MCQOPTIONS
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MCQOPTIONS
This section includes 15 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 equations of the line passing through the point(1,2,-4) and perpendicular to the two lines \[\frac{x-8}{3}=\frac{y+19}{-16}=\frac{z-10}{7}\] and \[\frac{x-15}{3}=\frac{y-29}{8}=\frac{z-5}{-5}\], will be [AI CBSE 1983] |
| A. | \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}\] |
| B. | \[\frac{x-1}{-2}=\frac{y-2}{3}=\frac{z+4}{8}\] |
| C. | \[\frac{x-1}{2}=\frac{y-2}{3}=\frac{z+4}{6}\] |
| D. | None of these |
| Answer» B. \[\frac{x-1}{-2}=\frac{y-2}{3}=\frac{z+4}{8}\] | |
| 2. |
The value of k such that \[\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}\] lies in the plane \[2x-4y+z=7\], is [IIT Screening 2003] |
| A. | 7 |
| B. | -7 |
| C. | No real value |
| D. | 4 |
| Answer» B. -7 | |
| 3. |
The distance of the point of intersection of the line \[\frac{x-3}{1}=\frac{y-4}{2}=\frac{z-5}{2}\]and the plane \[x+y+z=17\] from the point (3, 4, 5) is given by |
| A. | 3 |
| B. | 44230 |
| C. | \[\sqrt{3}\] |
| D. | None of these |
| Answer» B. 44230 | |
| 4. |
The distance of the point (1, -2, 3) from the plane \[x-y+z=5\] measured parallel to the line \[\frac{x}{2}=\frac{y}{3}=\frac{z}{-6},\]is [AI CBSE 1984] |
| A. | 1 |
| B. | 44383 |
| C. | 44354 |
| D. | None of these |
| Answer» B. 44383 | |
| 5. |
If \[4x+4y-kz=0\] is the equation of the plane through the origin that contains the line \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4},\]then k = [MP PET 1992] |
| A. | 1 |
| B. | 3 |
| C. | 5 |
| D. | 7 |
| Answer» D. 7 | |
| 6. |
If the lines \[\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}\] and \[\frac{x-3}{1}=\frac{y-k}{1}=\frac{z}{1}\] intersect, then k = [IIT Screening 2004] |
| A. | \[\frac{2}{9}\] |
| B. | \[\frac{9}{2}\] |
| C. | 0 |
| D. | None of these |
| Answer» C. 0 | |
| 7. |
The straight lines whose direction cosines are given by \[al+bm+cn=0,fmn+gnl+hlm=0\]are perpendicular, if |
| A. | \[\frac{f}{a}+\frac{g}{b}+\frac{h}{c}=0\] |
| B. | \[\sqrt{\frac{a}{f}}+\sqrt{\frac{b}{g}}+\sqrt{\frac{c}{h}}=0\] |
| C. | \[\sqrt{af}=\sqrt{bg}=\sqrt{ch}\] |
| D. | \[\sqrt{\frac{a}{f}}=\sqrt{\frac{b}{g}}=\sqrt{\frac{c}{h}}\] |
| Answer» B. \[\sqrt{\frac{a}{f}}+\sqrt{\frac{b}{g}}+\sqrt{\frac{c}{h}}=0\] | |
| 8. |
If three mutually perpendicular lines have direction cosines \[({{l}_{1}},{{m}_{1}},{{n}_{1}}),({{l}_{2}},{{m}_{2}},{{n}_{2}})\]and \[({{l}_{3}},{{m}_{3}},{{n}_{3}})\], then the line having direction cosines \[{{l}_{1}}+{{l}_{2}}+{{l}_{3}}\], \[{{m}_{1}}+\,\,{{m}_{2}}+\,\,{{m}_{3}}\]and \[{{n}_{1}}+{{n}_{2}}+{{n}_{3}}\] make an angle of..... with each other |
| A. | \[0{}^\circ \] |
| B. | \[30{}^\circ \] |
| C. | \[60{}^\circ \] |
| D. | \[90{}^\circ \] |
| Answer» B. \[30{}^\circ \] | |
| 9. |
The radius of the circle in which the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+2x-2y-4z-19=0\] is cut by the plane \[x+2y+2z+7=0\]is [AIEEE 2003] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 10. |
The shortest distance from the plane \[12x+4y+3z=327\] to the sphere \[{{x}^{2}}+{{y}^{2}}+{{z}^{2}}+\] \[4x-2y-6z=155\] is [AIEEE 2003] |
| A. | 26 |
| B. | \[11\frac{4}{13}\] |
| C. | 13 |
| D. | 39 |
| Answer» D. 39 | |
| 11. |
The equation of the plane passing through the points \[(1,-3,-2)\] and perpendicular to planes \[x+2y+2z=5\] and \[3x+3y+2z=8\], is [AISSE 1987] |
| A. | \[2x-4y+3z-8=0\] |
| B. | \[2x-4y-3z+8=0\] |
| C. | \[2x+4y+3z+8=0\] |
| D. | None of these |
| Answer» B. \[2x-4y-3z+8=0\] | |
| 12. |
The co-ordinates of the points A and B are (2, 3, 4) (-2, 5,-4) respectively. If a point P moves so that \[P{{A}^{2}}-P{{B}^{2}}=k\] where k is a constant, then the locus of P is |
| A. | A line |
| B. | A plane |
| C. | A sphere |
| D. | None of these |
| Answer» C. A sphere | |
| 13. |
The equation of the planes passing through the line of intersection of the planes \[3x-y-4z=0\] and \[x+3y+6=0\] whose distance from the origin is 1, are |
| A. | \[x-2y-2z-3=0\], \[2x+y-2z+3=0\] |
| B. | \[x-2y+2z-3=0\], \[2x+y+2z+3=0\] |
| C. | \[x+2y-2z-3=0\], \[2x-y-2z+3=0\] |
| D. | None of these |
| Answer» B. \[x-2y+2z-3=0\], \[2x+y+2z+3=0\] | |
| 14. |
The co-ordinates of the foot of perpendicular drawn from point \[P(1,\,0,\,3)\]to the join of points \[A(4,\,7,\,1)\]and \[B(3,\,5,\,3)\] is [RPET 2001] |
| A. | (5, 7, 1) |
| B. | \[\left( \frac{5}{3},\frac{7}{3},\frac{17}{3} \right)\] |
| C. | \[\left( \frac{2}{3},\frac{5}{3},\frac{7}{3} \right)\] |
| D. | \[\left( \frac{5}{3},\frac{2}{3},\frac{7}{3} \right)\] |
| Answer» C. \[\left( \frac{2}{3},\frac{5}{3},\frac{7}{3} \right)\] | |
| 15. |
If the straight lines \[x=1+s,\] \[y=-3-\lambda s,\] \[z=1+\lambda s\] and \[x=t/2,y=1+t,z=2-t\], with parameters s and \[t\] respectively, are co-planar, then \[\lambda \]equals [AIEEE 2004] |
| A. | 0 |
| B. | -1 |
| C. | -0.5 |
| D. | -2 |
| Answer» E. | |