MCQOPTIONS
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MCQOPTIONS
This section includes 25 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The length of the perpendicular from the point \[(b,a)\]to the line \[\frac{x}{a}-\frac{y}{b}=1\], is |
| A. | \[\left| \frac{{{a}^{2}}-ab+{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| B. | \[\left| \frac{{{b}^{2}}-ab-{{a}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| C. | \[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| D. | None of these |
| Answer» C. \[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] | |
| 2. |
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. | \[{{a}^{2}}\] |
| B. | \[{{b}^{2}}\] |
| C. | \[{{a}^{2}}+{{b}^{2}}\] |
| D. | \[{{a}^{2}}-{{b}^{2}}\] |
| Answer» C. \[{{a}^{2}}+{{b}^{2}}\] | |
| 3. |
In what direction a line be drawn through the point (1, 2) so that its points of intersection with the line \[x+y=4\] is at a distance \[\frac{\sqrt{6}}{3}\] from the given point [IIT 1966; MNR 1987] |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{75}^{o}}\] |
| Answer» E. | |
| 4. |
If the lines \[ax+y+1=0,x+by+1=0\] and \[x+y+c=0\] (a, b, c being distinct and different from 1) are concurrent, then \[\frac{1}{1-a}+\frac{1}{1-b}+\frac{1}{1-c}=\] |
| A. | 0 |
| B. | 1 |
| C. | \[\frac{1}{a+b+c}\] |
| D. | None of these |
| Answer» C. \[\frac{1}{a+b+c}\] | |
| 5. |
The pedal points of a perpendicular drawn from origin on the line \[3x+4y-5=0\],is [RPET 1990] |
| A. | \[\left( \frac{3}{5},2 \right)\] |
| B. | \[\left( \frac{3}{5},\frac{4}{5} \right)\] |
| C. | \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] |
| D. | \[\left( \frac{30}{17},\frac{19}{17} \right)\] |
| Answer» C. \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] | |
| 6. |
Which pair of points lie on the same side of \[3x-8y-7=0\] [Roorkee 1990] |
| A. | (0, -1) and (0, 0) |
| B. | (4, -3) and (0, 1) |
| C. | (-3, -4) and (1, 2) |
| D. | (-1, -1) and (3, 7) |
| Answer» E. | |
| 7. |
Distance between the lines \[5x+3y-7=0\] and \[15x+9y+14=0\] is [Kerala (Engg.) 2002] |
| A. | \[\frac{35}{\sqrt{34}}\] |
| B. | \[\frac{1}{3\sqrt{34}}\] |
| C. | \[\frac{35}{3\sqrt{34}}\] |
| D. | \[\frac{35}{2\sqrt{34}}\] |
| Answer» D. \[\frac{35}{2\sqrt{34}}\] | |
| 8. |
The equation of straight line passing through \[(-a,\ 0)\] and making the triangle with axes of area ?T? is [RPET 1987] |
| A. | \[2Tx+{{a}^{2}}y+2aT=0\] |
| B. | \[2Tx-{{a}^{2}}y+2aT=0\] |
| C. | \[2Tx-{{a}^{2}}y-2aT=0\] |
| D. | None of these |
| Answer» C. \[2Tx-{{a}^{2}}y-2aT=0\] | |
| 9. |
Let PS be the median of the triangle with vertices \[P(2,\ 2),\ Q(6,\ -\ 1)\]and \[R(7,\ 3)\]. The equation of the line passing through (1,? 1) and parallel to PS is [IIT Screening 2000] |
| A. | \[2x-9y-7=0\] |
| B. | \[2x-9y-11=0\] |
| C. | \[2x+9y-11=0\] |
| D. | \[2x+9y+7=0\] |
| Answer» E. | |
| 10. |
The medians AD and BE of a triangle with vertices \[A\ (0,\ b),\ B\ (0,\ 0)\] and \[C\ (a,\ 0)\] are perpendicular to each other, if [Karnataka CET 2000] |
| A. | \[a=\sqrt{2}\ b\] |
| B. | \[a=-\sqrt{2}\ b\] |
| C. | Both (a) and (b) |
| D. | None of these |
| Answer» D. None of these | |
| 11. |
A pair of straight lines drawn through the origin form with the line \[2x+3y=6\]an isosceles right angled triangle, then the lines and the area of the triangle thus formed is[Roorkee 1993] |
| A. | \[x-5y=0\]\[5x+y=0\]\[\Delta =\frac{36}{13}\] |
| B. | \[3x-y=0\]\[x+3y=0\]\[\Delta =\frac{12}{17}\] |
| C. | \[5x-y=0\]\[x+5y=0\]\[\Delta =\frac{13}{5}\] |
| D. | None of these |
| Answer» B. \[3x-y=0\]\[x+3y=0\]\[\Delta =\frac{12}{17}\] | |
| 12. |
The line \[3x+2y=24\]meets \[y\]-axis at A and x-axis at B. The perpendicular bisector of \[AB\]meets the line through \[(0,-1)\] parallel to x-axis at C. The area of the triangle \[ABC\] is |
| A. | \[182sq.\]units |
| B. | \[91sq.\]units |
| C. | \[48sq.\]units |
| D. | None of these |
| Answer» C. \[48sq.\]units | |
| 13. |
Given the four lines with equations \[x+2y=3,\] \[3x+4y=7,\,\,2x+3y=4\,\,\] and \[4x+5y=6,\] then these lines are [IIT 1980; Pb. CET 2003] |
| A. | Concurrent |
| B. | Perpendicular |
| C. | The sides of a rectangle |
| D. | None of these |
| Answer» E. | |
| 14. |
If the co-ordinates of the middle point of the portion of a line intercepted between coordinate axes (3,2), then the equation of the line will be [RPET 1985; MP PET 1984] |
| A. | \[2x+3y=12\] |
| B. | \[3x+2y=12\] |
| C. | \[4x-3y=6\] |
| D. | \[5x-2y=10\] |
| Answer» B. \[3x+2y=12\] | |
| 15. |
A ray of light coming from the point (1, 2) is reflected at a point A on the x-axis and then passes through the point (5, 3). The coordinates of the point A are [Orissa JEE 2003] |
| A. | \[\left( 13/5,\ 0 \right)\] |
| B. | \[\left( 5/13,\ 0 \right)\] |
| C. | (- 7, 0) |
| D. | None of these |
| Answer» B. \[\left( 5/13,\ 0 \right)\] | |
| 16. |
The number of integral values of m, for which the x-co-ordinate of the point of intersection of the lines \[3x+4y=9\] and \[y=mx+1\]is also an integer is [IIT Screening 2001] |
| A. | 2 |
| B. | 0 |
| C. | 4 |
| D. | 1 |
| Answer» B. 0 | |
| 17. |
The sides \[AB,BC,CD\] and \[DA\]of a quadrilateral are \[x+2y=3,\,x=1,\] \[x-3y=4,\,\] \[\,5x+y+12=0\] respectively.The angle between diagonals \[AC\]and \[BD\]is[Roorkee 1993] |
| A. | \[{{45}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» D. \[{{30}^{o}}\] | |
| 18. |
If straight lines \[ax+by+p=0\] and \[x\cos \alpha +y\sin \alpha -p=0\] include an angle \[\pi /4\] between them and meet the straight line \[x\sin \alpha -y\cos \alpha =0\] in the same point, then the value of \[{{a}^{2}}+{{b}^{2}}\]is equal to |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» C. 3 | |
| 19. |
The value of \[\lambda \] for which the lines \[3x+4y=5,\] \[5x+4y=4\]and \[\lambda x+4y=6\] meet at a point is [Kerala (Engg.) 2002] |
| A. | 2 |
| B. | 1 |
| C. | 4 |
| D. | 3 |
| Answer» C. 4 | |
| 20. |
For what value of 'a' the lines \[x=3,y=4\] and \[4x-3y+a=0\] are concurrent [RPET 1984] |
| A. | 0 |
| B. | -1 |
| C. | 2 |
| D. | 3 |
| Answer» B. -1 | |
| 21. |
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. | \[\frac{\sqrt{3}}{2}x+y=0\] |
| B. | \[x+\sqrt{3}y=0\] |
| C. | \[\sqrt{3}x+y=0\] |
| D. | \[x+\frac{\sqrt{3}}{2}y=0\] |
| Answer» D. \[x+\frac{\sqrt{3}}{2}y=0\] | |
| 22. |
The angle between the lines whose intercepts on the axes are a, -b and b, -a respectively, is |
| A. | \[{{\tan }^{-1}}\frac{{{a}^{2}}-{{b}^{2}}}{ab}\] |
| B. | \[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2}\] |
| C. | \[{{\tan }^{-1}}\frac{{{b}^{2}}-{{a}^{2}}}{2ab}\] |
| D. | None of these |
| Answer» D. None of these | |
| 23. |
The number of straight lines which is equally inclined to both the axes is [RPET 2002] |
| A. | 4 |
| B. | 2 |
| C. | 3 |
| D. | 1 |
| Answer» C. 3 | |
| 24. |
Angle between the lines \[2x-y-15=0\] and \[3x+y+4=0\]is [RPET 2003] |
| A. | \[{{90}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{180}^{o}}\] |
| D. | \[{{60}^{o}}\] |
| Answer» B. \[{{45}^{o}}\] | |
| 25. |
The line passes through (1, 0) and \[(-\ 2,\ \sqrt{3})\] makes an angle of ...... with x?axis [RPET 1985] |
| A. | \[{{60}^{o}}\] |
| B. | \[{{120}^{o}}\] |
| C. | \[{{150}^{o}}\] |
| D. | \[{{135}^{o}}\] |
| Answer» D. \[{{135}^{o}}\] | |