JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank

done Angle between the pair of straight lines, Condition for parallel and perpendicular lines Total Questions - 44

• question_answer1)
  If the lines represented by the equation \[a{{x}^{2}}-bxy-{{y}^{2}}=0\] make angles \[\alpha \] and \[\beta \] with the x-axis, then \[\tan (\alpha +\beta )\]=
  A)
             \[\frac{b}{1+a}\].                done clear
  B)
             \[\frac{-b}{1+a}\] done clear
  C)
             \[\frac{a}{1+b}\]                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer2)
  Angle between the lines represented by the equation \[{{x}^{2}}+2xy\sec \theta +{{y}^{2}}=0\] is
  A)
             \[\theta \]                              done clear
  B)
             \[2\theta \] done clear
  C)
             \[\frac{\theta }{2}\]           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer3)
  If the acute angles between the pairs of lines \[3{{x}^{2}}-7xy+4{{y}^{2}}=0\] and \[6{{x}^{2}}-5xy+{{y}^{2}}=0\] be \[{{\theta }_{1}}\] and \[{{\theta }_{2}}\] respectively, then
  A)
             \[{{\theta }_{1}}={{\theta }_{2}}\]                                   done clear
  B)
             \[{{\theta }_{1}}=2{{\theta }_{2}}\] done clear
  C)
             \[2{{\theta }_{1}}={{\theta }_{2}}\]                                done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer4)
  . The angle between the lines represented by the equation \[a{{x}^{2}}+xy+b{{y}^{2}}=0\] will be \[{{45}^{o}}\], if
  A)
             \[a=1,b=6\]                           done clear
  B)
             \[a=1,b=-6\] done clear
  C)
             \[a=6,b=1\]                           done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer5)
  The lines represented by the equation \[9{{x}^{2}}+24xy+16{{y}^{2}}+21x+28y+6=0\] are
  A)
             Parallel                                    done clear
  B)
             Coincident done clear
  C)
             Perpendicular                       done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer6)
  Acute angle between the lines represented by \[({{x}^{2}}+{{y}^{2}})\sqrt{3}=4xy\] is                                   [MP PET 1992]
  A)
             \[\pi /6\]                                 done clear
  B)
             \[\pi /4\] done clear
  C)
             \[\pi /3\]                                 done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer7)
  Angles made by the lines represented by the equation \[xy+y=0\]with \[y-\]axis are
  A)
             \[{{0}^{o}}\]and \[{{90}^{o}}\]                                          done clear
  B)
             \[{{0}^{o}}\]and \[{{30}^{o}}\] done clear
  C)
             \[{{30}^{o}}\]and \[{{60}^{o}}\]                                       done clear
  D)
             \[{{30}^{o}}\]and \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer8)
  If the angle between the lines represented by the equation \[{{y}^{2}}+kxy-{{x}^{2}}\]\[{{\tan }^{2}}A=0\]be \[2A\], then \[k=\]
  A)
             0     done clear
  B)
             1 done clear
  C)
             2     done clear
  D)
             \[\tan A\] done clear
  View Solution play_arrow

• question_answer9)
  . The angle between the lines \[xy=0\] is     [MP PET 1990, 92]
  A)
             \[{{45}^{o}}\]                        done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{90}^{o}}\]                        done clear
  D)
             \[{{180}^{o}}\] done clear
  View Solution play_arrow

• question_answer10)
  The angle between the lines represented by the equation \[4{{x}^{2}}-24xy+11{{y}^{2}}=0\] are                                              [MP PET 1990]
  A)
             \[{{\tan }^{-1}}\frac{3}{4},{{\tan }^{-1}}\left( -\frac{3}{4} \right)\]  done clear
  B)
             \[{{\tan }^{-1}}\frac{1}{3},{{\tan }^{-1}}\left( -\frac{1}{3} \right)\] done clear
  C)
             \[{{\tan }^{-1}}\frac{4}{3},{{\tan }^{-1}}\left( -\frac{4}{3} \right)\]  done clear
  D)
             \[{{\tan }^{-1}}\frac{1}{2},{{\tan }^{-1}}\left( -\frac{1}{2} \right)\] done clear
  View Solution play_arrow

• question_answer11)
  If the lines represented by the equation \[2{{x}^{2}}-3xy+{{y}^{2}}=0\] make angles \[\alpha \]and \[\beta \] with x-axis, then \[{{\cot }^{2}}\alpha +{{\cot }^{2}}\beta \]=
  A)
             0     done clear
  B)
             3/2 done clear
  C)
             7/4 done clear
  D)
             5/4 done clear
  View Solution play_arrow

• question_answer12)
  Angle between the line joining the origin to the points of intersection of the curves \[2{{x}^{2}}+3{{y}^{2}}+10x=0\] and \[3{{x}^{2}}+5{{y}^{2}}+16x=0\] is
  A)
             \[{{\tan }^{-1}}\frac{3}{2}\]    done clear
  B)
             \[{{\tan }^{-1}}\frac{4}{5}\] done clear
  C)
             \[{{90}^{o}}\]                        done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer13)
  The lines \[{{(lx+my)}^{2}}-3{{(mx-ly)}^{2}}=0\] and \[lx+my+n=0\] form                             
  A)
             An isosceles triangle          done clear
  B)
             A right angled triangle done clear
  C)
             An equilateral triangle      done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer14)
  The angle between the lines represented by the equation \[\lambda {{x}^{2}}+{{(1-\lambda )}^{2}}xy-\lambda {{y}^{2}}=0\], is
  A)
             \[{{30}^{o}}\]                        done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                        done clear
  D)
             \[{{90}^{o}}\] done clear
  View Solution play_arrow

• question_answer15)
  If the sum of the slopes of the lines represented by the equation \[{{x}^{2}}-2xy\tan A-{{y}^{2}}=0\]be 4, then \[\angle A=\]
  A)
              \[{{0}^{o}}\]                         done clear
  B)
              \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                        done clear
  D)
             \[{{\tan }^{-1}}(-2)\] done clear
  View Solution play_arrow

• question_answer16)
  . If \[(a+3b)(3a+b)=4{{h}^{2}}\], then the angle between the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is
  A)
             \[{{30}^{o}}\]                        done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{60}^{o}}\]                        done clear
  D)
             \[{{\tan }^{-1}}\frac{1}{2}\] done clear
  View Solution play_arrow

• question_answer17)
  The angle between the lines represented by the equation \[({{x}^{2}}+{{y}^{2}})\sin \theta +2xy=0\]is
  A)
             \[\theta \]                              done clear
  B)
             \[\frac{\theta }{2}\] done clear
  C)
             \[\frac{\pi }{2}-\theta \]   done clear
  D)
             \[\frac{\pi }{2}-\frac{\theta }{2}\] done clear
  View Solution play_arrow

• question_answer18)
  The straight lines joining the origin to the points of intersection of the line \[2x+y=1\] and curve \[3{{x}^{2}}+4xy-4x+1=0\] include an angle                              [MP PET 1993]
  A)
             p/2 done clear
  B)
             p/3 done clear
  C)
             p/4 done clear
  D)
             p/6 done clear
  View Solution play_arrow

• question_answer19)
  The angle between the pair of straight lines \[{{x}^{2}}+4{{y}^{2}}-7xy=0\], is                                     [MNR 1983]
  A)
             \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\]                      done clear
  B)
             \[{{\tan }^{-1}}3\] done clear
  C)
             \[{{\tan }^{-1}}\frac{\sqrt{33}}{5}\]                                done clear
  D)
             \[{{\tan }^{-1}}\frac{5}{\sqrt{33}}\] done clear
  View Solution play_arrow

• question_answer20)
  The angle between the pair of lines given by equation \[{{x}^{2}}+2xy-{{y}^{2}}=0\], is                                  [MNR 1990]
  A)
             p/3 done clear
  B)
             p/6 done clear
  C)
             p/2 done clear
  D)
             0 done clear
  View Solution play_arrow

• question_answer21)
  The angle between the pair of straight lines \[{{x}^{2}}-{{y}^{2}}-2y-1=0\], is         [MNR 1991; UPSEAT 2000]
  A)
             \[{{90}^{o}}\]                        done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{75}^{o}}\]                        done clear
  D)
             \[{{36}^{o}}\] done clear
  View Solution play_arrow

• question_answer22)
  If the angle between the two lines represented by \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+4=0\] is \[{{\tan }^{-1}}m\], then \[m=\]  [MNR 1993]
  A)
             1/5 done clear
  B)
             1 done clear
  C)
             7/5 done clear
  D)
             7 done clear
  View Solution play_arrow

• question_answer23)
  Pair of straight lines perpendicular to each other represented by                                                              [Roorkee 1990]
  A)
             \[2{{x}^{2}}=2y(2x+y)\]    done clear
  B)
             \[{{x}^{2}}+{{y}^{2}}+3=0\] done clear
  C)
             \[2{{x}^{2}}=y(2x+y)\]      done clear
  D)
             \[{{x}^{2}}=2(x-y)\] done clear
  View Solution play_arrow

• question_answer24)
  If the lines \[(p-q){{x}^{2}}+2(p+q)xy+(q-p){{y}^{2}}=0\] are mutually perpendicular, then          
  A)
             \[p=q\]                                    done clear
  B)
             \[q=0\]                                    done clear
  C)
             \[p=0\]                                    done clear
  D)
             p and q may have any value done clear
  View Solution play_arrow

• question_answer25)
  Which of the equation represents the pair of perpendicular straight lines
  A)
             \[{{y}^{2}}+xy-{{x}^{2}}=0\]   done clear
  B)
             \[{{y}^{2}}-xy+{{x}^{2}}=0\] done clear
  C)
             \[{{x}^{2}}+xy+{{y}^{2}}=0\]  done clear
  D)
             \[{{x}^{2}}+xy-2{{y}^{2}}=0\] done clear
  View Solution play_arrow

• question_answer26)
  The lines represented by the equation \[{{x}^{2}}+2\sqrt{3}xy+3{{y}^{2}}-3x-3\sqrt{3}y-4=0\], are
  A)
             Perpendicular to each other done clear
  B)
             Parallel done clear
  C)
             Inclined at \[{{45}^{o}}\]to each other done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer27)
  If two of the three lines represented by the equation \[a{{x}^{3}}+b{{x}^{2}}y+cx{{y}^{2}}+d{{y}^{3}}=0\] are perpendicular, then
  A)
             \[{{a}^{2}}+{{d}^{2}}=2ac\]    done clear
  B)
             \[{{a}^{2}}+{{d}^{2}}=2bd\] done clear
  C)
             \[{{a}^{2}}+ac+bd+{{d}^{2}}=0\]                                      done clear
  D)
             \[{{a}^{2}}+{{d}^{2}}=4bc\] done clear
  View Solution play_arrow

• question_answer28)
  If in general quadratic equation \[f(x,y)=0,\Delta =0\] and  \[a+b=0\], then the equation represents
  A)
             Two parallel straight lines done clear
  B)
             Two perpendicular straight lines done clear
  C)
             Two lines passing through origin done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer29)
  The angle between the lines represented by the equation \[{{x}^{2}}-2pxy+{{y}^{2}}=0\], is      
  A)
             \[{{\sec }^{-1}}p\]               done clear
  B)
             \[{{\cos }^{-1}}p\] done clear
  C)
             \[{{\tan }^{-1}}p\]               done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer30)
  The angle between the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is given by                 [RPET 1995]
  A)
             \[\tan \theta =\frac{2({{h}^{2}}-ab)}{(a+b)}\]            done clear
  B)
             \[\tan \theta =\frac{2\sqrt{{{h}^{2}}-ab}}{(a+b)}\] done clear
  C)
             \[\tan \theta =\frac{2({{h}^{2}}-ab)}{\sqrt{a+b}}\]  done clear
  D)
             \[\tan \theta =\frac{2\sqrt{{{h}^{2}}+ab}}{(a+b)}\] done clear
  View Solution play_arrow

• question_answer31)
  The equation \[{{x}^{2}}+{{k}_{1}}{{y}^{2}}+{{k}_{2}}xy=0\] represents a pair of perpendicular lines, if  
  A)
             \[{{k}_{1}}=-1\]                    done clear
  B)
             \[{{k}_{1}}=2{{k}_{2}}\] done clear
  C)
             \[2{{k}_{1}}={{k}_{2}}\]    done clear
  D)
             None of these done clear
  View Solution play_arrow

• question_answer32)
  The angle between the pair of lines \[2{{x}^{2}}+5xy+2{{y}^{2}}+3x+3y+1=0\] is                [EAMCET 1994]
  A)
             \[{{\cos }^{-1}}\left( \frac{4}{5} \right)\]                      done clear
  B)
             \[{{\tan }^{-1}}\left( \frac{4}{5} \right)\] done clear
  C)
             0     done clear
  D)
             p/2 done clear
  View Solution play_arrow

• question_answer33)
  The straight lines represented by the equation \[9{{x}^{2}}-12xy+4{{y}^{2}}=0\] are
  A)
             Coincident                             done clear
  B)
             Perpendicular done clear
  C)
             Parallel                                    done clear
  D)
             Inclined at an angle of\[{{45}^{o}}\] done clear
  View Solution play_arrow

• question_answer34)
  The angle between the two straight lines  \[2{{x}^{2}}-5xy+2{{y}^{2}}-3x+3y+1=0\] is
  A)
             \[{{45}^{o}}\]                        done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{\tan }^{-1}}\frac{4}{3}\]    done clear
  D)
             \[{{\tan }^{-1}}\frac{3}{4}\] done clear
  View Solution play_arrow

• question_answer35)
  The acute angle formed between the lines joining the origin to the points of intersection of the curves \[{{x}^{2}}+{{y}^{2}}-2x-1=0\] and \[x+y=1\], is [MP PET 1998]
  A)
             \[{{\tan }^{-1}}\left( -\frac{1}{2} \right)\]                     done clear
  B)
             \[{{\tan }^{-1}}2\] done clear
  C)
             \[{{\tan }^{-1}}\frac{1}{2}\]    done clear
  D)
             \[{{60}^{o}}\] done clear
  View Solution play_arrow

• question_answer36)
  The angle between the lines given by \[{{x}^{2}}-{{y}^{2}}=0\] is [MP PET 1999]
  A)
             \[{{15}^{o}}\]                        done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{75}^{o}}\]                        done clear
  D)
             \[9{{0}^{o}}\] done clear
  View Solution play_arrow

• question_answer37)
  Condition that the two lines represented by the  equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]to be perpendicular is [Kurukshetra CEE 1998; MP PET 2001]
  A)
             \[ab=-1\]                                done clear
  B)
             \[a=-b\] done clear
  C)
             \[a=b\]                                    done clear
  D)
             \[ab=1\] done clear
  View Solution play_arrow

• question_answer38)
  The equation \[12{{x}^{2}}+7xy+a{{y}^{2}}+13x-y+3=0\] represents a pair of perpendicular lines. Then the value of ?a? is [Karnataka CET 2001]
  A)
             \[\frac{7}{2}\]                       done clear
  B)
             - 19 done clear
  C)
             - 12                                            done clear
  D)
             12 done clear
  View Solution play_arrow

• question_answer39)
  The angle between the lines \[{{x}^{2}}+4xy+{{y}^{2}}=0\] is [Karnataka CET 2001; Pb. CET 2001]
  A)
             \[{{60}^{o}}\]                        done clear
  B)
             \[{{15}^{o}}\] done clear
  C)
             \[{{30}^{o}}\]                        done clear
  D)
             \[{{45}^{o}}\] done clear
  View Solution play_arrow

• question_answer40)
  If the equation \[12{{x}^{2}}+7xy-p{{y}^{2}}-18x+qy+6=0\] represents a pair of perpendicular straight lines, then [Kurukshetra CEE 2002]
  A)
             \[p=12,q=1\]                         done clear
  B)
             \[p=1,q=12\] done clear
  C)
             \[p=-1,q=12\]                       done clear
  D)
             \[p=1,q=-12\] done clear
  View Solution play_arrow

• question_answer41)
  The angle between the pair of lines represented by \[2{{x}^{2}}-7xy+3{{y}^{2}}=0\], is                                  [Kurukshetra CEE 2002]
  A)
             \[{{60}^{o}}\]                        done clear
  B)
             \[{{45}^{o}}\] done clear
  C)
             \[{{\tan }^{-1}}\left( \frac{7}{6} \right)\]                      done clear
  D)
             \[{{30}^{o}}\] done clear
  View Solution play_arrow

• question_answer42)
  If the angle \[2\theta \]is acute, then the acute angle between \[{{x}^{2}}(\cos \theta -\sin \theta )+2xy\cos \theta +{{y}^{2}}(\cos \theta +\sin \theta )=0\] is [EAMCET 2002]
  A)
             \[2\theta \]                           done clear
  B)
             \[\theta /3\] done clear
  C)
             \[\theta \]                              done clear
  D)
             \[\theta /2\] done clear
  View Solution play_arrow

• question_answer43)
  If the angle between the pair of straight lines represented by the equation \[{{x}^{2}}-3xy+\lambda {{y}^{2}}+3x-5y+2=0\] is \[{{\tan }^{-1}}\left( \frac{1}{3} \right)\], where \['\lambda \,'\]is a non negative real number. Then\[\lambda \]is [Orissa JEE 2002]
  A)
             2     done clear
  B)
             0 done clear
  C)
             3     done clear
  D)
             1 done clear
  View Solution play_arrow

• question_answer44)
  The angle between the lines \[{{x}^{2}}-xy-6{{y}^{2}}-7x+31y-18=0\] is  [Karnataka CET 2003]
  A)
             \[{{45}^{o}}\]                        done clear
  B)
             \[{{60}^{o}}\] done clear
  C)
             \[{{90}^{o}}\]                        done clear
  D)
             \[{{30}^{o}}\] done clear
  View Solution play_arrow