InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
`vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)` The position vector of L, the foot of the perpendicular from P on the line `vec(r)=vec(a)+lamdavec(b)` is -A. `6hat(i)+7hat(j)+7hat(k)`B. `3hat(i)+2hat(j)-2hat(k)`C. `3hat(i)+5hat(j)+9hat(k)`D. `9hat(i)+9hat(j)+5hat(k)` |
| Answer» Correct Answer - C | |
| 2. |
`vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3)` If A is the point with position vector `vec(a)` then area of the `DeltaPLA` in square units is equal to -A. `3sqrt(6)`B. `7sqrt((17)/(2))`C. `sqrt(17)`D. `(7)/(2)` |
| Answer» Correct Answer - B | |
| 3. |
State which of the following statement is true ?A. The line koining the points (1,2,3) and (1,5,3) makes angle `(pi)/(2)` with the positive y-axis.B. The line joining the points (1,-1,0) and (2,-1,0) is parallel with the positive x-axis.C. The angle between the lines `(x-5)/(7)=(y+2)/(-5)=(z-2)/(1)` and `(x-1)/(1)=(y)/(2)=(z-1)/(3)` is `(pi)/(3)`D. The anlge between the lines `2x=3y=-z` and `6x=-y=-4z` is `(pi)/(4)`. |
| Answer» Correct Answer - B | |
| 4. |
The equation of a line passing through the points (5,2,7) and paraleel to y - axis is -A. `(x-5)/(b)=(y-2)/(0)=(z-7)/(b),bne0`B. `(x+5)/(b)=(y+2)/(0)=(z+7)/(b),bne0`C. `(x-5)/(0)=(y-2)/(b)=(z-7)/(0),bne0`D. `(x+5)/(0)=(y+2)/(b)=(z+7)/(b),bne0` |
| Answer» Correct Answer - C | |
| 5. |
State which of the following statement is true ?A. The line `(x-x_(1))/(a)=(y-y_(1))/(b)=(z-z_(1))/(c)` is parellel to x-axis, is `ane0` and `b=c=0` is satisfied.B. The line `(x-x_(1))/(a)=(y-y_(1))/(b)=(z-z_(1))/(c)` is passing through the origin, if `(x_(1))/(a)=(y_(1))/(b)=-(z_(1))/(c)` is satisfied.C. The vector equation of a line passing through the points (1,0,0) and (0,5,0) is given by `vec(r)=hat(i)+t(-hat(i)-5hat(j)+3hat(k))`D. The line `x=3+2t,y=5,z=3` is parallel to y-axis. |
| Answer» Correct Answer - A | |
| 6. |
The equation of a line passing through the points (1,2,3) and (4,0,6) is -A. `(x-1)/(4)=(y-2)/(0)=(z-3)/(6)`B. `(x-4)/(1)=(y-0)/(2)=(z-6)/(3)`C. `(x-1)/(-3)=(y-2)/(2)=(z-3)/(-3)`D. `(x-4)/(3)=(y-0)/(-2)=(z-6)/(3)` |
| Answer» Correct Answer - D | |
| 7. |
The equation of a line passing through the points (1,2,3) and (4,5,6) is given by -A. `(x-1)/(1-4)=(y-2)/(2-5)=(z-3)/(3-6)`B. `(x-1)/(4-1)=(y-2)/(5-2)=(z-3)/(4-2)`C. `(x-4)/(4-1)=(y-5)/(5-2)=(z-6)/(5-3)`D. `(x-4)/(4-1)=(y-5)/(2-5)=(z-6)/(3-6)` |
| Answer» Correct Answer - A | |
| 8. |
The angle between the straight lines `x=5,y=4t+5,z=4t+3` and `(x-5)/(5)=(y-6)/(0)=(z-(1)/(2))/(0)` is-A. `(pi)/(2)`B. `(pi)/(3)`C. `(pi)/(4)`D. 0 |
| Answer» Correct Answer - D | |
| 9. |
The angle between the straight lines `(x-4)/(2)=(y-5)/(0)=(z-6)/(0)` and `(3-x)/(3)=(y-7)/(0)=(z-3)/(0)` is -A. `pi`B. `(pi)/(2)`C. `(pi)/(3)`D. `(pi)/(6)` |
| Answer» Correct Answer - A | |
| 10. |
`L_(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L_(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2)` The lines `L_(1)` and `L_(2)` intersect at the pointA. (-3,2,1)B. (2,1,-3)C. (1,-3,2)D. none of these |
| Answer» Correct Answer - B | |
| 11. |
The direction ratios of the line `3x-2=2y+1=2z-4` are proportional to -A. `(1)/(3),-(1)/(2),(1)/(2)`B. `-(1)/(3),(1)/(2),(1)/(2)`C. `1/3,1/2,1/2`D. `1/3,1/2-(1)/(2)` |
| Answer» Correct Answer - C | |
| 12. |
The direction ratios of the line parallel to the line `(x-1)/(3)=(y-5)/(1)=(z-3)/(0)` are proportional to -A. 3,1,0B. 3,-1,0C. 1,5,3D. `-3,1,0` |
| Answer» Correct Answer - A | |
| 13. |
Statement - I: The point A (1,0,7) is the mirror image of the point B(1,6,3) in the line `(x)/(1)=(y-1)/(2)=(z-2)/(3)`. Statement - II : The line `(x)/(1)=(y-1)/(2)=(z-2)/(3)` bsects the line segment joining A(1,0,7) and B (1,6,3).A. Statement - I True, Statement - II is True , Statement - II is a correct explanation for Statement - IB. Statement -I is True, Statement - II is True , Statement - II is not a correct explanation for Statement -IC. Statement-I is True, Statement -II is False.D. Statement-I False, Statement -II is True. |
| Answer» Correct Answer - B | |
| 14. |
If the points P (1,2,3), Q(4,5,6) and R(7,8,9) are collinear then Q divides PR in the ratios of -A. `2:1`B. `1:2`C. `1:1`D. `1:3` |
| Answer» Correct Answer - C | |
| 15. |
The symmetrical from of the lines `x+y+z-1=0` and `4x+y-2z+2=0` are -A. `(x-1)/(2)=(y+2)/(-1)=(z-2)/(2)`B. `(x+(1)/(2))/(1)=(y-1)/(-2)=(z-(1)/(2))/(1)`C. `(x)/(1)=(y)/(-2)=(z-1)/(1)`D. `(x+1)/(1)=(y-2)/(-2)=(z-0)/(1)` |
| Answer» Correct Answer - B::C::D | |
| 16. |
The equation of line passing through the point `vec(a)` parallel to the plane `vec(r)*vec(n)=q` and perpendicular to the line `vec(r)=vec(b)+tvec(c)` is -A. `vec(r)=vec(a)+lamda(vec(n)xxvec(c))`B. `(vec(r)-vec(a))xx(vec(n)xxvec(c))=0`C. `vec(r)=vec(b)+lamda(vec(n)xxvec(c))`D. none of these |
| Answer» Correct Answer - A::B | |
| 17. |
The condition for intersecting the lines `vec(r)=vec(a)_(1)+tvec(b)_(1)` and `vec(r)=vec(a)_(2)+svec(b)_(2)` isA. `(vec(a)_(2)+vec(a)_(1))*(vec(b)_(1)xxvec(b)_(2))=0`B. `(vec(a)_(2)-vec(a)_(1))*(vec(b)_(1)xxvec(b)_(2))=0`C. `(vec(a)_(1)xxvec(a)_(2))*(vec(b)_(1)+vec(b)_(2))=0`D. `(vec(a)_(1)xxvec(a)_(2))*(vec(b)_(1)-vec(b)_(2))=0` |
| Answer» Correct Answer - B | |
| 18. |
The lines `vec(r)=hat(i)+t(5hat(i)+2hat(j)+hat(k))` and `vec(r)=hat(i)+s(-10hat(i)-4hat(j)-2hat(k))` are -A. parallelB. skewC. coincidentD. none of these |
| Answer» Correct Answer - C | |
| 19. |
The angle between the lines`(x-5)/(1)=(y-1)/(0)=(z-9)/(0)` and `2x-1=5-2y=sqrt(2)z` is - |
| Answer» Correct Answer - C | |
| 20. |
Consider the lines `(x-5)/(3)=(y-7)/(-16)=(z-3)/(7)` and `(x-9)/(3)=(y-13)/(8)=(z-15)/(-5)` , then-A. the two lines intersectB. the two lines are skewC. the shortest distance between the lines is 14D. direction numbers of the line of shortest distance are 2,3,6 |
| Answer» Correct Answer - B::C::D | |
| 21. |
The angles between the lines `(x-5)/(2)=(y-3)/(2)=(z)/(0)` and `x=5,y=8,z=6t` is - |
| Answer» Correct Answer - D | |
| 22. |
The lines `(x)/(1)=(y)/(2)=(z)/(3)` and `(x-1)/(-2)=(y-2)/(-4)=(3-z)/(6)` areA. coincidentB. skewC. intersectingD. parallel |
| Answer» Correct Answer - D | |
| 23. |
The perpendicula distance of the points (1,1,1) from the x-axis is -A. 1 unitsB. `sqrt(2)` unitsC. `2.14` unitsD. `sqrt(7)` units |
| Answer» Correct Answer - B | |
| 24. |
The perpendicular distance of the point (1,1,0) from the z-axis is -A. `sqrt(2)` unitsB. `4.18` unitsC. 9 unitsD. `sqrt(13` units |
| Answer» Correct Answer - A | |
| 25. |
The perpendicular distance of the points (1,0,0) from the y-axis is -A. 7 unitsB. `sqrt(5)` unitsC. 1 unitsD. `sqrt(2)` units |
| Answer» Correct Answer - C | |
| 26. |
The perpendicular distance of the point (1,2,3) from the x-axis is -A. `sqrt(5)` unitsB. `sqrt(13)` unitsC. 9 unitsD. 13 units |
| Answer» Correct Answer - B | |
| 27. |
The shortest distance between the lines `vec(r)=vec(a)_(1)+tvec(b)_(1)` and `vec(r)=vec(a)_(2)+svec(b)_(2)` is -A. `(|(vec(a)_(2)-veca_(1))*(vec(b_(1))xxvec(b)_(2))|)/(|vec(b)_(1)xxvec(b)_(2)|)`B. `(|(vec(a)_(2)+veca_(1))*(vec(b_(1))xxvec(b)_(2))|)/(|vec(b)_(1)xxvec(b)_(2)|)`C. `(|(vec(a)_(2)-veca_(1))*(vec(b_(1))xxvec(b)_(2))|)/(|vec(b)_(1)xxvec(b)_(2)|^(2))`D. `(|(vec(a)_(2)+veca_(1))*(vec(b_(1))xxvec(b)_(2))|)/(|vec(b)_(1)xxvec(b)_(2)|^(2))` |
| Answer» Correct Answer - A | |
| 28. |
`L_(1):(x+1)/(-3)=(y-3)/(2)=(z+2)/(1),L_(2):(x)/(1)=(y-7)/(-3)=(z+7)/(2)` Equation of plane containinng `L_(1)` and `L_(2)` is -A. `x+y+z=0`B. `3x-2y-z=0`C. `x-3y+2z=0`D. `x+y+z=42` |
| Answer» Correct Answer - A | |
| 29. |
The straight lines `(x)/(a_(1))=(y)/(b_(1))=(z)/(c_(1))` and `(x-2)/(a_(2))=(y-3)/(b_(2))=(z)/(c_(2))` will be parallel if -A. `a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0`B. `a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=1`C. `(A_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))`D. `(a_(1))/(a_(2))=(b_(1))/(b_(2))=(c_(1))/(c_(2))` |
| Answer» Correct Answer - C | |
| 30. |
If a line passing through the point with position vector `vec(alpha)` and parallel to vector `vec(beta)` then the vector equation of the line is-A. `vec(r)=vec(alpha)+vec(beta)`B. `vec(r)=vec(alpha)-vec(tbeta)`C. `vec(r)=vec(alpha)+vec(tbeta)`D. none of these |
| Answer» Correct Answer - C | |
| 31. |
The cartisian equation parallel to x-axis is -A. `(x-x_(1))/(0)=(y-y_(1))/(a)=(z-z_(1))/(a),ane0`B. `(x-x_(1))/(a)=(y-y_(1))/(0)=(z-z_(1))/(0),ane0`C. `(x-x_(1))/(0)=(y-y_(1))/(a)=(z-z_(1))/(0),ane0`D. `(x-x_(1))/(0)=(y-y_(1))/(0)=(z-z_(1))/(a),ane0` |
| Answer» Correct Answer - B | |