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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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