-
question_answer1)
The equation \[{{(x+y)}^{2}}-({{x}^{2}}+{{y}^{2}})=0\] represents
A)
A circle done
clear
B)
Two lines done
clear
C)
Two parallel lines done
clear
D)
Two mutually perpendicular lines done
clear
View Solution play_arrow
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question_answer2)
If the slope of one of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be the square of the other, then
A)
\[{{a}^{2}}b+a{{b}^{2}}-6abh+8{{h}^{3}}=0\] done
clear
B)
\[{{a}^{2}}b+a{{b}^{2}}+6abh+8{{h}^{3}}=0\] done
clear
C)
\[{{a}^{2}}b+a{{b}^{2}}-3abh+8{{h}^{3}}=0\] done
clear
D)
\[{{a}^{2}}b+a{{b}^{2}}-6abh-8{{h}^{3}}=0\] done
clear
View Solution play_arrow
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question_answer3)
Two lines represented by equation \[{{x}^{2}}+xy+{{y}^{2}}=0\] are
A)
Coincident done
clear
B)
Parallel done
clear
C)
Mutually perpendicular done
clear
D)
Imaginary done
clear
View Solution play_arrow
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question_answer4)
If the equation \[hxy+gx+fy+c=0\] represents a pair of straight lines, then
A)
\[fh=cg\] done
clear
B)
\[fg=ch\] done
clear
C)
\[{{h}^{2}}=gf\] done
clear
D)
\[fgh=c\] done
clear
View Solution play_arrow
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question_answer5)
The equation of pair of straight lines perpendicular to the pair \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is [MP PET 1989]
A)
\[a{{x}^{2}}-2hxy+b{{y}^{2}}=0\] done
clear
B)
\[b{{x}^{2}}+2hxy+a{{y}^{2}}=0\] done
clear
C)
\[a{{y}^{2}}-2hxy+b{{x}^{2}}=0\] done
clear
D)
\[a{{y}^{2}}-b{{x}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer6)
The values of h for which the equation \[3{{x}^{2}}+2hxy-3{{y}^{2}}-40x+30y-75=0\] represents a pair of straight lines, are [MP PET 1989]
A)
4, 4 done
clear
B)
4, 6 done
clear
C)
4, - 4 done
clear
D)
0, 4 done
clear
View Solution play_arrow
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question_answer7)
The equation of lines passing through the origin and parallel to the lines \[y={{m}_{1}}x+{{c}_{1}}\] and \[y={{m}_{2}}x+{{c}_{2}}\] is
A)
\[{{m}_{1}}{{m}_{2}}{{x}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] done
clear
B)
\[{{m}_{1}}{{m}_{2}}{{x}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{y}^{2}}=0\] done
clear
C)
\[{{m}_{1}}{{m}_{2}}{{y}^{2}}-({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] done
clear
D)
\[{{m}_{1}}{{m}_{2}}{{y}^{2}}+({{m}_{1}}+{{m}_{2}})xy+{{x}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer8)
The equation of the lines represented by the equation \[ab({{x}^{2}}-{{y}^{2}})+({{a}^{2}}-{{b}^{2}})xy=0\] are
A)
\[ax-by=0,\ bx+ay=0\] done
clear
B)
\[ax-by=0,\ bx-ay=0\] done
clear
C)
\[ax+by=0,\ bx+ay=0\] done
clear
D)
\[ax+by=0,\ bx-ay=0\] done
clear
View Solution play_arrow
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question_answer9)
The equation \[{{(x-5)}^{2}}+(x-5)\,(y-6)\,-2\,{{(y-6)}^{2}}=0\] represents
A)
A circle done
clear
B)
Two straight lines passing through origin done
clear
C)
Two straight lines passing through the point (5, 6) done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer10)
A second degree homogenous equation in x and y always represents
A)
A pair of straight lines done
clear
B)
A circle done
clear
C)
A conic section done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer11)
If \[6{{x}^{2}}+11xy-10{{y}^{2}}+x+31y+k=0\] represents a pair of straight lines, then \[k=\] [MP PET 1991]
A)
- 15 done
clear
B)
6 done
clear
C)
- 10 done
clear
D)
- 4 done
clear
View Solution play_arrow
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question_answer12)
If \[4ab=3{{h}^{2}}\], then the ratio of slopes of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] will be
A)
\[\sqrt{2}:1\] done
clear
B)
\[\sqrt{3}:1\] done
clear
C)
\[2:1\] done
clear
D)
\[1:3\] done
clear
View Solution play_arrow
-
question_answer13)
The lines represented by the equation \[a{{x}^{2}}(b-c)-xy(ab-bc)+c{{y}^{2}}(a-b)=0\] are
A)
\[a(b-c)x-c(a-b)y=0\], \[x+y=0\] done
clear
B)
\[x+y=0\], \[x-y=0\] done
clear
C)
\[a(b-c)x-c(a-b)y=0\], \[x-y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer14)
If the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] represents two lines \[y={{m}_{1}}x\] and \[y={{m}_{2}}x\], then [CEE 1993; MP PET 1988]
A)
\[{{m}_{1}}+{{m}_{2}}=\frac{-2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done
clear
B)
\[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{-a}{b}\] done
clear
C)
\[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=\frac{a}{b}\] done
clear
D)
\[{{m}_{1}}+{{m}_{2}}=\frac{2h}{b}\] and \[{{m}_{1}}{{m}_{2}}=-ab\] done
clear
View Solution play_arrow
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question_answer15)
The nature of straight lines represented by the equation \[4{{x}^{2}}+12xy+9{{y}^{2}}=0\] is [MP PET 1988]
A)
Real and coincident done
clear
B)
Real and different done
clear
C)
Imaginary and different done
clear
D)
None of the above done
clear
View Solution play_arrow
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question_answer16)
The equation of the perpendiculars drawn from the origin to the lines represented by the equation \[2{{x}^{2}}-10xy+12{{y}^{2}}+5x-16y-3=0\] is
A)
\[6{{x}^{2}}+5xy+{{y}^{2}}=0\] done
clear
B)
\[6{{y}^{2}}+5xy+{{x}^{2}}=0\] done
clear
C)
\[6{{x}^{2}}-5xy+{{y}^{2}}=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
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question_answer17)
Which of the following second degree equation represented a pair of straight lines [MP PET 1990]
A)
\[{{x}^{2}}-xy-{{y}^{2}}=1\] done
clear
B)
\[-{{x}^{2}}+xy-{{y}^{2}}=1\] done
clear
C)
\[4{{x}^{2}}-4xy+{{y}^{2}}=4\] done
clear
D)
\[{{x}^{2}}+{{y}^{2}}=4\] done
clear
View Solution play_arrow
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question_answer18)
. The lines \[{{a}^{2}}{{x}^{2}}+bc{{y}^{2}}=a(b+c)xy\] will be coincident, if
A)
\[a=0\] or \[b=c\] done
clear
B)
\[a=b\] or \[a=c\] done
clear
C)
\[c=0\] or \[a=b\] done
clear
D)
\[a=b+c\] done
clear
View Solution play_arrow
-
question_answer19)
If the equation \[2{{x}^{2}}-2hxy+2{{y}^{2}}=0\] represents two coincident straight lines passing through the origin, then \[h=\]
A)
\[\pm \text{ }6\] done
clear
B)
\[\sqrt{6}\] done
clear
C)
\[-\sqrt{6}\] done
clear
D)
\[\pm \text{ }2\] done
clear
View Solution play_arrow
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question_answer20)
If one of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be \[y=mx\], then [UPSEAT 1999]
A)
\[b{{m}^{2}}+2hm+a=0\] done
clear
B)
\[b{{m}^{2}}+2hm-a=0\] done
clear
C)
\[a{{m}^{2}}+2hm+b=0\] done
clear
D)
\[b{{m}^{2}}-2hm+a=0\] done
clear
View Solution play_arrow
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question_answer21)
The equation of the lines passing through the origin and parallel to the lines represented by the equation \[2{{x}^{2}}-xy-6{{y}^{2}}+7x+21y-15=0\], is
A)
\[2{{x}^{2}}-xy-6{{y}^{2}}=0\] done
clear
B)
\[6{{x}^{2}}-xy+2{{y}^{2}}=0\] done
clear
C)
\[6{{x}^{2}}-xy-2{{y}^{2}}=0\] done
clear
D)
\[2{{x}^{2}}+xy-6{{y}^{2}}=0\] done
clear
View Solution play_arrow
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question_answer22)
The equation \[2{{x}^{2}}+4xy-p{{y}^{2}}+4x+qy+1=0\] will represent two mutually perpendicular straight lines, if
A)
p = 1 and q = 2 or 6 done
clear
B)
p = 2 and q = 0 or 6 done
clear
C)
p = 2 and q = 0 or 8 done
clear
D)
p = - 2 and q = - 2 or 8 done
clear
View Solution play_arrow
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question_answer23)
If the equation \[A{{x}^{2}}+2Bxy+C{{y}^{2}}+Dx+Ey+F=0\] represents a pair of straight lines, then \[{{B}^{2}}-AC\] [MP PET 1992]
A)
< 0 done
clear
B)
= 0 done
clear
C)
> 0 done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer24)
The equation of the lines passing through the origin and having slopes 3 and \[-\frac{1}{3}\] is
A)
\[3{{y}^{2}}+8xy-3{{x}^{2}}=0\] done
clear
B)
\[3{{x}^{2}}+8xy-3{{y}^{2}}=0\] done
clear
C)
\[3{{y}^{2}}-8xy+3{{x}^{2}}=0\] done
clear
D)
\[3{{x}^{2}}+8xy+3{{y}^{2}}=0\] done
clear
View Solution play_arrow
-
question_answer25)
The equation \[xy+{{a}^{2}}=a(x+y)\] represents [MP PET 1991]
A)
A parabola done
clear
B)
A pair of straight lines done
clear
C)
An ellipse done
clear
D)
Two parallel straight lines done
clear
View Solution play_arrow
-
question_answer26)
If the slope of one of the line represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] be l times that of the other, then
A)
\[4\lambda h=ab(1+\lambda )\] done
clear
B)
\[\lambda h=ab{{(1+\lambda )}^{2}}\] done
clear
C)
\[4\lambda {{h}^{2}}=ab{{(1+\lambda )}^{2}}\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer27)
If one of the line represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is coincident with one of the line represented by \[{a}'{{x}^{2}}+2{h}'xy+{b}'{{y}^{2}}=0\], then
A)
\[{{(a{b}'-{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done
clear
B)
\[{{(a{b}'+{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done
clear
C)
\[{{(a{b}'-{a}'b)}^{2}}=(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer28)
The equation \[4{{x}^{2}}+12xy+9{{y}^{2}}+2gx+2fy+c=0\] will represents two real parallel straight lines, if
A)
g = 4, f = 9, c = 0 done
clear
B)
g = 2, f = 3, c = 1 done
clear
C)
g = 2, f = 3, c is any number done
clear
D)
g = 4, f = 9, c > 1 done
clear
View Solution play_arrow
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question_answer29)
The equation \[2{{y}^{2}}-xy-{{x}^{2}}+6x-8=0\] represents [MP PET 1992]
A)
A pair of straight lines done
clear
B)
A circle done
clear
C)
An ellipse done
clear
D)
A parabola done
clear
View Solution play_arrow
-
question_answer30)
One of the lines represented by the equation \[{{x}^{2}}+6xy=0\] is
A)
Parallel to x-axis done
clear
B)
Parallel to y-axis done
clear
C)
x-axis done
clear
D)
y-axis done
clear
View Solution play_arrow
-
question_answer31)
The equation of the lines represented by the equation \[{{x}^{2}}-5xy+6{{y}^{2}}=0\] are
A)
\[y+2x=0\], \[y-3x=0\] done
clear
B)
\[y-2x=0\], \[y-3x=0\] done
clear
C)
\[y+2x=0\], \[y+3x=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer32)
If the equation \[a{{x}^{2}}+b{{y}^{2}}+cx+cy=0\] represents a pair of straight lines, then
A)
\[a(b+c)=0\] done
clear
B)
\[b(c+a)=0\] done
clear
C)
\[c(a+b)=0\] done
clear
D)
\[a+b+c=0\] done
clear
View Solution play_arrow
-
question_answer33)
The equations of the lines represented by the equation \[a{{x}^{2}}+(a+b)xy+b{{y}^{2}}+x+y=0\] are
A)
\[ax+by+1=0\], \[x+y=0\] done
clear
B)
\[ax+by-1=0\], \[x+y=0\] done
clear
C)
\[ax+by+1=0\], \[x-y=0\] done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer34)
The equation \[{{x}^{2}}-7xy+12{{y}^{2}}=0\] represents [BIT Ranchi 1991]
A)
Circle done
clear
B)
Pair of parallel straight lines done
clear
C)
Pair of perpendicular straight lines done
clear
D)
Pair of non-perpendicular intersecting straight lines done
clear
View Solution play_arrow
-
question_answer35)
The equation \[{{y}^{2}}-{{x}^{2}}+2x-1=0\] represents [MNR 1991]
A)
A pair of straight lines done
clear
B)
A circle done
clear
C)
A parabola done
clear
D)
An ellipse done
clear
View Solution play_arrow
-
question_answer36)
If the equation \[\lambda {{x}^{2}}+2{{y}^{2}}-5xy+5x-7y+3=0\] represents two straight lines, then the value of l will be [RPET 1989]
A)
3 done
clear
B)
2 done
clear
C)
8 done
clear
D)
- 8 done
clear
View Solution play_arrow
-
question_answer37)
The equation of one of the line represented by the equation \[{{x}^{2}}+2xy\cot \theta -{{y}^{2}}=0\], is
A)
\[x-y\cot \theta =0\] done
clear
B)
\[x+y\tan \theta =0\] done
clear
C)
\[x\sin \theta +y(\cos \theta +1)=0\] done
clear
D)
\[x\cos \theta +y(\sin \theta +1)=0\] done
clear
View Solution play_arrow
-
question_answer38)
The equation of one of the line represented by the equation \[pq({{x}^{2}}-{{y}^{2}})+({{p}^{2}}-{{q}^{2}})xy=0\], is
A)
\[px+qy=0\] done
clear
B)
\[px-qy=0\] done
clear
C)
\[{{p}^{2}}x+{{q}^{2}}y=0\] done
clear
D)
\[{{q}^{2}}x-{{p}^{2}}y=0\] done
clear
View Solution play_arrow
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question_answer39)
The pair of straight lines passes through the point (1, 2) and perpendicular to the pair of straight lines \[3{{x}^{2}}-8xy+5{{y}^{2}}=0\], is
A)
\[(5x+3y+11)(x+y+3)=0\] done
clear
B)
\[(5x+3y-11)(x+y-3)=0\] done
clear
C)
\[(3x+5y-11)(x+y+3)=0\] done
clear
D)
\[(3x-5y+11)(x+y-3)=0\] done
clear
View Solution play_arrow
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question_answer40)
If in general quadratic equation \[f(x,\,y)=0\], \[\Delta =0\] and \[{{h}^{2}}=ab\], then the equation represents
A)
Two parallel straight lines done
clear
B)
Two perpendicular straight lines done
clear
C)
Two coincident lines done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer41)
The condition of representing the coincident lines by the general quadratic equation \[f(x,\,y)=0\], is
A)
\[\Delta =0\] and \[{{h}^{2}}=ab\] done
clear
B)
\[\Delta =0\] and \[a+b=0\]
done
clear
C)
\[\Delta =0\] and \[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\], \[{{f}^{2}}=bc\] done
clear
D)
\[{{h}^{2}}=ab\], \[{{g}^{2}}=ac\] and \[{{f}^{2}}=bc\] done
clear
View Solution play_arrow
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question_answer42)
The equation \[{{x}^{2}}+k{{y}^{2}}+4xy=0\]represents two coincident lines, if k = [MP PET 1995]
A)
0 done
clear
B)
1 done
clear
C)
4 done
clear
D)
16 done
clear
View Solution play_arrow
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question_answer43)
The joint equation of the straight lines \[x+y=1\]and \[x-y=4\]is [Karnataka CET 1993]
A)
\[{{x}^{2}}-{{y}^{2}}=-4\] done
clear
B)
\[{{x}^{2}}-{{y}^{2}}=4\] done
clear
C)
\[(x+y-1)\,(x-y-4)=0\] done
clear
D)
\[(x+y+1)(x-y+4)=0\] done
clear
View Solution play_arrow
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question_answer44)
The value of \[\lambda \] for which the equation \[{{x}^{2}}-\lambda xy+2{{y}^{2}}+3x-5y+2=0\] may represent a pair of straight lines is [Kurukshetra CEE 1996]
A)
2 done
clear
B)
3 done
clear
C)
4 done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer45)
\[2{{x}^{2}}+7xy+3{{y}^{2}}+8x+14y+\lambda =0\] will represent a pair of straight lines, when \[\lambda \]= [MP PET 1996]
A)
2 done
clear
B)
4 done
clear
C)
6 done
clear
D)
8 done
clear
View Solution play_arrow
-
question_answer46)
The gradient of one of the lines \[{{x}^{2}}+hxy+2{{y}^{2}}=0\] is twice that of the other, then h = [MP PET 1996]
A)
\[\pm \,3\] done
clear
B)
\[\pm \,\frac{3}{2}\] done
clear
C)
\[\pm \,2\] done
clear
D)
\[\pm \,1\] done
clear
View Solution play_arrow
-
question_answer47)
If the point (2,-3) lies on \[k{{x}^{2}}-3{{y}^{2}}+2x+y-2=0\], then k is equal to
A)
\[\frac{1}{7}\] done
clear
B)
16 done
clear
C)
7 done
clear
D)
12 done
clear
View Solution play_arrow
-
question_answer48)
If \[L{{x}^{2}}-10xy+12{{y}^{2}}\]\[+5x-16y-3=0\] represents a pair of straight lines, then L is [MP PET 2001]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
-1 done
clear
View Solution play_arrow
-
question_answer49)
If the ratio of gradients of the lines represented by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is 1 : 3, then the value of the ratio \[{{h}^{2}}:ab\]is [MP PET 1998]
A)
\[\frac{1}{3}\] done
clear
B)
\[\frac{3}{4}\] done
clear
C)
\[\frac{4}{3}\] done
clear
D)
1 done
clear
View Solution play_arrow
-
question_answer50)
If the slope of one line of the pair of lines represented by \[a{{x}^{2}}+4xy+{{y}^{2}}=0\]is 3 times the slope of the other line, then a is [DCE 1999]
A)
1 done
clear
B)
2 done
clear
C)
3 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer51)
If the sum of slopes of the pair of lines represented by \[4{{x}^{2}}+2hxy-7{{y}^{2}}=0\]is equal to the product of the slopes, then the value of\[h\]is [Karnataka CET 1999]
A)
- 6 done
clear
B)
- 2 done
clear
C)
- 4 done
clear
D)
4 done
clear
View Solution play_arrow
-
question_answer52)
The gradient of one of the lines of \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] is twice that of the other, then [MP PET 2000; Pb. CET 2002]
A)
\[{{h}^{2}}=ab\] done
clear
B)
\[h=a+b\] done
clear
C)
\[8{{h}^{2}}=9ab\] done
clear
D)
\[9{{h}^{2}}=8ab\] done
clear
View Solution play_arrow
-
question_answer53)
The equation \[{{x}^{2}}+kxy+{{y}^{2}}-5x-7y+6=0\] represents a pair of straight lines, then k is [MP PET 2000]
A)
5/3 done
clear
B)
10/3 done
clear
C)
3/2 done
clear
D)
3/10 done
clear
View Solution play_arrow
-
question_answer54)
The equation \[2{{x}^{2}}+4xy-k{{y}^{2}}+4x+2y-1=0\] represents a pair of lines. The value of k is [Karnataka CET 2001]
A)
\[-\frac{5}{3}\] done
clear
B)
\[\frac{5}{3}\] done
clear
C)
\[\frac{1}{3}\] done
clear
D)
\[-\frac{1}{3}\] done
clear
View Solution play_arrow
-
question_answer55)
Separate equations of lines, for a pair of lines, whose equation is \[{{x}^{2}}+xy-12{{y}^{2}}=0\], are [Karnataka CET 2001; Pb. CET 2000]
A)
\[x+4y=0\]and \[x+3y=0\] done
clear
B)
\[2x-3y=0\] and \[x-4y=0\] done
clear
C)
\[x-6y=0\]and \[x-3y=0\] done
clear
D)
\[x+4y=0\]and \[x-3y=0\] done
clear
View Solution play_arrow
-
question_answer56)
The value of k so that the equation \[2{{x}^{2}}+5xy+3{{y}^{2}}+6x+7y+k=0\] represents a pair of straight lines, is [Kurukshetra CEE 2002]
A)
4 done
clear
B)
6 done
clear
C)
0 done
clear
D)
8 done
clear
View Solution play_arrow
-
question_answer57)
If the equation \[3{{x}^{2}}+xy-{{y}^{2}}-3x+6y+k=0\] represents a pair of lines, then k is equal to [Karnataka CET 2002]
A)
9 done
clear
B)
1 done
clear
C)
0 done
clear
D)
- 9 done
clear
View Solution play_arrow
-
question_answer58)
Equation \[3{{x}^{2}}+7xy+2{{y}^{2}}+5x+5y+2=0\] represents [UPSEAT 2002]
A)
Pair of straight line done
clear
B)
Ellipse done
clear
C)
Hyperbola done
clear
D)
None of these done
clear
View Solution play_arrow
-
question_answer59)
For what value of \['p'\], \[{{y}^{2}}+xy+p{{x}^{2}}-x-2y=0\] represents two straight lines [UPSEAT 2002]
A)
2 done
clear
B)
\[\frac{1}{3}\] done
clear
C)
\[\frac{1}{4}\] done
clear
D)
\[\frac{1}{2}\] done
clear
View Solution play_arrow
-
question_answer60)
If the equation \[2{{x}^{2}}+7xy+3{{y}^{2}}-9x-7y+k=0\] represents a pair of lines, then k is equal to [Kerala (Engg.) 2002]
A)
4 done
clear
B)
2 done
clear
C)
1 done
clear
D)
- 4 done
clear
View Solution play_arrow
-
question_answer61)
If the equation \[12{{x}^{2}}-10xy+2{{y}^{2}}+11x-5y+k=0\] represents two straight lines, then the value of k is [MP PET 2003]
A)
1 done
clear
B)
2 done
clear
C)
0 done
clear
D)
3 done
clear
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question_answer62)
If two sides of a triangle are represented by \[{{x}^{2}}-7xy+6{{y}^{2}}=0\] and the centroid is (1, 0) then the equation of third side is
A)
\[2x+7y+3=0\] done
clear
B)
\[2x-7y+3=0\] done
clear
C)
\[2x+7y-3=0\] done
clear
D)
\[2x-7y-3=0\] done
clear
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question_answer63)
The equation \[4{{x}^{2}}-24xy+11{{y}^{2}}=0\]represents [Orissa JEE 2003]
A)
Two parallel lines done
clear
B)
Two perpendicular lines done
clear
C)
Two lines through the origin done
clear
D)
A circle done
clear
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question_answer64)
If the slope of one of the lines given by \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\]is 5 times the other, then [Karnataka CET 2003]
A)
\[5{{h}^{2}}=ab\] done
clear
B)
\[5{{h}^{2}}=9ab\] done
clear
C)
\[9{{h}^{2}}=5ab\] done
clear
D)
\[{{h}^{2}}=ab\] done
clear
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question_answer65)
The equation to the pair of straight lines through the origin which are perpendicular to the lines \[2{{x}^{2}}-5xy+{{y}^{2}}=0,\]is [MP PET 1990]
A)
\[2{{x}^{2}}+5xy+{{y}^{2}}=0\] done
clear
B)
\[{{x}^{2}}+2{{y}^{2}}+5xy=0\] done
clear
C)
\[{{x}^{2}}-5xy+2{{y}^{2}}=0\] done
clear
D)
\[2{{x}^{2}}+{{y}^{2}}-5xy=0\] done
clear
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question_answer66)
The area of the triangle formed by the lines \[{{x}^{2}}-4{{y}^{2}}=0\]and \[x=a\], is
A)
\[2{{a}^{2}}\] done
clear
B)
\[\frac{{{a}^{2}}}{2}\] done
clear
C)
\[\frac{\sqrt{3}{{a}^{2}}}{2}\] done
clear
D)
\[\frac{2{{a}^{2}}}{\sqrt{3}}\] done
clear
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question_answer67)
If the lines represented by the equation \[6{{x}^{2}}+41xy-7{{y}^{2}}=0\] make angles \[\alpha \]and \[\beta \] with x-axis, then \[\tan \alpha .\tan \beta \]=
A)
- 6/7 done
clear
B)
6/ 7 done
clear
C)
7/6 done
clear
D)
- 7/6 done
clear
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question_answer68)
Difference of slopes of the lines represented by equation \[{{x}^{2}}({{\sec }^{2}}\theta -{{\sin }^{2}}\theta )-2xy\tan \theta +{{y}^{2}}{{\sin }^{2}}\theta =0\]is [Kurukshetra CEE 2002]
A)
4 done
clear
B)
3 done
clear
C)
2 done
clear
D)
None of these done
clear
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question_answer69)
The value of \[\lambda ,\] for which the equation \[{{x}^{2}}-{{y}^{2}}-x\]?\[\lambda y-2=0\]represent a pair of straight line, are [MP PET 2004]
A)
3, - 3 done
clear
B)
- 3, 1 done
clear
C)
3, 1 done
clear
D)
-1, 1 done
clear
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question_answer70)
If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET 2004]
A)
- 16 done
clear
B)
16 done
clear
C)
4 done
clear
D)
- 4 done
clear
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question_answer71)
If one of the lines given by \[6{{x}^{2}}-xy+4c{{y}^{2}}=0\] is \[3x+4y=0\], then c equals [AIEEE 2004]
A)
- 3 done
clear
B)
- 1 done
clear
C)
3 done
clear
D)
1 done
clear
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question_answer72)
If the sum of the slopes of the lines given by \[{{x}^{2}}-2cxy-7{{y}^{2}}=0\] is four times their product, then c has the value [AIEEE 2004]
A)
- 2 done
clear
B)
- 1 done
clear
C)
2 done
clear
D)
1 done
clear
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question_answer73)
If \[\frac{{{x}^{2}}}{a}+\frac{{{y}^{2}}}{b}+\frac{2xy}{h}=0\] represent pair of straight lines and slope of one line is twice the other. Then \[ab:{{h}^{2}}\] is [DCE 2005]
A)
9 : 8 done
clear
B)
8 : 9 done
clear
C)
1 : 2 done
clear
D)
2 : 1 done
clear
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