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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.
| 51. |
If is the angle between plane `bar(r).bar(n)=p` and the line `bar(r).bar(a)=lamdabar(b)`A. `"cos "theta=(bar(b).bar(n))/(|bar(b)||bar(n)|)`B. `"cos "theta=(bar(a).bar(n))/(|bar(a)||bar(n)|)`C. `"sin "theta=(bar(a).bar(n))/(|bar(a)||bar(n)|)`D. `"sin "theta=(bar(b).bar(n))/(|bar(b)||bar(n)|)` |
| Answer» Correct Answer - D | |
| 52. |
The length of perpendicular drawn from point A `(bar(a))` to the plance `bar(r).bar(n)=p` isA. `|((bara.barn)+p)/(|barn|)|`B. `|((bara.barn)-p)/(|barn|)|`C. `|((baraxxbarn)+p)/(|barn|)|`D. `|((baraxxbarn)-p)/(|barn|)|` |
| Answer» Correct Answer - B | |
| 53. |
The plane `2x+3y+kz-7=0` is parallel to the line whose direction ratios are `2, -3,1,` then k =A. 5B. 8C. 1D. 4 |
| Answer» Correct Answer - A | |
| 54. |
The equation to the perpendicular from the point `(alpha, beta gamma)` to the plane `ax+by+cz+d=0` isA. x + y+ z = abcB. `a(x-alpha)+b(y-beta)+c(z-gamma)=0`C. `a(x-alpha)+b(y-beta)+c(z-gamma)=abc`D. `(x-alpha)/(a)=(y-beta)/(b)=(z-gamma)/(c)` |
| Answer» Correct Answer - D | |
| 55. |
The plane `ax+by+cz=105` contain the lines `2x-y+z=3and3x+y+z=5` . If point (2 ,1, -1) is at a distance of `(1)/(sqrt(6))` from the plane , then `a+b+c=` |
| Answer» Correct Answer - B | |
| 56. |
In three dimenisonal space , the equation by+cz = 0 representsA. a plane containing x-axisB. a plane containing Y- axisC. a plane containing Z-axisD. a plance containing point (abc) |
| Answer» Correct Answer - A | |
| 57. |
In the space the equation `by+cz+d=0` represents a plane perpendicular to the planeA. YOZB. ZOXC. XOYD. z=k |
| Answer» Correct Answer - A | |
| 58. |
The value of k for which the planes `3x-6y-2z=7 and 2x+y-kz=5` areperpendicular to each other is |
| Answer» Correct Answer - A | |
| 59. |
If the planes `ax+by+cz+d=0anda_(1)x+b_(1)y+c_(1)z+d_(1)=0` be mutually perpendicular , thenA. `(a)/(a_(1))=(b)/(b_(1))=(c)/(c_(1))`B. `(a)/(a_(1))=(b)/(b_(1))=(c)/(c_(1))=0`C. `aa_(1)+b b_(1)+c c_(1)=1`D. `aa_(1)+b b_(1)+c c_(1)=0` |
| Answer» Correct Answer - D | |
| 60. |
The vector equation of the plane `barr=(2hati+hatk)+lamdahati+mu(hati+2hatj-3hatk)` isA. `barr.(2hati+3hatj+2hatk)=2`B. `barr.(2hati+3hatj-2hatk)=2`C. `barr.(3hatj+2hatk)=2`D. `barr.(3hatj-2hatk)=2` |
| Answer» Correct Answer - C | |
| 61. |
The direaction cosines of perpendicular from orgin to the plane `barr.(2hati+3hatj+6hatk)+7=0` areA. `(-2)/(7),(-3)/(7),(-6)/(7)`B. `(2)/(7),(3)/(7),(6)/(7)`C. `(2)/(7),(-3)/(7),(6)/(7)`D. `(2)/(7),(-3)/(7),(-6)/(7)` |
| Answer» Correct Answer - A | |
| 62. |
The equation of plance through the points (1 , 1 ,0 ) and (2 , 2 ,3 ) and parallel to the line `(x-1)/(1) =(y-1)/(-2)=(z-2)/(3)` isA. `barr.(10hati-hatj-4hatk)=9`B. `barr.(10hati-hatj-4hatk)=-9`C. `barr.(10hati-hatj+4hatk)=9`D. `barr.(10hati-hatj+4hatk)=-9` |
| Answer» Correct Answer - A | |
| 63. |
The angle between planes `3x-6y+2z=8and 2x+2y-2z=10` isA. `30^(@)`B. `60^(@)`C. `45^(@)`D. `90^(@)` |
| Answer» Correct Answer - D | |
| 64. |
The direction cosines of the normal to the plance `4x + 8y + z= 5` areA. `(4)/(5),(8)/(5),(1)/(5)`B. `(4)/(9),(8)/(9),(1)/(9)`C. `(4)/(45),(8)/(45),(1)/(45)`D. `(4)/(3),(8)/(3),(1)/(3)` |
| Answer» Correct Answer - B | |
| 65. |
If `d_(1)andd_(2)` are the distances of points (2 ,3 ,4 ) and (1 , 1 ,4 ) respectively from the plane `3x-6y+2z+11=0,"then" d_(1)andd_(2)` are the roots ofA. `16d^(2)+23d+7=0`B. `16d^(2)-23d+7=0`C. `7d^(2)+23d+16=0`D. `7d^(2)-23d+16=0` |
| Answer» Correct Answer - D | |
| 66. |
If the angle `theta` between the line `(x+1)/1=(y-1)/2=(z-2)/2` and the plane `2x-y+sqrt(lamdaz)+4=0` is such that `sin theta=1/3`, the value of `lamda` isA. `(-4)/(3)`B. `(4)/(3)`C. `(-3)/(5)`D. `(5)/(3)` |
| Answer» Correct Answer - D | |
| 67. |
The acute angle between the two planes ` x + y + 2z` = 3 and 3x - 2y + 2z = 7 ` is …….A. `"cos"^(-1)((3)/(sqrt(102)))`B. `"cos"^(-1)((1)/(sqrt(102)))`C. `"cos"^(-1)((9)/(sqrt(102)))`D. `"cos"^(-1)((5)/(sqrt(102)))` |
| Answer» Correct Answer - D | |
| 68. |
The equation of plane passing through the line of intersection of planes `2x-y+z=3,4x-3y-5z+9=0` and parallel to the line `(x+1)/(2)=(y+3)/(4)=(z-3)/(5)` isA. `11x-3y-2z-54=0`B. `11x-3y+2z-54=0`C. `11x+3y-2z-54=0`D. `11x-3y-2z+54=0` |
| Answer» Correct Answer - A | |
| 69. |
The equation of plance passing through the point (1 ,1 -2) having 2, 3, 2 as direction ratios of normal to the plance isA. `2x + 3y + 2z = 7`B. `2x + 3y + 2z = -7`C. `2x + 3y + 2z = 9 `D. `2x + 3y + 2z =-9` |
| Answer» Correct Answer - C | |
| 70. |
If the angle `theta` between Z-axis and the plane `3x-4y+5z+7=0 " is cos" ^(-1)(k),"then "k=`A. `(1)/(2)`B. `(1)/(sqrt(2))`C. 2D. `sqrt(2)` |
| Answer» Correct Answer - B | |
| 71. |
The angle between the line `(x)/(3)=(y)/(4)=(z)/(5) "and the plane " 2x+y-2z=7` isA. `0^(@)`B. `30^(@)`C. `60^(@)`D. `90^(@)` |
| Answer» Correct Answer - A | |
| 72. |
The acute angle between the line `(x+1)/(2) = (y)/(3)= (z-3)/(6)` and the plane `10 x + 2y -11z = 8` isA. `"sin"^(-1)((4)/(21))`B. `"sin"^(-1)((4)/(7))`C. `"sin"^(-1)((8)/(21))`D. `"sin"^(-1)((8)/(7))` |
| Answer» Correct Answer - C | |
| 73. |
The direation ratios of the normal to the plane passing through the point (2 ,1 ,0 ) and the line of intersection of the planes `x-2y+3z=4andx-y+z=3` isA. 1 , 1 , 0B. `1 , -1 , 0`C. 1 ,0 ,1D. ` 1 ,0 , -1` |
| Answer» Correct Answer - D | |
| 74. |
Find the equation of the plane passing through the point `(1,-1,2)`having `2,3,2`as direction ratios of normal to the plane.A. `barr.(3hati+2hatj+3hatk)=11`B. `barr.(3hati+2hatj+3hatk)=5`C. `barr.(3hati+2hatj+3hatk)=1`D. `barr.(3hati+2hatj+3hatk)=-1` |
| Answer» Correct Answer - D | |
| 75. |
If `|barn|=3sqrt(3)` such that `barn` makes equal acute angles with co-ordinate isA. `3(hati+hatj+hatk)`B. `hati+hatj+hatk`C. `sqrt(3)(hati+hatj+hatk)`D. `3sqrt(3)(hati+hatj+hatk)` |
| Answer» Correct Answer - A | |
| 76. |
If the angle between the line `x=(y-1)/(2)=(z-3)(lambda)` and the plane `x+2y+3z=4 is cos^(-1)(sqrt((5)/(14)))`, then `lambda` equalsA. `(2)/(3)`B. `(3)/(2)`C. `(-2)/(3)`D. `(-3)/(2)` |
| Answer» Correct Answer - A | |
| 77. |
Find the angle between the line `(x-1)/(3)=(y+1)/(2)=(z+2)/(4)` and the plane `2x + y - 3z + 4 = 0` .A. `"sin"^(-1)((-8)/(sqrt(406)))`B. `"sin"^(-1)((-4)/(sqrt(406)))`C. `"sin"^(-1)((-16)/(sqrt(406)))`D. `"sin"^(-1)((-2)/(sqrt(406)))` |
| Answer» Correct Answer - B | |
| 78. |
If the foot of the perpendicular drawn from the point (0,0,0) to the plane is (4,-2,-5) then the equation of the plane is . . .A. `4x - 2y -5z =16`B. `4x -2y -5z =4`C. `4x -2y -5z =25`D. `4x -2y -5z =45` |
| Answer» Correct Answer - D | |
| 79. |
If the foot of the perpendicular drawn from the point (0,0,0) to the plane is (4,-2,-5) then the equation of the plane is . . .A. `barr.(hati+2hatj+3hatk)=1`B. `barr.(hati+2hatj+3hatk)=14`C. `barr.(hati+2hatj+3hatk)=9`D. `barr.(hati+2hatj+3hatk)=4` |
| Answer» Correct Answer - B | |
| 80. |
If `(-3,5,-8)` is the foot of the perpendicular drawn from origin to a plane , then the equation of plane isA. `3x+y-5z-11=0`B. `3x-5y+8z+98=0`C. `x-5y+8z-15=0`D. `2x+4y-3z+29=0` |
| Answer» Correct Answer - B | |
| 81. |
Statement -I: A plane passes through the point `A(2,1,-3)`. If distance of this plane from origin is maximum , then its equation is `2x+y-3z=14` Statement -II: If the plane passing through the point `A( veca)` is at maximum distance from origin then normal to plane a vector `vec a`A. Statement - I is True, Statement - II is True , Statement - II is a correct explanation for Statement - OB. 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 is False, Statement - II is True. |
| Answer» Correct Answer - a | |
| 82. |
Find the coordinates of the foot of the perpendicular from the point(1, 1, 2) to the plane `2x-2y+4+5=0.`Also the find the length of the perpendicular.A. `((10)/(12),(25)/(12),(2)/(12))`B. `(-(1)/(12),(25)/(12),-(2)/(12))`C. `((1)/(12),(25)/(12),-(2)/(12))`D. none of these |
| Answer» Correct Answer - B | |
| 83. |
If A and B are foot of perpendicular drawn from point Q(a,b,c) to the planes yz and zx, then equation of plane through the point A,B, and O isA. `(x)/(a)+(y)/(b)+(z)/(c)=0`B. `(x)/(a)-(y)/(b)+(z)/(c)=0`C. `(x)/(a)-(y)/(b)-(z)/(c)=0`D. `(x)/(a)+(y)/(b)+(z)/(c)=0` |
| Answer» Correct Answer - A | |
| 84. |
The foot of the perpendicular drow from origin to the plane `x+y+3z-4=0` isA. `((1)/(11),(1)/(11),(3)/(11))`B. `((4)/(11),(4)/(11),(12)/(11))`C. `((1)/sqrt(11),(1)/sqrt(11),(3)/sqrt(11))`D. `((4)/sqrt(11),(4)/sqrt(11),(12)/sqrt(11))` |
| Answer» Correct Answer - B | |
| 85. |
Find the length and thefoot of the perpendicular from the point `(7,14 ,5)`to the plane `2x+4y-z=2.`A. `sqrt(21)`B. `4sqrt(21)`C. `2sqrt(21)`D. `3sqrt(21)` |
| Answer» Correct Answer - D | |
| 86. |
The foot of prependicular from P onto the plane p is __A. `((-1)/(3),(1)/(3),(-1)/(3))`B. `((-2)/(3),(5)/(3),(-8)/(3))`C. `((-2)/(3),(-5)/(3),(8)/(3))`D. `((1)/(3),(5)/(3),(8)/(3))` |
| Answer» Correct Answer - A | |
| 87. |
The foot of the prependicular from the origin to the line joining `A(-9, 4, 5) and B( 11, 0, -1)` lies on the plane___A. `2x+y+z=6`B. `x-y+z=1`C. `x+y+z=1`D. `x-y-z=1` |
| Answer» Correct Answer - A::B | |
| 88. |
The coordinates of the foot of prependicular from `(7,14,5)` to the plane `2x+4y-z=2` is __A. `(-1,-2,-8)`B. `(1,2,8)`C. `(1,-2,8)`D. `(1,2,-8)` |
| Answer» Correct Answer - B | |
| 89. |
The value of `k`such that `(x-4)/1=(y-2)/1=(z-k)/2`lies in the plane `2x-4y=z=7`isa. 7 b. -7 c. no real value d. 4A. 7B. `-7`C. 3D. 4 |
| Answer» Correct Answer - B | |
| 90. |
If the image of the point `P(1,-2,3)`in the plane, `2x+3y-4z+22=0`measured parallel to the line, `x/1-y/4-z/5`is `Q`, then `P Q`is equal to :`sqrt(42)`(2) `6sqrt(5)`(3) `3sqrt(5)`(4) `3sqrt(42)`A. `6sqrt(5)`B. `3sqrt(5)`C. `2sqrt(42)`D. `sqrt(5)` |
| Answer» Correct Answer - C | |
| 91. |
The equation of plane passing through the point (1 ,2 ,3) and parallel to the plane `2x+3y-4z=0` isA. `2x+3y+4z-4=0`B. `2x+3y+4z+4=0`C. `2x-3y+4z+4=0`D. `2x+3y-4z+4=0` |
| Answer» Correct Answer - D | |
| 92. |
The length of the perpendicular from origin to the plane `x-3y+4z=6` isA. `(3)/sqrt(26)`B. `(6)/sqrt(26)`C. `(3)/sqrt(13)`D. `(6)/sqrt(13)` |
| Answer» Correct Answer - B | |
| 93. |
The value of m for which straight line `3x-2y+z+3=0=4x-3y+4z+1` is parallel to the plane `2x-y+mz-2=0` is ___A. `-2`B. 8C. -18D. 11 |
| Answer» Correct Answer - A | |