
question_answer1) Slope of a line which cuts intercepts of equal lengths on the axes is [MP PET 1986]o00000
A)  1
B) 0
C) 2
D) \[\sqrt{3}\]
View Answer play_arrow

question_answer2) If the coordinates of the points A and B be (3, 3) and (7, 6), then the length of the portion of the line AB intercepted between the axes is
A) \[\frac{5}{4}\]
B) \[\frac{\sqrt{10}}{4}\]
C) \[\frac{\sqrt{13}}{3}\]
D) None of these
View Answer play_arrow

question_answer3) If the line \[2x+3y=5\]and \[y=mx+c\]be parallel, then
A) m = 2/3, c = 5
B) m =  2/3, c = 5
C) m =  2/3, c = any real number
D) None of these
View Answer play_arrow

question_answer4) The line \[(3xy+5)+\lambda (2x3y4)=0\]will be parallel to yaxis, if l =
A) \[\frac{1}{3}\]
B) \[\frac{1}{3}\]
C) \[\frac{3}{2}\]
D) \[\frac{3}{2}\]
View Answer play_arrow

question_answer5) If the transversal y = mr x; r = 1, 2, 3 cut off equal intercepts on the transversal \[x+y=1,\]then \[1+{{m}_{1}},\]\[1+{{m}_{2}},\] \[1+{{m}_{3}}\] are in
A) A. P.
B) G. P.
C) H. P.
D) None of these
View Answer play_arrow

question_answer6) The gradient of the line joining the points on the curve \[y={{x}^{2}}+2x\]whose abscissa are 1 and 3, is [MP PET 1997]
A) 6
B) 5
C) 4
D) 3
View Answer play_arrow

question_answer7) The parallelism condition for two straight lines one of which is specified by the equation \[ax+by+c=0\]the other being represented parametrically by \[x=\alpha \text{ }t+\beta ,\] \[y=\gamma \text{ }t+\delta \] is given by [AMU 2000]
A) \[\alpha \gamma b\alpha =0\], \[\beta =\delta =c=0\]
B) \[a\alpha b\gamma =0\], \[\beta =\delta =0\]
C) \[a\alpha +b\gamma =0\]
D) \[a\gamma =b\alpha =0\]
View Answer play_arrow

question_answer8) The equation of the straight line which passes through the point (1,  2) and cuts off equal intercepts from axes, is [MNR 1978]
A) \[x+y=1\]
B) \[xy=1\]
C) \[x+y+1=0\]
D) \[xy2=0\]
View Answer play_arrow

question_answer9) The equations of the lines which cuts off an intercept 1 from yaxis are equally inclined to the axes are
A) \[xy+1=0,\ \ x+y+1=0\]
B) \[xy1=0,\ \ x+y1=0\]
C) \[xy1=0,\ \ x+y+1=0\]
D) None of these
View Answer play_arrow

question_answer10) A line L is perpendicular to the line \[5xy=1\]and the area of the triangle formed by the line L and coordinate axes is 5. The equation of the line L is [IIT 1980; RPET 1997]
A) \[x+5y=5\]
B) \[x+5y=\pm 5\sqrt{2}\]
C) \[x5y=5\]
D) \[x5y=5\sqrt{2}\]
View Answer play_arrow

question_answer11) The equation of the line whose slope is 3 and which cuts off an intercept 3 from the positive x ? axis is
A) \[y=3x9\]
B) \[y=3x+3\]
C) \[y=3x+9\]
D) None of these
View Answer play_arrow

question_answer12) If the coordinates of the points A, B, C, D, be \[(a,\ b),\] \[({a}',\ {b}'),\] \[(a,\ b)\] and \[({a}',\ {b}')\] respectively, then the equation of the line bisecting the line segments AB and CD is
A) \[2{a}'y2bx=ab{a}'{b}'\]
B) \[2ay2{b}'\ x=ab{a}'{b}'\]
C) \[2ay2{b}'x={a}'ba{b}'\]
D) None of these
View Answer play_arrow

question_answer13) The equation of the straight line passing through the point (3, 2) and perpendicular to the line y = x is [MNR 1979]
A) \[xy=5\]
B) \[x+y=5\]
C) \[x+y=1\]
D) \[xy=1\]
View Answer play_arrow

question_answer14) If the coordinates of A and B be (1, 1) and (5, 7), then the equation of the perpendicular bisector of the line segment AB is
A) \[2x+3y=18\]
B) \[2x3y+18=0\]
C) \[2x+3y1=0\]
D) \[3x2y+1=0\]
View Answer play_arrow

question_answer15) If the coordinates of the points A, B, C be (1, 5), (0, 0) and (2, 2) respectively and D be the middle point of BC, then the equation of the perpendicular drawn from B to the line AD is
A) \[x+2y=0\]
B) \[2x+y=0\]
C) \[x2y=0\]
D) \[2xy=0\]
View Answer play_arrow

question_answer16) The equation of the line passing through the point \[({x}',\ {y}')\] and perpendicular to the line \[y{y}'=2a\,(x+{x}')\] is
A) \[x{y}'+2ay+2a{y}'{x}'{y}'=0\]
B) \[x{y}'+2ay2a{y}'{x}'{y}'=0\]
C) \[x{y}'+2ay+2a{y}'+{x}'{y}'=0\]
D) \[x{y}'+2ay2a{y}'+{x}'{y}'=0\]
View Answer play_arrow

question_answer17) If the middle points of the sides BC, CA and AB of the triangle ABC be (1, 3), (5, 7) and (5, 7), then the equation of the side AB is
A) \[xy2=0\]
B) \[xy+12=0\]
C) \[x+y12=0\]
D) None of these
View Answer play_arrow

question_answer18) If the coordinates of the vertices of the triangle ABC be (1, 6), (3, 9), and (5, 8) respectively, then the equation of the median through C is
A) \[13x14y47=0\]
B) \[13x14y+47=0\]
C) \[13x+14y+47=0\]
D) \[13x+14y47=0\]
View Answer play_arrow

question_answer19) The equation of the line perpendicular to the line \[\frac{x}{a}\frac{y}{b}=1\] and passing through the point at which it cuts xaxis, is [RPET 1996; Kerala (Engg.) 2002]
A) \[\frac{x}{a}+\frac{y}{b}+\frac{a}{b}=0\]
B) \[\frac{x}{b}+\frac{y}{a}=\frac{b}{a}\]
C) \[\frac{x}{b}+\frac{y}{a}=0\]\[\]
D) \[\frac{x}{b}+\frac{y}{a}=\frac{a}{b}\]
View Answer play_arrow

question_answer20) The equation of the line passing through the point (1, 2) and perpendicular to the line \[x+y+1=0\] is [MNR 1981]
A) \[yx+1=0\]
B) \[yx1=0\]
C) \[yx+2=0\]
D) \[yx2=0\]
View Answer play_arrow

question_answer21) A line passes through the point (3, 4) and cuts off intercepts from the coordinates axes such that their sum is 14. The equation of the line is
A) \[4x3y=24\]
B) \[4x+3y=24\]
C) \[3x4y=24\]
D) \[3x+4y=24\]
View Answer play_arrow

question_answer22) The equation of the line bisecting the line segment joining the points (a, b) and \[({a}',\ {b}')\]at right angle, is
A) \[2(a{a}')x+2(b{b}')y={{a}^{2}}+{{b}^{2}}{{{a}'}^{2}}{{{b}'}^{2}}\]
B) \[(a{a}')x+(b{b}')y={{a}^{2}}+{{b}^{2}}{{{a}'}^{2}}{{{b}'}^{2}}\]
C) \[2(a{a}')x+2(b{b}')y={{{a}'}^{2}}+b{{'}^{2}}{{a}^{2}}{{b}^{2}}\]
D) None of these
View Answer play_arrow

question_answer23) The equations of the lines which pass through the origin and are inclined at an angle \[{{\tan }^{1}}m\] to the line \[y=mx+c,\] are
A) \[x=0,\ \ 2mx+({{m}^{2}}1)\ y=0\]
B) \[y=0,\ \ 2mx+({{m}^{2}}1)\ y=0\]
C) \[y=0,\ \ 2mx+(1{{m}^{2}})\ y=0\]
D) None of these
View Answer play_arrow

question_answer24) A line meets x?axis and yaxis at the points A and B respectively. If the middle point of AB be \[({{x}_{1}},\ {{y}_{1}}),\]then the equation of the line is
A) \[{{y}_{1}}x+{{x}_{1}}y=2{{x}_{1}}{{y}_{1}}\]
B) \[{{x}_{1}}x+{{y}_{1}}y=2{{x}_{1}}{{y}_{1}}\]
C) \[{{y}_{1}}x+{{x}_{1}}y={{x}_{1}}{{y}_{1}}\]
D) \[{{x}_{1}}x+{{y}_{1}}y={{x}_{1}}{{y}_{1}}\]
View Answer play_arrow

question_answer25) The equation of the line parallel to the line \[2x3y=1\] and passing through the middle point of the line segment joining the points (1, 3) and (1,  7), is
A) \[2x3y+8=0\]
B) \[2x3y=8\]
C) \[2x3y+4=0\]
D) \[2x3y=4\]
View Answer play_arrow

question_answer26) The equation of the lines which passes through the point (3,  2) and are inclined at \[{{60}^{o}}\]to the line\[\sqrt{3}x+y=1\] [IIT 1974; MP PET 1996]
A) \[y+2=0,\ \ \sqrt{3}xy23\sqrt{3}=0\]
B) \[x2=0,\ \ \sqrt{3}xy+2+3\sqrt{3}=0\]
C) \[\sqrt{3}xy23\sqrt{3}=0\]
D) None of these
View Answer play_arrow

question_answer27) The equations of the lines passing through the point (1, 0) and at a distance \[\frac{\sqrt{3}}{2}\] from the origin, are
A) \[\sqrt{3}x+y\sqrt{3}=0,\ \ \sqrt{3}xy\sqrt{3}=0\]
B) \[\sqrt{3}x+y+\sqrt{3}=0,\ \ \sqrt{3}xy+\sqrt{3}=0\]
C) \[x+\sqrt{3}y\sqrt{3}=0,\ \ x\sqrt{3}y\sqrt{3}=0\]
D) None of these
View Answer play_arrow

question_answer28) The equation of a straight line passing through \[x+2y=2\]and cutting an intercept equal in magnitude but opposite in sign from the axes is given by [RPET 1984; MP PET 1993]
A) \[xy+5=0\]
B) \[x+y5=0\]
C) \[xy5=0\]
D) \[x+y+5=0\]
View Answer play_arrow

question_answer29) The equation of a line passing through the point of intersection of the lines \[x+5y+7=0,\ \ 3x+2y5=0,\] and perpendicular to the line \[7x+2y5=0,\] is given by [RPET 1987; MP PET 1993; Pb. CET 2000]
A) \[2x7y20=0\]
B) \[2x+7y20=0\]
C) \[2x+7y20=0\]
D) \[2x+7y+20=0\]
View Answer play_arrow

question_answer30) A line passes through the point of intersection of \[2x+y=5\] and \[x+3y+8=0\] and parallel to the line \[3x+4y=7\] is [RPET 1984; MP PET 1991]
A) \[3x+4y+3=0\]
B) \[3x+4y=0\]
C) \[4x3y+3=0\]
D) \[4x3y=3\]
View Answer play_arrow

question_answer31) The equation of the line joining the origin to the point (4, 5), is [MP PET 1984]
A) \[5x+4y=0\]
B) \[3x+4y=2\]
C) \[5x4y=0\]
D) \[4x5y=0\]
View Answer play_arrow

question_answer32) The equation of the line which cuts off an intercept 3 units on OX and an intercept 2 unit on OY, is [MP PET 1984]
A) \[\frac{x}{3}\frac{y}{2}=1\]
B) \[\frac{x}{3}+\frac{y}{2}=1\]
C) \[\frac{x}{2}+\frac{y}{3}=1\]
D) \[\frac{x}{2}\frac{y}{3}=1\]
View Answer play_arrow

question_answer33) The equation of a line through \[(3,\,4)\] and perpendicular to the line \[3x+4y=5\]is [RPET 1981, 84, 86; MP PET 1984]
A) \[4x+3y=24\]
B) \[y4=(x+3)\]
C) \[3y4x=24\]
D) \[y+4=\frac{4}{3}(x3)\]
View Answer play_arrow

question_answer34) Equation of the line passing through (1, 2) and parallel to the line \[y=3x1\]is [MP PET 1984]
A) \[y+2=x+1\]
B) \[y+2=3(x+1)\]
C) \[y2=3(x1)\]
D) \[y2=x1\]
View Answer play_arrow

question_answer35) Equation of the line passing through (1,1) and perpendicular to the line \[4/\sqrt{15}\]is [MP PET 1984]
A) \[2(y1)=3(x+1)\]
B) \[3(y1)=\ 2(x+1)\]
C) \[y1=2(x+1)\]
D) \[3(y1)=x+1\]
View Answer play_arrow

question_answer36) The equation of a line through the intersection of lines \[x=0\] and \[y=0\]and through the point (2, 2), is [MP PET 1984]
A) \[y=x1\]
B) \[y=x\]
C) \[y=x\]
D) \[y=x+2\]
View Answer play_arrow

question_answer37) Equation of a line through the origin and perpendicular to, the line joining (a, 0) and ( a, 0), is [MP PET 1984]
A) \[y=0\]
B) \[x=0\]
C) \[x=\ a\]
D) \[y=\ a\]
View Answer play_arrow

question_answer38) For specifying a straight line how many geometrical parameters should be known [MP PET 1982]
A) 1
B) 2
C) 4
D) 3
View Answer play_arrow

question_answer39) The points A (1, 3) and C (5, 1) are the opposite vertices of rectangle. The equation of line passing through other two vertices and of gradient 2, is [RPET 1991]
A) \[2x+y8=0\]
B) \[2xy4=0\]
C) \[2xy+4=0\]
D) \[2x+y+7=0\]
View Answer play_arrow

question_answer40) The intercept cut off from y?axis is twice that from x?axis by the line and line is passes through (1, 2) then its equation is [AMU 1972; RPET 1985]
A) \[2x+y=4\]
B) \[2x+y+4=0\]
C) \[2xy=4\]
D) \[2xy+4=0\]
View Answer play_arrow

question_answer41) The equation of line, which bisect the line joining two points (2, 19) and (6, 1) and perpendicular to the line joining two points (1, 3) and (5,  1), is [RPET 1987]
A) \[3x2y=30\]
B) \[2xy3=0\]
C) \[2x+3y=20\]
D) None of these
View Answer play_arrow

question_answer42) The equation of line whose mid point is \[({{x}_{1}},\ {{y}_{1}})\] in between the axes, is [RPET 1988]
A) \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=2\]
B) \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=\frac{1}{2}\]
C) \[\frac{x}{{{x}_{1}}}+\frac{y}{{{y}_{1}}}=1\]
D) None of these
View Answer play_arrow

question_answer43) The equation of line passing through (c, d) and parallel to \[ax+by+c=0,\]is [RPET 1987]
A) \[a(x+c)+b\,(y+d)=0\]
B) \[a(x+c)b(y+d)=0\]
C) \[a(xc)+b(yd)=0\]
D) None of these
View Answer play_arrow

question_answer44) The equation of line passing through point of intersection of lines \[3x2y1=0\] and \[x4y+3=0\]and the point \[(\pi ,\ 0),\] is [RPET 1987]
A) \[xy=\pi \]
B) \[xy=\pi (y+1)\]
C) \[xy=\pi (1y)\]
D) \[x+y=\pi (1y)\]
View Answer play_arrow

question_answer45) A line perpendicular to the line \[ax+by+c=0\] and passes through \[(a,\ b).\] The equation of the line is [RPET 1988; MP PET 1995]
A) \[bxay+({{a}^{2}}{{b}^{2}})=0\]
B) \[bxay({{a}^{2}}{{b}^{2}})=0\]
C) \[bxay=0\]
D) None of these
View Answer play_arrow

question_answer46) The equation of line passing through the point of intersection of the lines \[4x3y1=0\]and \[5x2y3=0\] and parallel to the line \[2y3x+2=0,\] is [RPET 1985, 86, 88]
A) \[x3y=1\]
B) \[3x2y=1\]
C) \[2x3y=1\]
D) \[2xy=1\]
View Answer play_arrow

question_answer47) The equation of the line passing through (4, 6) and makes an angle \[{{45}^{o}}\]with positive xaxis, is [RPET 1984]
A) \[xy10=0\]
B) \[x2y16=0\]
C) \[x3y22=0\]
D) None of these
View Answer play_arrow

question_answer48) The equation of the line passes through \[(a,\ b)\]and parallel to the line \[\frac{x}{a}+\frac{y}{b}=1,\]is [RPET 1986, 95]
A) \[\frac{x}{a}+\frac{y}{b}=3\]
B) \[\frac{x}{a}+\frac{y}{b}=2\]
C) \[\frac{x}{a}+\frac{y}{b}=0\]
D) \[\frac{x}{a}+\frac{y}{b}+2=0\]
View Answer play_arrow

question_answer49) Equation of the hour hand at 4 O? clock is
A) \[x\sqrt{3}\ y=0\]
B) \[\sqrt{3}\ xy=0\]
C) \[x+\sqrt{3}\ y=0\]
D) \[\sqrt{3}\ x+y=0\]
View Answer play_arrow

question_answer50) Equation of a straight line on which length of perpendicular from the origin is four units and the line makes an angle of \[{{120}^{o}}\]with the x?axis, is [MNR 1986]
A) \[x\sqrt{3}+y+8=0\]
B) \[x\sqrt{3}y=8\]
C) \[x\sqrt{3}y=8\]
D) \[x\sqrt{3}\ y+8=0\]
View Answer play_arrow

question_answer51) The straight line passes through the point of inter section of the straight lines \[x+2y10=0\] and \[2x+y+5=0,\] is [IIT 1983]
A) \[5x4y=0\]
B) \[5x+4y=0\]
C) \[4x5y=0\]
D) \[4x+5y=0\]
View Answer play_arrow

question_answer52) The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is [AMU 1975]
A) \[x\cos \theta y\sin \theta =a\cos \ 2\theta \]
B) \[x\cos \theta +y\sin \theta =a\cos \ 2\theta \]
C) \[x\sin \theta +y\cos \theta =a\cos \ 2\theta \]
D) None of these
View Answer play_arrow

question_answer53) Equation of the perpendicular bisector of the line segment joining the points (7, 4) and (1, 2), is [AMU 1979]
A) \[4x3y=15\]
B) \[3x+4y=15\]
C) \[4x+3y=15\]
D) None of these
View Answer play_arrow

question_answer54) Equations of the two straight lines passing through the point (3, 2) and making an angle of \[{{45}^{o}}\]with the line \[x2y=3,\] are [AMU 1978]
A) \[3x+y+7=0\] and \[x+3y+9=0\]
B) \[3xy7=0\] and \[x+3y9=0\]
C) \[x+3y7=0\] and \[x+3y9=0\]
D) None of these
View Answer play_arrow

question_answer55) Equations of lines which passes through the points of intersection of the lines \[4x3y1=0\] and \[2x5y+3=0\] and are equally inclined to the axes are [AMU 1981]
A) \[y\pm x=0\]
B) \[y1=\pm \ 1(x1)\]
C) \[x1=\pm \ 2(y1)\]
D) None of these
View Answer play_arrow

question_answer56) The equations of two lines through \[(0,\ a)\]which are at distance ?a? from the point \[(2a,\ 2a)\]are [Dhanbad Engg. 1972]
A) \[ya=0\] and \[4x3y3a=0\]
B) \[ya=0\] and \[3x4y+3a=0\]
C) \[ya=0\] and \[4x3y+3a=0\]
D) None of these
View Answer play_arrow

question_answer57) A line is such that its segment between the straight lines \[5xy4=0\] and \[3x+4y4=0\] is bisected at the point (1, 5), then its equation is [Roorkee 1988]
A) \[83x35y+92=0\]
B) \[35x83y+92=0\]
C) \[35x+35y+92=0\]
D) None of these
View Answer play_arrow

question_answer58) Equation of the line which passes through the point \[(4,\ 3)\] and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point, is [AMU 1973; Dhanbad Engg. 1971]
A) \[9x+20y+96=0\]
B) \[20x+9y+96=0\]
C) \[9x20y+96=0\]
D) None of these
View Answer play_arrow

question_answer59) The equation of a straight line passing through the points \[(5,\ 6)\] and (3, 10), is [MNR 1974]
A) \[x2y=4\]
B) \[2xy+4=0\]
C) \[2x+y=4\]
D) None of these
View Answer play_arrow

question_answer60) The equations of the lines through the point of intersection of the lines \[xy+1=0\] and \[2x3y+5=0\] and whose distance from the point (3, 2) is \[\frac{7}{5},\]is [IIT 1963]
A) \[3x4y6=0\] and \[4x+3y+1=0\]
B) \[3x4y+6=0\] and \[4x3y1=0\]
C) \[3x4y+6=0\] and \[4x3y+1=0\]
D) None of these
View Answer play_arrow

question_answer61) The equation of the line which cuts off the intercepts \[2a\sec \theta \] and \[2a\,\text{cosec}\,\theta \] on the axes is
A) \[x\sin \theta +y\cos \theta 2a=0\]
B) \[x\cos \theta +y\sin \theta 2a=0\]
C) \[x\sec \theta +y\,\text{cosec}\theta 2a=0\]
D) \[x\,\text{cosec}\theta +y\sec \theta 2a=0\]
View Answer play_arrow

question_answer62) If the equation \[y=mx+c\] and \[x\cos \alpha +y\sin \alpha =p\] represents the same straight line, then
A) \[p=c\sqrt{1+{{m}^{2}}}\]
B) \[c=p\sqrt{1+{{m}^{2}}}\]
C) \[cp=\sqrt{1+{{m}^{2}}}\]
D) \[{{p}^{2}}+{{c}^{2}}+{{m}^{2}}=1\]
View Answer play_arrow

question_answer63) The equation to the straight line passing through the point of intersection of the lines \[5x6y1=0\] and \[3x+2y+5=0\] and perpendicular to the line \[3x5y+11=0\] is [MP PET 1994]
A) \[5x+3y+8=0\]
B) \[3x5y+8=0\]
C) \[5x+3y+11=0\]
D) \[3x5y+11=0\]
View Answer play_arrow

question_answer64) Line passing through (1, 2) and (2, 5) is [RPET 1995]
A) \[3xy+1=0\]
B) \[3x+y+1=0\]
C) \[y3x+1=0\]
D) \[3x+y1=0\]
View Answer play_arrow

question_answer65) Equation of line passing through (1, 2) and perpendicular to \[3x+4y+5=0\] is [RPET 1995]
A) \[3y=4x2\]
B) \[3y=4x+3\]
C) \[3y=4x+4\]
D) \[3y=4x+2\]
View Answer play_arrow

question_answer66) The number of lines that are parallel to \[2x+6y+7=0\] and have an intercept of length 10 between the coordinate axes is
A) 1
B) 2
C) 4
D) Infinitely many
View Answer play_arrow

question_answer67) A line passes through (2, 2) and is perpendicular to the line \[3x+y=3.\] Its y?intercept is [IIT Screening 1992]
A) \[1/3\]
B) \[2/3\]
C) 1
D) \[4/3\]
View Answer play_arrow

question_answer68) A straight the makes an angle of \[{{135}^{o}}\]with the xaxis and cuts yaxis at a distance 5 from the origin. The equation of the line is [MP PET 1998]
A) \[2x+y+5=0\]
B) \[x+2y+3=0\]
C) \[x+y+5=0\]
D) \[x+y+3=0\]
View Answer play_arrow

question_answer69) A straight line through P(1, 2) is such that its intercept between the axes is bisected at P. Its equation is [EAMCET 1994]
A) \[x+2y=5\]
B) \[xy+1=0\]
C) \[x+y3=0\]
D) \[2x+y4=0\]
View Answer play_arrow

question_answer70) The equation of the straight line joining the point \[(a,\ b)\]to the point of intersection of the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{b}+\frac{y}{a}=1\] is
A) \[{{a}^{2}}y{{b}^{2}}x=ab\ (ab)\]
B) \[{{a}^{2}}y+{{b}^{2}}y=ab\ (a+b)\]
C) \[{{a}^{2}}y+{{b}^{2}}x=ab\]
D) \[{{a}^{2}}x+{{b}^{2}}y=ab\ (ab)\]
View Answer play_arrow

question_answer71) The equations of the lines through the origin making an angle of \[{{60}^{o}}\] with the line \[x+y\sqrt{3}+3\sqrt{3}=0\] are
A) \[y=0,\ xy\sqrt{3}=0\]
B) \[x=0,\ xy\sqrt{3}=0\]
C) \[x=0,\ x+y\sqrt{3}=0\]
D) \[y=0,\ x+y\sqrt{3}=0\]
View Answer play_arrow

question_answer72) The point \[P\,(a,\ b)\]lies on the straight line \[3x+2y=13\] and the point \[Q\ (b,\ a)\] lies on the straight line \[4xy=5,\]then the equation of line PQ is [MP PET 1999]
A) \[xy=5\]
B) \[x+y=5\]
C) \[x+y=\ 5\]
D) \[xy=\ 5\]
View Answer play_arrow

question_answer73) The equation of the line passing through (1, 1) and parallel to the line \[2x+3y7=0\] is [RPET 1996]
A) \[2x+3y5=0\]
B) \[3x+2y5=0\]
C) \[3x2y7=0\]
D) \[2x+3y+5=0\]
View Answer play_arrow

question_answer74) If the intercept made by the line between the axis is bisected at the point (5, 2), then its equation is [RPET 1996]
A) \[5x+2y=20\]
B) \[2x+5y=20\]
C) \[5x2y=20\]
D) \[2x5y=20\]
View Answer play_arrow

question_answer75) The equation of straight line passing through the intersection of the lines \[x2y=1\] and \[x+3y=2\] and parallel to \[3x+4y=0\] is [MP PET 2000]
A) \[3x+4y+5=0\]
B) \[3x+4y10=0\]
C) \[3x+4y5=0\]
D) \[3x+4y+6=0\]
View Answer play_arrow

question_answer76) Equation of a line passing through the point of intersection of lines \[2x3y+4=0,\] \[3x+4y5=0\] and perpendicular to \[6x7y+3=0,\] then its equation is [RPET 2000]
A) \[119x+102y+125=0\]
B) \[119x+102y=125\]
C) \[119x102y=125\]
D) None of these
View Answer play_arrow

question_answer77) If we reduce \[3x+3y+7=0\] to the form \[x\cos \alpha +y\sin \alpha =p,\] then the value of p is [MP PET 2001]
A) \[\frac{7}{2\sqrt{3}}\]
B) \[\frac{7}{3}\]
C) \[\frac{3\sqrt{7}}{2}\]
D) \[\frac{7}{3\sqrt{2}}\]
View Answer play_arrow

question_answer78) The equation of the straight line joining the origin to the point of intersection of \[yx+7=0\] and \[y+2x2=0\] is [MP PET 2001]
A) \[3x+4y=0\]
B) \[3x4y=0\]
C) \[4x3y=0\]
D) \[4x+3y=0\]
View Answer play_arrow

question_answer79) The equation of line perpendicular to \[x=c\]is [RPET 2001]
A) \[y=d\]
B) \[x=d\]
C) \[x=0\]
D) None of these
View Answer play_arrow

question_answer80) A line AB makes zero intercepts on x?axis and y?axis and it is perpendicular to another line CD, \[3x+4y+6=0.\] The equation of line AB is [Karnataka CET 2001]
A) \[y=4\]
B) \[4x3y+8=0\]
C) \[4x3y=0\]
D) \[4x3y+6=0\]
View Answer play_arrow

question_answer81) The equation of straight line passing through point of intersection of the straight lines \[3xy+2=0\] and \[5x2y+7=0\] and having infinite slope is [UPSEAT 2001]
A) \[x=2\]
B) \[x+y=3\]
C) \[x=3\]
D) \[x=4\]
View Answer play_arrow

question_answer82) The equation of the straight line which is perpendicular to \[y=x\] and passes through (3, 2) is [MP PET 2002]
A) \[xy=5\]
B) \[x+y=5\]
C) \[x+y=1\]
D) \[xy=1\]
View Answer play_arrow

question_answer83) Equation to the straight line cutting off an intercept 2 from the negative direction of the axis of y and inclined at 30o to the positive direction of axis of x, is [MP PET 2003]
A) \[y+x\sqrt{3}=0\]
B) \[yx+2=0\]
C) \[y\sqrt{3}\,x2=0\]
D) \[\sqrt{3}yx+2\sqrt{3}=0\]
View Answer play_arrow

question_answer84) The line passing through \[(1,\pi /2)\] and perpendicular to \[\sqrt{3}\sin \theta +2\cos \theta =\frac{4}{r}\] is [EAMCET 2003]
A) \[2=\sqrt{3}\,r\cos \theta 2\,r\sin \theta \]
B) \[5=2\sqrt{3}\,r\sin \theta +4\,r\cos \theta \]
C) \[2=\sqrt{3}\,r\cos \theta +2\,r\cos \theta \]
D) \[5=2\sqrt{3}\,r\sin \theta +4\,r\cos \theta \]
View Answer play_arrow

question_answer85) The equation of the line bisecting perpendicularly the segment joining the points (? 4, 6) and (8, 8) is [Karnataka CET 2003]
A) \[6x+y19=0\]
B) \[y=7\]
C) \[6x+2y19=0\]
D) \[x+2y7=0\]
View Answer play_arrow

question_answer86) Equation of a line passing through (1, 2) and perpendicular to the line \[3x5y+7=0\] is [RPET 2003]
A) \[5x+3y+1=0\]
B) \[3x+5y+1=0\]
C) \[5x3y1=0\]
D) \[3x5y+1=0\]
View Answer play_arrow

question_answer87) If the line \[\frac{x}{a}+\frac{y}{b}=1\] passes through the points (2, 3) and (4, 5), then \[(a,\ b)\]=
A) (1, 1)
B) ( 1, 1)
C) (1,  1)
D) ( 1,  1)
View Answer play_arrow

question_answer88) If the slope of a line passing through the point A (3, 2) be 3/4, then the points on the line which are 5 units away from A, are [IIT 1965]
A) (5, 5), ( 1,  1)
B) (7, 5), ( 1,  1)
C) (5, 7), ( 1,  1)
D) (7, 5), (1, 1)
View Answer play_arrow

question_answer89) For the lines \[2x+5y=7\]and \[2x5y=9,\]which of the following statement is true
A) Lines are parallel
B) Lines are coincident
C) Lines are intersecting
D) Lines are perpendicular
View Answer play_arrow

question_answer90) The opposite angular points of a square are \[(3,\ 4)\] and \[(1,\ \ 1)\]. Then the coordinates of other two points are [Roorkee 1985]
A) \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( \frac{1}{2},\,\,\frac{5}{2} \right)\]
B) \[D\,\left( \frac{1}{2},\,\,\frac{9}{2} \right)\,,\,\,B\,\left( \frac{1}{2},\,\,\frac{5}{2} \right)\]
C) \[D\,\left( \frac{9}{2},\,\,\frac{1}{2} \right)\,,\,\,B\,\left( \frac{1}{2},\,\,\frac{5}{2} \right)\]
D) None of these
View Answer play_arrow

question_answer91) Two consecutive sides of a parallelogram are \[4x+5y=0\] and \[7x+2y=0.\] If the equation to one diagonal is \[11x+7y=9,\] then the equation of the other diagonal is [IIT 1970]
A) \[x+2y=0\]
B) \[2x+y=0\]
C) \[xy=0\]
D) None of these
View Answer play_arrow

question_answer92) One diagonal of a square is along the line \[8x15y=0\] and one of its vertex is (1, 2). Then the equation of the sides of the square passing through this vertex, are [IIT 1962]
A) \[23x+7y=9,\ 7x+23y=53\]
B) \[23x7y+9=0,\ 7x+23y+53=0\]
C) \[23x7y9=0,\ 7x+23y53=0\]
D) None of these
View Answer play_arrow

question_answer93) The opposite vertices of a square are (1, 2) and (3, 8), then the equation of a diagonal of the square passing through the point (1, 2), is [Roorkee 1981]
A) \[3xy1=0\]
B) \[3yx1=0\]
C) \[3x+y+1=0\]
D) None of these
View Answer play_arrow

question_answer94) The ends of the base of an isosceles triangle are at \[(2a,\ 0)\]and\[(0,\ a).\] The equation of one side is \[(lx+my)(a+b)=(l+m)\ ab\] The equation of the other side is
A) \[x+2ya=0\]
B) \[x+2y=2a\]
C) \[3x+4y4a=0\]
D) \[3x4y+4a=0\]
View Answer play_arrow

question_answer95) The equation of the lines on which the perpendiculars from the origin make \[{{30}^{o}}\]angle with x?axis and which form a triangle of area \[\frac{50}{\sqrt{3}}\] with axes, are
A) \[x+\sqrt{3}y\pm 10=0\]
B) \[\sqrt{3}x+y\pm 10=0\]
C) \[x\pm \sqrt{3}y10=0\]
D) None of these
View Answer play_arrow

question_answer96) The base BC of a triangle ABC is bisected at the point (p, q) and the equations to the sides AB and AC are respectively \[x+y+3=0\] and \[qx+py=1.\] Then the equation to the median through A is
A) \[2xy=9\]
B) \[({{p}^{2}}+{{q}^{2}}1)(px+qy1)=(2p1)(qx+py1)\]
C) \[(pq1)(px+qy1)=({{p}^{2}}+{{q}^{2}}1)(qx+py1)\]
D) None of these
View Answer play_arrow

question_answer97) The equation of the line which makes right angled triangle with axes whose area is 6 sq. units and whose hypotenuse is of 5 units, is
A) \[\frac{x}{4}+\frac{y}{3}=\pm \ 1\]
B) \[\frac{x}{4}\frac{y}{3}=\pm \ 3\]
C) \[\frac{x}{6}+\frac{y}{1}=\pm \ 1\]
D) \[\frac{x}{1}\frac{y}{6}=\pm \ 1\]
View Answer play_arrow

question_answer98) A(1, 1), B(5, 3) are opposite vertices of a square in xyplane. The equation of the other diagonal (not passing through (A, B) of the square is given by [EAMCET 1993]
A) \[x3y+4=0\]
B) \[2xy+3=0\]
C) \[y+3x8=0\]
D) \[x+2y1=0\]
View Answer play_arrow

question_answer99) In an isosceles triangle ABC, the coordinates of the points B and C on the base BC are respectively (1, 2) and (2, 1). If the equation of the line AB is \[y=2x\], then the equation of the line AC is [Roorkee 2000]
A) \[y=\frac{1}{2}(x1)\]
B) \[y=\frac{x}{2}\]
C) \[y=x1\]
D) \[2y=x+3\]
View Answer play_arrow

question_answer100) Equations of diagonals of square formed by lines \[x=0,\] \[y=0,\]\[x=1\] and \[y=1\]are [MP PET 1984]
A) \[y=x,\ y+x=1\]
B) \[y=x,\ x+y=2\]
C) \[2y=x,\ y+x=\frac{1}{3}\]
D) \[y=2x,\ y+2x=1\]
View Answer play_arrow

question_answer101) The diagonal passing through origin of a quadrilateral formed by \[x=0,\ y=0,\ x+y=1\] and \[6x+y=3,\] is [IIT 1973]
A) \[3x2y=0\]
B) \[2x3y=0\]
C) \[3x+2y=0\]
D) None of these
View Answer play_arrow

question_answer102) The vertices of a triangle OBC are \[(0,\ 0),\ (3,\ 1)\] and \[(1,\ 3)\ \]respectively. Then the equation of line parallel to BC which is at \[\frac{1}{2}\]unit distant from origin and cuts OB and OC, is [IIT 1976]
A) \[2x+2y+\sqrt{2}=0\]
B) \[2x+2y\sqrt{2}=0\]
C) \[2x2y+\sqrt{2}=0\]
D) None of these
View Answer play_arrow

question_answer103) A vertex of square is (3, 4) and diagonal \[x+2y=1,\] then the second diagonal which passes through given vertex will be
A) \[2xy+2=0\]
B) \[x+2y=11\]
C) \[2xy=2\]
D) None of these
View Answer play_arrow

question_answer104) A vertex of equilateral triangle is (2, 3) and equation of opposite side is \[x+y=2,\] then the equation of one side from rest two, is [IIT 1975]
A) \[y3=2(x2)\]
B) \[y3=(2\sqrt{3})(x2)\]
C) \[y3=(\sqrt{3}1)(x2)\]
D) None of these
View Answer play_arrow

question_answer105) A straight line moves so that the sum of the reciprocals of its intercepts on two perpendicular lines is constant, then the line passes through [IIT 1977]
A) A fixed point
B) A variable point
C) Origin
D) None of these
View Answer play_arrow

question_answer106) If a, b, c are in harmonic progression, then straight line \[\frac{x}{a}+\frac{y}{b}+\frac{1}{c}=0\] always passes through a fixed point, that point is [MP PET 1999; AIEEE 2005]
A) \[(1,\ 2)\]
B) \[(1,\ 2)\]
C) \[(1,\ 2)\]
D) \[(1,\ 1/2)\]
View Answer play_arrow

question_answer107) If the straight line \[ax+by+c=0\] always passes through (1, 2), then a, b, c are [AMU 2000]
A) In A.P.
B) In H.P.
C) In G.P.
D) None of these
View Answer play_arrow

question_answer108) If \[u={{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0,\] \[v={{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\] and \[\frac{{{a}_{1}}}{{{a}_{2}}}=\frac{{{b}_{1}}}{{{b}_{2}}}=\frac{{{c}_{1}}}{{{c}_{2}}},\] then the curve \[u+kv=0\]is [MNR 1987]
A) The same straight line u
B) Different straight line
C) It is not a straight line
D) None of these
View Answer play_arrow

question_answer109) For what values of a and b the intercepts cut off on the coordinate axes by the line \[ax+by+8=0\] are equal in length but opposite in signs to those cut off by the line \[2x3y+6=0\] on the axes [MP PET 1983]
A) \[a=\frac{8}{3},\ b=\ 4\]
B) \[a=\frac{8}{3},\ b=\ 4\]
C) \[a=\frac{8}{3},\ b=4\]
D) \[a=\frac{8}{3},\ b=4\]
View Answer play_arrow

question_answer110) If a and b are two arbitrary constants, then the straight line \[(a2b)x+(a+3b)y+3a+4b=0\]will pass through [RPET 1990]
A) \[(1,\ 2)\]
B) (1, 2)
C) \[(2,\ 3)\]
D) (2, 3)
View Answer play_arrow

question_answer111) If \[a+b+c=0\] and \[p\ne 0,\] the lines \[ax+(b+c)y=p,\] \[bx+(c+a)y=p\] and \[cx+(a+b)y=p\]
A) Do not intersect
B) Intersect
C) Are concurrent
D) None of these
View Answer play_arrow

question_answer112) The symmetry in curve \[{{x}^{3}}+{{y}^{3}}=3axy\]along
A) xaxis
B) yaxis
C) Line y = x
D) Opposite quadrants
View Answer play_arrow

question_answer113) The point of intersection of the lines \[\frac{x}{a}+\frac{y}{b}=1\] and \[\frac{x}{b}+\frac{y}{a}=1\] lies on the line
A) \[xy=0\]
B) \[(x+y)(a+b)=2ab\]
C) \[(lx+my)(a+b)=(l+m)\ ab\]
D) All of these
View Answer play_arrow

question_answer114) The equations \[(bc)x+(ca)y+(ab)=0\] and \[({{b}^{3}}{{c}^{3}})x+({{c}^{3}}{{a}^{3}})y+{{a}^{3}}{{b}^{3}}=0\] will represent the same line, if
A) b = c
B) c = a
C) a = b
D) a + b + c = 0
E) (e) All the above
View Answer play_arrow

question_answer115) A straight line makes an angle of \[{{135}^{o}}\] with xaxis and cuts yaxis at a distance of 5 from the origin. The equation of the line is [Pb. CET 2001]
A) \[2x+y+5=0\]
B) \[x+2y+3=0\]
C) \[x+y+5=0\]
D) \[x+y+3=0\]
View Answer play_arrow

question_answer116) Equation of the straight line making equal intercepts on the axes and passing through the point (2, 4) is [Karnataka CET 2004]
A) \[4xy4=0\]
B) \[2x+y8=0\]
C) \[x+y6=0\]
D) \[x+2y10=0\]
View Answer play_arrow

question_answer117) The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose sum is ? 1 is [AIEEE 2004]
A) \[\frac{x}{2}\frac{y}{3}=1\]and\[\frac{x}{2}+\frac{y}{1}=1\]
B) \[\frac{x}{2}\frac{y}{3}=1\] and \[\frac{x}{2}+\frac{y}{1}=1\]
C) \[\frac{x}{2}\frac{y}{3}=1\] and \[\frac{x}{2}+\frac{y}{1}=1\]
D) \[\frac{\pi }{3}\] and \[\frac{x}{2}+\frac{y}{1}=1\]
View Answer play_arrow

question_answer118) The line which is parallel to x?axis and crosses the curve \[y=\sqrt{x}\] at an angle of \[{{45}^{o}}\] is equal to [Pb. CET 2002]
A) \[x=\frac{1}{4}\]
B) \[y=\frac{1}{4}\]
C) \[y=\frac{1}{2}\]
D) \[y=1\]
View Answer play_arrow

question_answer119) The equation of the line perpendicular to line \[ax+by+c=0\] and passing through \[(a,\ b)\]is equal to [Pb. CET 2002]
A) \[bxay=0\]
B) \[bx+ay2ab=0\]
C) \[bx+ay=0\]
D) None of these
View Answer play_arrow

question_answer120) The points (1, 3) and (5, 1) are the opposite vertices of a rectangle. The other two vertices lie on the line \[y=2x+c,\] then the value of c will be [Pb. CET 2003; IIT 1981]
A) 4
B)  4
C) 2
D)  2
View Answer play_arrow

question_answer121) The triangle PQR is inscribed in the circle \[{{x}^{2}}+{{y}^{2}}=25\]. If Q and R have coordinates (3,4) and (? 4, 3) respectively, then \[\angle QPR\] is equal to [IIT Screening 2000]
A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{6}\]
View Answer play_arrow

question_answer122) The point \[({{t}^{2}}+2t+5,\,2{{t}^{2}}+t2)\] lies on the line \[x+y=2\] for
A) All real values of t
B) Some real values of t
C) \[t=\frac{3\pm \sqrt{3}}{6}\]
D) None of these
View Answer play_arrow

question_answer123) The line joining the points (1, 3) and (4, 2) will pass through the point (p, q) if
A) \[pq=1\]
B) \[p+q=1\]
C) \[pq=2\]
D) \[p+q=2\]
View Answer play_arrow

question_answer124) The line parallel to the xaxis and passing through the intersection of the lines \[ax+2by+3b=0\] and \[bx2ay3a=0\], where \[(a,\,b)\ne (0,\,0)\] is [AIEEE 2005]
A) Above the xaxis at a distance of 3/2 from it
B) Above the xaxis at a distance of 2/3 from it
C) Below the xaxis at a distance of 3/2 from it
D) Below the xaxis at a distance of 2/3 from it
View Answer play_arrow

question_answer125) Two points (a, 0) and (0, b) are joined by a straight line, Another point on this line is [Orissa JEE 2005]
A) \[(3a,2b)\]
B) \[({{a}^{2}},ab)\]
C) \[(3a,\,2b)\]
D) \[(a,\,b)\]
View Answer play_arrow

question_answer126) The equation to the line bisecting the join of (3, 4) and (5, 2) and having its intercepts on the xaxis and the yaxis in the ratio 2 : 1 is [Karnataka CET 2005]
A) \[x+y3=0\]
B) \[2xy=9\]
C) \[x+2y=2\]
D) \[2x+y=7\]
View Answer play_arrow

question_answer127) If the coordinates of the points A and B be (1, 0) and \[(2,\sqrt{3})\], then the angle made by the line AB with xaxis is
A) \[{{30}^{o}}\]
B) \[{{45}^{o}}\]
C) \[{{60}^{o}}\]
D) \[{{75}^{o}}\]
View Answer play_arrow

question_answer128) The line \[lx+my+n=0\] will be parallel to xaxis, if
A) \[l=m=0\]
B) \[m=n=0\]
C) \[l=n=0\]
D) \[l=0\]
View Answer play_arrow

question_answer129) A line passing through origin and is perpendicular to two given lines \[2x+y+6=0\] and \[4x+2y9=0\], then the ratio in which the origin divides this line is [DCE 2005]
A) 1 : 2
B) 2 : 1
C) 4 : 3
D) 3 : 4
View Answer play_arrow