-
question_answer1)
The acute angle between the lines \[y=3\] and \[y=\sqrt{3}x+9\] is [RPET 1984, 87, 88]
A)
\[{{30}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{45}^{o}}\] done
clear
D)
\[{{90}^{o}}\] done
clear
View Solution play_arrow
-
question_answer2)
The angle between the lines \[y=(2-\sqrt{3})x+5\] and \[y=(2+\sqrt{3})x-7\] is [MP PET 1997]
A)
\[{{30}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{45}^{o}}\] done
clear
D)
\[{{90}^{o}}\] done
clear
View Solution play_arrow
-
question_answer3)
The angle between the lines whose intercepts on the axes are a, -b and b, -a respectively, is
A)
\[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{ab}\] done
clear
B)
\[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2}\] done
clear
C)
\[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2ab}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer4)
If the coordinates of the vertices A, B, C of the triangle ABC be \[(-\ 4,\ 2),\] \[(12,\ -2)\] and \[(8,\ 6)\]respectively, then \[\angle \ B\]=
A)
\[{{\tan }^{-1}}\left( -\frac{6}{7} \right)\] done
clear
B)
\[{{\tan }^{-1}}\left( \frac{6}{7} \right)\] done
clear
C)
\[{{\tan }^{-1}}\left( -\frac{7}{6} \right)\] done
clear
D)
\[{{\tan }^{-1}}\left( \frac{7}{6} \right)\] done
clear
View Solution play_arrow
-
question_answer5)
Angle between the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{a}-\frac{y}{b}=1\] is [MP PET 1995]
A)
\[2{{\tan }^{-1}}\frac{b}{a}\] done
clear
B)
\[{{\tan }^{-1}}\frac{2ab}{{{a}^{2}}+{{b}^{2}}}\] done
clear
C)
\[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{{{a}^{2}}+{{b}^{2}}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer6)
If the lines \[y=3x+1\] and \[2y=x+3\] are equally inclined to the line \[y=mx+4,\] then m = [ISM Dhanbad 1976]
A)
\[\frac{1+3\sqrt{2}}{7}\] done
clear
B)
\[\frac{1-3\sqrt{2}}{7}\] done
clear
C)
\[\frac{1\pm 3\sqrt{2}}{7}\] done
clear
D)
\[\frac{1\pm 5\sqrt{2}}{7}\] done
clear
View Solution play_arrow
-
question_answer7)
The angle between the lines \[x\cos {{\alpha }_{1}}+y\sin {{\alpha }_{1}}={{p}_{1}}\] and \[x\cos {{\alpha }_{2}}+y\sin {{\alpha }_{2}}={{p}_{2}}\]is
A)
\[({{\alpha }_{1}}+{{\alpha }_{2}})\] done
clear
B)
\[({{\alpha }_{1}}\tilde{\ }{{\alpha }_{2}})\] done
clear
C)
\[2{{\alpha }_{1}}\] done
clear
D)
\[2{{\alpha }_{2}}\] done
clear
View Solution play_arrow
-
question_answer8)
The angle between the lines \[x\cos {{30}^{o}}+y\sin 30{}^\circ =3\] and \[x\cos {{60}^{o}}+y\sin {{60}^{o}}=5\] is
A)
\[{{90}^{o}}\] done
clear
B)
\[{{30}^{o}}\] done
clear
C)
\[{{60}^{o}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer9)
The angle between the two lines \[y-2x=9\] and \[x+2y=-\ 7,\] is [RPET 1981, 85, 86; MP PET 1984]
A)
\[{{60}^{o}}\] done
clear
B)
\[{{30}^{o}}\] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{45}^{o}}\] done
clear
View Solution play_arrow
-
question_answer10)
If \[\frac{1}{a{b}'}+\frac{1}{b{a}'}=0,\] then lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{{{b}'}}+\frac{y}{{{a}'}}=1\] are [MP PET 1984]
A)
Parallel done
clear
B)
Inclined at \[{{60}^{o}}\]to each other done
clear
C)
Perpendicular to each other done
clear
D)
Inclined at \[{{30}^{o}}\]to each other done
clear
View Solution play_arrow
-
question_answer11)
To which of the following types the straight lines represented by \[2x+3y-7=0\] and \[2x+3y-5=0\] belong [MP PET 1982]
A)
Parallel to each other done
clear
B)
Perpendicular to each other done
clear
C)
Inclined at \[{{45}^{o}}\]to each other done
clear
D)
Coincident pair of straight lines done
clear
View Solution play_arrow
-
question_answer12)
The obtuse angle between the lines \[y=-\ 2\] and \[y=x+2\] is [RPET 1984]
A)
\[{{120}^{o}}\] done
clear
B)
\[{{135}^{o}}\] done
clear
C)
\[{{150}^{o}}\] done
clear
D)
\[{{160}^{o}}\] done
clear
View Solution play_arrow
-
question_answer13)
The line passes through (1, 0) and \[(-\ 2,\ \sqrt{3})\] makes an angle of ...... with x?axis [RPET 1985]
A)
\[{{60}^{o}}\] done
clear
B)
\[{{120}^{o}}\] done
clear
C)
\[{{150}^{o}}\] done
clear
D)
\[{{135}^{o}}\] done
clear
View Solution play_arrow
-
question_answer14)
Angle between \[x=2\] and \[x-3y=6\] is [MNR 1988]
A)
\[\infty \] done
clear
B)
\[{{\tan }^{-1}}(3)\] done
clear
C)
\[{{\tan }^{-1}}\left( \frac{1}{3} \right)\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer15)
If the lines \[y=(2+\sqrt{3})x+4\] and \[y=kx+6\]are inclined at an angle \[{{60}^{o}}\]to each other, then the value of k will be
A)
1 done
clear
B)
2 done
clear
C)
1 done
clear
D)
2 done
clear
View Solution play_arrow
-
question_answer16)
A straight line \[(\sqrt{3}-1)x=(\sqrt{3}+1)y\] makes an angle \[{{75}^{o}}\]with another straight line which passes through origin. Then the equation of the line is
A)
\[x=0\] done
clear
B)
\[y=0\] done
clear
C)
\[x+y=0\] done
clear
D)
\[x-y=0\] done
clear
View Solution play_arrow
-
question_answer17)
The angle between the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0,\] is [MP PET 1994]
A)
\[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{2}}+{{a}_{2}}{{b}_{1}}}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}\] done
clear
B)
\[{{\cot }^{-1}}\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\] done
clear
C)
\[{{\cot }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] done
clear
D)
\[{{\tan }^{-1}}\frac{{{a}_{1}}{{b}_{1}}-{{a}_{2}}{{b}_{2}}}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] done
clear
View Solution play_arrow
-
question_answer18)
The inclination of the straight line passing through the point (-3, 6) and the midpoint of the line joining the point (4, -5) and (-2, 9) is [Kerala (Engg.) 2002]
A)
\[\pi /4\] done
clear
B)
\[\pi /6\] done
clear
C)
\[\pi /3\] done
clear
D)
\[3\pi /4\] done
clear
View Solution play_arrow
-
question_answer19)
The angle between the lines \[2x-y+3=0\] and \[x+2y+3=0\] is [Kerala (Engg.) 2002]
A)
\[{{90}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{45}^{o}}\] done
clear
D)
\[{{30}^{o}}\] done
clear
View Solution play_arrow
-
question_answer20)
The angle between the straight lines \[x-y\sqrt{3}=5\] and \[\sqrt{3x}+y=7\]is [MP PET 2003]
A)
\[{{90}^{o}}\] done
clear
B)
\[{{60}^{o}}\] done
clear
C)
\[{{75}^{o}}\] done
clear
D)
\[{{30}^{o}}\] done
clear
View Solution play_arrow
-
question_answer21)
Angle between the lines \[2x-y-15=0\] and \[3x+y+4=0\]is [RPET 2003]
A)
\[{{90}^{o}}\] done
clear
B)
\[{{45}^{o}}\] done
clear
C)
\[{{180}^{o}}\] done
clear
D)
\[{{60}^{o}}\] done
clear
View Solution play_arrow
-
question_answer22)
The angle between the lines \[xy=0\]is equal to [Pb. CET 2003]
A)
\[{{45}^{o}}\] done
clear
B)
\[60{}^\circ \] done
clear
C)
\[{{90}^{o}}\] done
clear
D)
\[{{180}^{o}}\] done
clear
View Solution play_arrow
-
question_answer23)
The line passing through the points (3, -4) and (-2, 6) and a line passing through (-3,6) and (9, -18) are [AMU 1974]
A)
Perpendicular done
clear
B)
Parallel done
clear
C)
Makes an angle \[{{60}^{o}}\]with each other done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer24)
If the line \[2x+3ay-1=0\] and \[3x+4y+1=0\] are mutually perpendicular, then the value of a will be [MNR 1975]
A)
\[\frac{1}{2}\] done
clear
B)
2 done
clear
C)
\[-\frac{1}{2}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer25)
A straight line through origin bisect the line passing through the given points \[(a\cos \alpha ,a\sin \alpha )\]and \[(a\cos \beta ,a\sin \beta )\], then the lines are
A)
Perpendicular done
clear
B)
Parallel done
clear
C)
Angle between them is \[\frac{\pi }{4}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer26)
The lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] are perpendicular to each other, if [MP PET 1996]
A)
\[{{a}_{1}}{{b}_{2}}-{{b}_{1}}{{a}_{2}}=0\] done
clear
B)
\[{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}=0\] done
clear
C)
\[a_{1}^{2}{{b}_{2}}+b_{1}^{2}{{a}_{2}}=0\] done
clear
D)
\[{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}=0\] done
clear
View Solution play_arrow
-
question_answer27)
The lines \[y=2x\]and \[x=-2y\]are [MP PET 1993]
A)
Parallel done
clear
B)
Perpendicular done
clear
C)
Equally inclined to axes done
clear
D)
Coincident done
clear
View Solution play_arrow
-
question_answer28)
If the line passing through (4, 3) and (2, k) is perpendicular to \[y=2x+3\], then k = [RPET 1985; MP PET 1999]
A)
-1 done
clear
B)
1 done
clear
C)
4 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer29)
The number of straight lines which is equally inclined to both the axes is [RPET 2002]
A)
4 done
clear
B)
2 done
clear
C)
3 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer30)
The equation of the bisector of the acute angle between the lines \[3x-4y+7=0\]and \[12x+5y-2=0\]is [IIT 1975, 1983; RPET 2003; UPSEAT 2004]
A)
\[21x+77y-101=0\] done
clear
B)
\[11x-3y+9=0\] done
clear
C)
\[31x+77y+101=0\] done
clear
D)
\[11x-3y-9=0\] done
clear
View Solution play_arrow
-
question_answer31)
The equation of the line which bisects the obtuse angle between the lines \[x-2y+4=0\] and \[4x-3y+2=0\], is [IIT 1979]
A)
\[(4-\sqrt{5})x-(3-2\sqrt{5})y+(2-4\sqrt{5})=0\] done
clear
B)
\[(4+\sqrt{5})x-(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] done
clear
C)
\[(4+\sqrt{5})x+(3+2\sqrt{5})y+(2+4\sqrt{5})=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer32)
Equation of angle bisectors between x and y -axes are [MP PET 1984]
A)
\[y=\pm x\] done
clear
B)
\[y=\pm 2x\] done
clear
C)
\[y=\pm \frac{1}{\sqrt{2}}x\] done
clear
D)
\[y=\pm 3x\] done
clear
View Solution play_arrow
-
question_answer33)
The equation of the bisector of that angle between the lines \[x+2y-11=0\], \[3x-6y-5=0\]which contains the point (1, ?3) is
A)
\[3x=19\] done
clear
B)
\[3y=7\] done
clear
C)
\[3x=19\]and \[3y=7\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer34)
Equation of angle bisector between the lines \[3x+4y-7=0\] and \[12x+5y+17=0\]are [RPET 1995]
A)
\[\frac{3x+4y-7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\] done
clear
B)
\[\frac{3x+4y+7}{\sqrt{25}}=\frac{12x+5y+17}{\sqrt{169}}\] done
clear
C)
\[\frac{3x+4y+7}{\sqrt{25}}=\pm \frac{12x+5y+17}{\sqrt{169}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer35)
The bisector of the acute angle formed between the lines \[4x-3y+7=0\]and \[3x-4y+14=0\]has the equation [Pb. CET 2004]
A)
\[x+y+3=0\] done
clear
B)
\[x-y-3=0\] done
clear
C)
\[x-y+3=0\] done
clear
D)
\[3x+y-7=0\] done
clear
View Solution play_arrow
-
question_answer36)
If vertices of a parallelogram are respectively (0, 0), (1, 0), (2, 2) and (1, 2), then angle between diagonals is [RPET 1996]
A)
\[\pi /3\] done
clear
B)
\[\pi /2\] done
clear
C)
\[3\pi /2\] done
clear
D)
\[\pi /4\] done
clear
View Solution play_arrow
-
question_answer37)
Let \[P(-1,\,0),\,\] \[Q(0,\,0)\] and \[R\,(3,\,3\sqrt{3})\] be three points. Then the equation of the bisector of the angle PQR is [IIT Screening 2002]
A)
\[\frac{\sqrt{3}}{2}x+y=0\] done
clear
B)
\[x+\sqrt{3}y=0\] done
clear
C)
\[\sqrt{3}x+y=0\] done
clear
D)
\[x+\frac{\sqrt{3}}{2}y=0\] done
clear
View Solution play_arrow