done clear
  D)
  3 done clear
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• question_answer8)
  The lines \[15x-18y+1=0,\] \[12x+10y-3=0\] and \[6x+66y-11=0\] are                                [AMU 1978]
  A)
             Parallel                                       done clear
  B)
             Perpendicular done clear
  C)
             Concurrent                                 done clear
  D)
             None of these done clear
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• question_answer9)
  The straight lines \[x+2y-9=0,\] \[3x+5y-5=0\] and \[ax+by-1=0\] are concurrent, if the straight line \[35x-22y+1=0\] passes through the point
  A)
             \[(a,b)\]                                     done clear
  B)
             \[(b,a)\] done clear
  C)
             \[(-a,-b)\]                                   done clear
  D)
             None of these done clear
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• question_answer10)
  If the lines \[ax+y+1=0,x+by+1=0\] and \[x+y+c=0\] (a, b, c being distinct and different from 1) are concurrent, then \[\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=\]
  A)
             0      done clear
  B)
             1 done clear
  C)
             \[\frac{1}{a+b+c}\]                    done clear
  D)
             None of these done clear
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• question_answer11)
  If the lines \[ax+2y+1=0,bx+3y+1=0\] and \[cx+4y+1=0\] are concurrent, then a, b, c are in
  A)
             A. P.                                            done clear
  B)
             G. P. done clear
  C)
             H. P.                                           done clear
  D)
             None of these done clear
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• question_answer12)
  The lines \[2x+y-1=0,ax+3y-3=0\] and \[3x+2y-2=0\] are concurrent for             [EAMCET 1994]
  A)
             All a                                            done clear
  B)
             \[a=4\]only done clear
  C)
             \[-1\le a\le 3\]                          done clear
  D)
             \[a>0\]only done clear
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• question_answer13)
  If lines \[4x+3y=1,y=x+5\] and \[5y+bx=3\] are concurrent, then b equals [RPET 1996; MP PET 1997; EAMCET 2003; Pb. CET 2002]
  A)
             1      done clear
  B)
             3 done clear
  C)
             6      done clear
  D)
             0 done clear
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• question_answer14)
  Three lines \[3x-y=2,\,\,5x+ay=3\] and \[2x+y=3\] are concurrent, then a =                                       [MP PET 1996]
  A)
             2      done clear
  B)
             3 done clear
  C)
             -1    done clear
  D)
             -2 done clear
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• question_answer15)
  The three lines \[lx+my+n=0\], \[mx+ny+l=0\], \[nx+ly+m=0\] are concurrent if                                [Pb. CET 2002]
  A)
             \[l=m+n\]                                   done clear
  B)
             \[m=l+n\] done clear
  C)
             \[n=l+m\]                                   done clear
  D)
             \[l+m+n=0\] done clear
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• question_answer16)
  The straight lines \[4ax+3by+c=0\]where \[a+b+c=0\], will be concurrent, if point is                                        [RPET 2002]
  A)
             (4, 3)                                          done clear
  B)
             (1/4, 1/3) done clear
  C)
             (1/2, 1/3)                                   done clear
  D)
             None of these done clear
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• question_answer17)
  If the lines \[x+q=0,y-2=0\] and \[3x+2y+5=0\] are concurrent, then value of q will be      [DCE 2002]
  A)
             1      done clear
  B)
             2 done clear
  C)
             3      done clear
  D)
             5 done clear
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• question_answer18)
  The value of \[\lambda \] for which the lines \[3x+4y=5,\] \[5x+4y=4\]  and \[\lambda x+4y=6\] meet at a point is   [Kerala (Engg.) 2002]
  A)
             2      done clear
  B)
             1 done clear
  C)
             4      done clear
  D)
             3 done clear
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• question_answer19)
  The three straight lines \[ax+by=c,\,\,bx+cy=a\] and \[cx+ay=b\] are collinear, if                                              [MP PET 2004]
  A)
             \[a+b+c=0\]                               done clear
  B)
             \[b+c=a\] done clear
  C)
             \[c+a=b\]                                   done clear
  D)
             \[a+b=c\] done clear
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• question_answer20)
  The solution of equations \[x+y=10,2x+y=18\] and \[4x-3y=26\] will be                                             [DCE 2005]
  A)
             Only one solution                       done clear
  B)
             No Solution                                done clear
  C)
             Infinite solution                         done clear
  D)
             None of these done clear
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