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question_answer1)
The points on the x-axis whose perpendicular distance from the line \[\frac{x}{a}+\frac{y}{b}=1\] is a, are [RPET 2001; MP PET 2003]
A)
\[\left[ \frac{a}{b}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\] done
clear
B)
\[\left[ \frac{b}{a}(b\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\] done
clear
C)
\[\left[ \frac{a}{b}(a\pm \sqrt{{{a}^{2}}+{{b}^{2}}}),\,0 \right]\] done
clear
D)
None of these done
clear
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question_answer2)
The length of the perpendicular from the point \[(b,a)\]to the line \[\frac{x}{a}-\frac{y}{b}=1\], is
A)
\[\left| \frac{{{a}^{2}}-ab+{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] done
clear
B)
\[\left| \frac{{{b}^{2}}-ab-{{a}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] done
clear
C)
\[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] done
clear
D)
None of these done
clear
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question_answer3)
The distance between the lines \[3x+4y=9\]and \[6x+8y=15\]is [MNR 1982; RPET 1995; MP PET 2002]
A)
3/2 done
clear
B)
3/10 done
clear
C)
6 done
clear
D)
None of these done
clear
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question_answer4)
The distance of the point of intersection of the lines \[2x-3y+5=0\] and \[3x+4y=0\]from the line \[5x-2y=0\] is
A)
\[\frac{130}{17\sqrt{29}}\] done
clear
B)
\[\frac{13}{7\sqrt{29}}\] done
clear
C)
\[\frac{130}{17}\] done
clear
D)
None of these done
clear
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question_answer5)
The point on the line \[x+y=4\]which lie at a unit distance from the line \[4x+3y=10\], are [IIT 1976]
A)
\[(3,\,1),(-7,\,11)\] done
clear
B)
\[(3,\,1),(7,\,11)\] done
clear
C)
\[(-3,\,1),(-7,\,11)\] done
clear
D)
\[(1,\,3),(-7,\,11)\] done
clear
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question_answer6)
If the length of the perpendicular drawn from the origin to the line whose intercepts on the axes are a and b be p, then [Karnataka CET 2003]
A)
\[{{a}^{2}}+{{b}^{2}}={{p}^{2}}\] done
clear
B)
\[{{a}^{2}}+{{b}^{2}}=\frac{1}{{{p}^{2}}}\] done
clear
C)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{2}{{{p}^{2}}}\] done
clear
D)
\[\frac{1}{{{a}^{2}}}+\frac{1}{{{b}^{2}}}=\frac{1}{{{p}^{2}}}\] done
clear
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question_answer7)
The length of perpendicular drawn from origin on the line joining \[({x}',{y}')\] and \[({x}'',{y}'')\], is
A)
\[\frac{x'y''+x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\] done
clear
B)
\[\frac{x'y''-x''y'}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\] done
clear
C)
\[\frac{x'x''+y'y''}{\sqrt{{{(x''+x')}^{2}}+{{(y''+y')}^{2}}}}\] done
clear
D)
\[\frac{x'x''+y'y''}{\sqrt{{{(x''-x')}^{2}}+{{(y''-y')}^{2}}}}\] done
clear
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question_answer8)
If p and \[p'\]be the distances of origin from the lines \[x\sec \alpha +y\text{cosec }\alpha =k\] and \[x\cos \alpha -y\sin \alpha =k\cos 2\alpha \], then \[4{{p}^{2}}+{{{p}'}^{2}}\]=
A)
k done
clear
B)
\[2k\] done
clear
C)
\[{{k}^{2}}\] done
clear
D)
\[2{{k}^{2}}\] done
clear
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question_answer9)
The perpendicular distance of the straight line \[12x+5y=7\] from the origin is given by [MP PET 1993]
A)
\[\frac{7}{13}\] done
clear
B)
\[\frac{12}{13}\] done
clear
C)
\[\frac{5}{13}\] done
clear
D)
\[\frac{1}{13}\] done
clear
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question_answer10)
The length of perpendicular from (3, 1) on line \[4x+3y+20=0\], is [RPET 1989; MP PET 1984]
A)
6 done
clear
B)
7 done
clear
C)
5 done
clear
D)
8 done
clear
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question_answer11)
The distance between two parallel lines \[3x+4y-8=0\]and \[3x+4y-3=0\], is given by [MP PET 1984]
A)
4 done
clear
B)
5 done
clear
C)
3 done
clear
D)
1 done
clear
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question_answer12)
The distance between \[4x+3y=11\] and \[8x+6y=15\], is [AMU 1979; MNR 1987; UPSEAT 2000]
A)
\[\frac{7}{2}\] done
clear
B)
4 done
clear
C)
\[\frac{7}{10}\] done
clear
D)
None of these done
clear
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question_answer13)
The vertex of an equilateral triangle is (2,-1) and the equation of its base in\[x+2y=1\]. The length of its sides is [UPSEAT 2003]
A)
\[4/\sqrt{15}\] done
clear
B)
\[2/\sqrt{15}\] done
clear
C)
\[4/3\sqrt{3}\] done
clear
D)
\[1/\sqrt{5}\] done
clear
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question_answer14)
The product of the perpendiculars drawn from the points \[(\pm \sqrt{{{a}^{2}}-{{b}^{2}},}0)\] on the line\[\frac{x}{a}\cos \theta +\frac{y}{b}\sin \theta =1\], is
A)
\[{{a}^{2}}\] done
clear
B)
\[{{b}^{2}}\] done
clear
C)
\[{{a}^{2}}+{{b}^{2}}\] done
clear
D)
\[{{a}^{2}}-{{b}^{2}}\] done
clear
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question_answer15)
The ratio in which the line \[3x+4y+2=0\] divides the distance between \[3x+4y+5=0\] and \[3x+4y-5=0\], is
A)
\[7:3\] done
clear
B)
3 : 7 done
clear
C)
\[2:3\] done
clear
D)
None of these done
clear
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question_answer16)
If \[2p\] is the length of perpendicular from the origin to the lines \[\frac{x}{a}+\frac{y}{b}=1\], then \[{{a}^{2}},8{{p}^{2}},{{b}^{2}}\]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_answer17)
The length of the perpendicular drawn from origin upon the straight line \[\frac{x}{3}-\frac{y}{4}=1\]is [MP PET 1997]
A)
\[2\frac{2}{5}\] done
clear
B)
\[3\frac{1}{5}\] done
clear
C)
\[4\frac{2}{5}\] done
clear
D)
\[3\frac{2}{5}\] done
clear
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question_answer18)
The distance between the lines \[3x-2y=1\]and \[6x+9=4y\] is [MP PET 1998]
A)
\[\frac{1}{\sqrt{52}}\] done
clear
B)
\[\frac{11}{\sqrt{52}}\] done
clear
C)
\[\frac{4}{\sqrt{13}}\] done
clear
D)
\[\frac{6}{\sqrt{13}}\] done
clear
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question_answer19)
Two points A and B have coordinates (1, 1) and (3, -2) respectively. The co-ordinates of a point distant \[\sqrt{85}\]from B on the line through B perpendicular to AB are [AMU 2000]
A)
(4, 7) done
clear
B)
(7, 4) done
clear
C)
(5, 7) done
clear
D)
(-5, -3) done
clear
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question_answer20)
The distance of the point (-2, 3) from the line \[x-y=5\]is [MP PET 2001]
A)
\[5\sqrt{2}\] done
clear
B)
\[2\sqrt{5}\] done
clear
C)
\[3\sqrt{5}\] done
clear
D)
\[5\sqrt{3}\] done
clear
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question_answer21)
The distance of the lines \[2x-3y=4\]from the point (1, 1) measured parallel to the line \[x+y=1\] is [Orissa JEE 2002]
A)
\[\sqrt{2}\] done
clear
B)
\[\frac{5}{\sqrt{2}}\] done
clear
C)
\[\frac{1}{\sqrt{2}}\] done
clear
D)
6 done
clear
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question_answer22)
Distance between the lines \[5x+3y-7=0\] and \[15x+9y+14=0\] is [Kerala (Engg.) 2002]
A)
\[\frac{35}{\sqrt{34}}\] done
clear
B)
\[\frac{1}{3\sqrt{34}}\] done
clear
C)
\[\frac{35}{3\sqrt{34}}\] done
clear
D)
\[\frac{35}{2\sqrt{34}}\] done
clear
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question_answer23)
Distance between the parallel lines \[3x+4y+7=0\] and \[3x+4y-5=0\] is [RPET 2003]
A)
\[\frac{2}{5}\] done
clear
B)
\[\frac{12}{5}\] done
clear
C)
\[\frac{5}{12}\] done
clear
D)
\[\frac{3}{5}\] done
clear
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question_answer24)
The position of the point (8,-9) with respect to the lines \[2x+3y-4=0\] and \[6x+9y+8=0\] is
A)
Point lies on the same side of the lines done
clear
B)
Point lies on the different sides of the line done
clear
C)
Point lies on one of the line done
clear
D)
None of these done
clear
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question_answer25)
The length of perpendicular from the point \[(a\cos \alpha ,a\sin \alpha )\] upon the straight line \[y=x\tan \alpha +c,\] \[c>0\] is [MP PET 2004]
A)
\[c\cos \alpha \] done
clear
B)
\[c{{\sin }^{2}}\alpha \] done
clear
C)
\[c{{\sec }^{2}}\alpha \] done
clear
D)
\[c{{\cos }^{2}}\alpha \] done
clear
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question_answer26)
The distance of point (-2, 3) from the line \[x-y=5\]is [Pb. CET 2001]
A)
\[5\sqrt{2}\] done
clear
B)
\[2\sqrt{5}\] done
clear
C)
\[3\sqrt{5}\] done
clear
D)
\[5\sqrt{3}\] done
clear
View Solution play_arrow
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question_answer27)
Distance between the two parallel lines \[y=2x+7\]and \[y=2x+5\] is [Orissa JEE 2004]
A)
\[\frac{\sqrt{5}}{2}\] done
clear
B)
\[\frac{2}{5}\] done
clear
C)
\[\frac{2}{\sqrt{5}}\] done
clear
D)
\[\frac{1}{\sqrt{5}}\] done
clear
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question_answer28)
In what ratio the line \[y-x+2=0\]divides the line joining the points (3, -1) and (8, 9) [Karnataka CET 2002]
A)
1 : 2 done
clear
B)
2 : 1 done
clear
C)
2 : 3 done
clear
D)
3 : 4 done
clear
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question_answer29)
The perpendicular distance of the straight line \[12x+5y=7\]from the origin is equal to [Pb. CET 2002]
A)
\[\frac{7}{13}\] done
clear
B)
\[\frac{12}{13}\] done
clear
C)
\[\frac{5}{13}\] done
clear
D)
\[\frac{1}{13}\] done
clear
View Solution play_arrow
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question_answer30)
A point equidistant from the lines \[4x+3y+10=0\], \[5x-12y+26=0\] and \[7x+24y-50=0\] is [EAMCET 1994]
A)
\[(1,\,-1)\] done
clear
B)
\[(1,\,1)\] done
clear
C)
\[(0,0)\] done
clear
D)
\[(0,\,1)\] done
clear
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question_answer31)
The equation of the base of an equilateral triangle is \[x+y=2\] and the vertex is (2, -1). The length of the side of the triangle is [IIT 1973, 83, MP PET 1995; RPET 1999, 2000]
A)
\[\sqrt{3/2}\] done
clear
B)
\[\sqrt{2}\] done
clear
C)
\[\sqrt{2/3}\] done
clear
D)
None of these done
clear
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question_answer32)
\[(\sin \theta ,\cos \theta )\] and \[(3,\,2)\] lies on the same side of the line \[x+y=1\], then \[\theta \] lies between [DCE 2005]
A)
\[(0,\,\,\pi /2)\] done
clear
B)
\[(0,\,\pi )\] done
clear
C)
\[(\pi /4,\pi /2)\] done
clear
D)
\[(0,\,\,\pi /4)\] done
clear
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question_answer33)
Which pair of points lie on the same side of \[3x-8y-7=0\] [Roorkee 1990]
A)
(0, -1) and (0, 0) done
clear
B)
(4, -3) and (0, 1) done
clear
C)
(-3, -4) and (1, 2) done
clear
D)
(-1, -1) and (3, 7) done
clear
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question_answer34)
Let \[\alpha \] be the distance between the lines \[-x+y=2\] and \[x-y=2\], and \[\beta \] be the distance between the lines \[4x-3y=5\] and \[6y-8x=1\], then [J & K 2005]
A)
\[20\sqrt{2}\beta =11\alpha \] done
clear
B)
\[20\sqrt{2}\alpha =11\beta \] done
clear
C)
\[11\sqrt{2}\beta =20\alpha \] done
clear
D)
None of these done
clear
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question_answer35)
Choose the correct statement which describe the position of the point (?6, 2) relative to straight lines \[2x+3y-4=0\] and \[6x+9y+8=0\] [MP PET 1983]
A)
Below both the lines done
clear
B)
Above both the lines done
clear
C)
In between the lines done
clear
D)
None of these done
clear
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question_answer36)
The position of the points (3, 4) and (2, ?6) with respect to the line \[3x-4y=8\] are [Roorkee 1972; MP PET 1984]
A)
On the same side of the line done
clear
B)
On different side of the line done
clear
C)
One point on the line and the other outside the line done
clear
D)
Both point on the line done
clear
View Solution play_arrow