MCQOPTIONS
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MCQOPTIONS
This section includes 32 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
If \[a{{x}^{2}}-{{y}^{2}}+4x-y=0\]represents a pair of lines then \[a=\] [Karnataka CET2004] |
| A. | -16 |
| B. | 16 |
| C. | 4 |
| D. | -4 |
| Answer» C. 4 | |
| 2. |
If two sides of atriangle are represented by \[{{x}^{2}}-7xy+6{{y}^{2}}=0\] and the centroid is (1, 0) then the equation of third side is |
| A. | \[2x+7y+3=0\] |
| B. | \[2x-7y+3=0\] |
| C. | \[2x+7y-3=0\] |
| D. | \[2x-7y-3=0\] |
| Answer» E. | |
| 3. |
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. | \[-\frac{5}{3}\] |
| B. | \[\frac{5}{3}\] |
| C. | \[\frac{1}{3}\] |
| D. | \[-\frac{1}{3}\] |
| Answer» B. \[\frac{5}{3}\] | |
| 4. |
The gradientof one of the lines \[{{x}^{2}}+hxy+2{{y}^{2}}=0\] is twice that of the other, then h =[MP PET 1996] |
| A. | \[\pm \,3\] |
| B. | \[\pm \,\frac{3}{2}\] |
| C. | \[\pm \,2\] |
| D. | \[\pm \,1\] |
| Answer» B. \[\pm \,\frac{3}{2}\] | |
| 5. |
The equation \[{{y}^{2}}-{{x}^{2}}+2x-1=0\] represents [MNR 1991] |
| A. | A pair of straight lines |
| B. | A circle |
| C. | A parabola |
| D. | An ellipse |
| Answer» B. A circle | |
| 6. |
One of the lines represented by the equation \[{{x}^{2}}+6xy=0\] is |
| A. | Parallel to x-axis |
| B. | Parallel to y-axis |
| C. | x-axis |
| D. | y-axis |
| Answer» E. | |
| 7. |
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 |
| B. | p = 2 and q = 0 or 6 |
| C. | p = 2 and q = 0 or 8 |
| D. | p = - 2 and q = - 2 or 8 |
| Answer» D. p = - 2 and q = - 2 or 8 | |
| 8. |
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. | \[{{(a{b}'-{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] |
| B. | \[{{(a{b}'+{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] |
| C. | \[{{(a{b}'-{a}'b)}^{2}}=(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] |
| D. | None of these |
| Answer» B. \[{{(a{b}'+{a}'b)}^{2}}=4(a{h}'-{a}'h)\,(h{b}'-{h}'b)\] | |
| 9. |
If the equation \[2{{x}^{2}}-2hxy+2{{y}^{2}}=0\] represents two coincident straight lines passing through the origin, then \[h=\] |
| A. | \[\pm \text{ }6\] |
| B. | \[\sqrt{6}\] |
| C. | \[-\sqrt{6}\] |
| D. | \[\pm \text{ }2\] |
| Answer» E. | |
| 10. |
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 |
| B. | 6 |
| C. | -10 |
| D. | -4 |
| Answer» B. 6 | |
| 11. |
The equation \[{{(x+y)}^{2}}-({{x}^{2}}+{{y}^{2}})=0\] represents |
| A. | A circle |
| B. | Two lines |
| C. | Two parallel lines |
| D. | Two mutually perpendicular lines |
| Answer» E. | |
| 12. |
If the lines joining origin to the points of intersection of the line \[fx-gy=\lambda \] and the curve \[{{x}^{2}}+hxy-{{y}^{2}}+gx+fy=0\] be mutually perpendicular, then |
| A. | \[\lambda =h\] |
| B. | \[\lambda =g\] |
| C. | \[\lambda =fg\] |
| D. | \[\lambda \]may have any value |
| Answer» E. | |
| 13. |
The distance between the pair of parallel lines \[{{x}^{2}}+2xy+{{y}^{2}}-8ax-8ay-9{{a}^{2}}=0\] is [Karnataka CET 2005] |
| A. | \[2\sqrt{5}a\] |
| B. | \[\sqrt{10}\,a\] |
| C. | \[10\,a\] |
| D. | \[5\sqrt{2}\,a\] |
| Answer» E. | |
| 14. |
If the distance of two lines passing through origin from the point \[({{x}_{1}},{{y}_{1}})\] is \['d'\], then the equation of lines is |
| A. | \[{{(x{{y}_{1}}-y{{x}_{1}})}^{2}}={{d}^{2}}({{x}^{2}}+{{y}^{2}})\] |
| B. | \[{{({{x}_{1}}{{y}_{1}}-xy)}^{2}}=({{x}^{2}}+{{y}^{2}})\] |
| C. | \[{{(x{{y}_{1}}+y{{x}_{1}})}^{2}}=({{x}^{2}}-{{y}^{2}})\] |
| D. | \[({{x}^{2}}-{{y}^{2}})=2({{x}_{1}}+{{y}_{1}})\] |
| Answer» B. \[{{({{x}_{1}}{{y}_{1}}-xy)}^{2}}=({{x}^{2}}+{{y}^{2}})\] | |
| 15. |
The product of perpendiculars drawn from the origin to the lines represented by the equation\[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\], will be [Bihar CEE 1994] |
| A. | \[\frac{ab}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\] |
| B. | \[\frac{bc}{\sqrt{{{a}^{2}}-{{b}^{2}}+4{{h}^{2}}}}\] |
| C. | \[\frac{ca}{\sqrt{({{a}^{2}}+{{b}^{2}})+4{{h}^{2}}}}\] |
| D. | \[\frac{c}{\sqrt{{{(a-b)}^{2}}+4{{h}^{2}}}}\] |
| Answer» E. | |
| 16. |
The orthocentre of the triangle formed by the lines \[xy=0\]and \[x+y=1\]is [IIT 1995] |
| A. | \[(0,0)\] |
| B. | \[\left( \frac{1}{2},\frac{1}{2} \right)\] |
| C. | \[\left( \frac{1}{3},\frac{1}{3} \right)\] |
| D. | \[\left( \frac{1}{4},\frac{1}{4} \right)\] |
| Answer» B. \[\left( \frac{1}{2},\frac{1}{2} \right)\] | |
| 17. |
The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a, b), is |
| A. | \[{{x}^{2}}+{{y}^{2}}-ax-by=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}-2ax-2by=0\] |
| D. | None of these |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+ax+by=0\] | |
| 18. |
If the lines \[a{{x}^{2}}+2hxy+b{{y}^{2}}=0\] represents the adjacent sides of a parallelogram, then the equation of second diagonal if one is \[lx+my=1\], will be |
| A. | \[(am+hl)x=(bl+hm)y\] |
| B. | \[(am-hl)x=(bl-hm)y\] |
| C. | \[(am-hl)x=(bl+hm)y\] |
| D. | None of these |
| Answer» C. \[(am-hl)x=(bl+hm)y\] | |
| 19. |
The angle between the lines joining the points of intersection of line \[y=3x+2\] and the curve \[{{x}^{2}}+2xy+3{{y}^{2}}+4x+8y-11=0\] to the origin, is |
| A. | \[{{\tan }^{-1}}\left( \frac{3}{2\sqrt{2}} \right)\] |
| B. | \[{{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)\] |
| C. | \[{{\tan }^{-1}}\left( \sqrt{3} \right)\] |
| D. | \[{{\tan }^{-1}}\left( \frac{2}{2\sqrt{2}} \right)\] |
| Answer» C. \[{{\tan }^{-1}}\left( \sqrt{3} \right)\] | |
| 20. |
The lines joining the origin to the points of intersection of the line \[y=mx+c\]and the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]will be mutually perpendicular, if [Roorkee 1977] |
| A. | \[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\] |
| B. | \[{{a}^{2}}({{m}^{2}}-1)={{c}^{2}}\] |
| C. | \[{{a}^{2}}({{m}^{2}}+1)={{c}^{2}}\] |
| D. | \[{{a}^{2}}({{m}^{2}}-1)=2{{c}^{2}}\] |
| Answer» D. \[{{a}^{2}}({{m}^{2}}-1)=2{{c}^{2}}\] | |
| 21. |
If the bisectors of the lines \[{{x}^{2}}-2pxy-{{y}^{2}}=0\] be \[{{x}^{2}}-2qxy-{{y}^{2}}=0,\] then[MP PET 1993; DCE 1999; RPET 2003; AIEEE 2003; Kerala (Engg.) 2005] |
| A. | \[pq+1=0\] |
| B. | \[pq-1=0\] |
| C. | \[p+q=0\] |
| D. | \[p-q=0\] |
| Answer» B. \[pq-1=0\] | |
| 22. |
The equation of the pair of straight lines, each of which makes an angle \[\alpha \]with the line \[y=x\], is[MP PET 1990] |
| A. | \[{{x}^{2}}+2xy\sec 2\alpha +{{y}^{2}}=0\] |
| B. | \[{{x}^{2}}+2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| C. | \[{{x}^{2}}-2xy\,\text{cosec}\,2\alpha +{{y}^{2}}=0\] |
| D. | \[{{x}^{2}}-2xy\sec 2\alpha +{{y}^{2}}=0\] |
| Answer» E. | |
| 23. |
The square of distance between the point of intersection of the lines represented by the equation \[a{{x}^{2}}+2hxy+b{{y}^{2}}+2gx+2fy+c=0\] and origin, is |
| A. | \[\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab-{{h}^{2}}}\] |
| B. | \[\frac{c(a-b)+{{f}^{2}}+{{g}^{2}}}{\sqrt{ab-{{h}^{2}}}}\] |
| C. | \[\frac{c(a+b)-{{f}^{2}}-{{g}^{2}}}{ab+{{h}^{2}}}\] |
| D. | None of these |
| Answer» B. \[\frac{c(a-b)+{{f}^{2}}+{{g}^{2}}}{\sqrt{ab-{{h}^{2}}}}\] | |
| 24. |
If \[y=mx\]be one of the bisectors of the angle between the lines \[a{{x}^{2}}-2hxy+b{{y}^{2}}=0\], then |
| A. | \[h\,(1+{{m}^{2}})+m(a-b)=0\] |
| B. | \[h\,(1-{{m}^{2}})+m(a+b)=0\] |
| C. | \[h\,(1-{{m}^{2}})+m(a-b)=0\] |
| D. | \[h\,(1+{{m}^{2}})+m(a+b)=0\] |
| Answer» D. \[h\,(1+{{m}^{2}})+m(a+b)=0\] | |
| 25. |
The equation of the bisectors of the angle between lines represented by equation \[4{{x}^{2}}-16xy-7{{y}^{2}}=0\]is |
| A. | \[8{{x}^{2}}+11xy-8{{y}^{2}}=0\] |
| B. | \[8{{x}^{2}}-11xy-8{{y}^{2}}=0\] |
| C. | \[16{{x}^{2}}+11xy-16{{y}^{2}}=0\] |
| D. | \[16{{x}^{2}}+11xy+16{{y}^{2}}=0\] |
| Answer» B. \[8{{x}^{2}}-11xy-8{{y}^{2}}=0\] | |
| 26. |
If the bisectors of the angles of the lines represented by \[3{{x}^{2}}-4xy+5{{y}^{2}}=0\] and \[5{{x}^{2}}+4xy+3{{y}^{2}}=0\] are same, then the angle made by the lines represented by first with the second, is |
| A. | \[{{30}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{45}^{o}}\] |
| D. | \[{{90}^{o}}\] |
| Answer» E. | |
| 27. |
Acute angle between the lines represented by \[({{x}^{2}}+{{y}^{2}})\sqrt{3}=4xy\] is [MP PET 1992] |
| A. | \[\pi /6\] |
| B. | \[\pi /4\] |
| C. | \[\pi /3\] |
| D. | None of these |
| Answer» B. \[\pi /4\] | |
| 28. |
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. | \[2\theta \] |
| B. | \[\theta /3\] |
| C. | \[\theta \] |
| D. | \[\theta /2\] |
| Answer» D. \[\theta /2\] | |
| 29. |
The angle between the lines \[{{x}^{2}}+4xy+{{y}^{2}}=0\] is [Karnataka CET 2001; Pb. CET 2001] |
| A. | \[{{60}^{o}}\] |
| B. | \[{{15}^{o}}\] |
| C. | \[{{30}^{o}}\] |
| D. | \[{{45}^{o}}\] |
| Answer» B. \[{{15}^{o}}\] | |
| 30. |
The equation \[{{x}^{2}}+{{k}_{1}}{{y}^{2}}+{{k}_{2}}xy=0\] represents a pair of perpendicular lines, if |
| A. | \[{{k}_{1}}=-1\] |
| B. | \[{{k}_{1}}=2{{k}_{2}}\] |
| C. | \[2{{k}_{1}}={{k}_{2}}\] |
| D. | None of these |
| Answer» B. \[{{k}_{1}}=2{{k}_{2}}\] | |
| 31. |
Pair of straight lines perpendicular to each other represented by[Roorkee 1990] |
| A. | \[2{{x}^{2}}=2y(2x+y)\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+3=0\] |
| C. | \[2{{x}^{2}}=y(2x+y)\] |
| D. | \[{{x}^{2}}=2(x-y)\] |
| Answer» B. \[{{x}^{2}}+{{y}^{2}}+3=0\] | |
| 32. |
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. | \[{{0}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{\tan }^{-1}}(-2)\] |
| Answer» E. | |