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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. |
The equation of the line which passes through (4,7) and divides the join of (1,7) and (6,-3) internally in the ratio 2:3, isA. y=4x-9B. x=4y-9C. 4x+y=9D. none of these |
| Answer» Correct Answer - A | |
| 52. |
In relation to the line : `(x)/(3)-(y)/(4)=1`, the point (-2,-4) lies onA. the lineB. the origin side of the lineC. the non- origin side of the lineD. none of these |
| Answer» Correct Answer - B | |
| 53. |
If A is (1,-2), B (3,k), C(-3,1) and D(k,4) where lines AB`bot` CD then :k=A. `-5/12`B. `5//12`C. `-12//5`D. `12//5` |
| Answer» Correct Answer - C | |
| 54. |
The slope of the line which bisects the angles in the first and third quadrants isA. -1B. 0C. 1D. none of these |
| Answer» Correct Answer - C | |
| 55. |
The points (1,5) , (2,4) and (3,3) areA. vertices of an equilateral triangleB. vertices of an isosceles triangleC. vertices of a right-angle triangleD. collinear |
| Answer» Correct Answer - D | |
| 56. |
The vertices of a triangle are `(2, 4), B (2,6),C (2+ sqrt3,5).` The triangle is :A. isosceles and right- angledB. always isoscelesC. right- angledD. equilateral |
| Answer» Correct Answer - D | |
| 57. |
If A `-=` (0,0) and B `-=` (4,-3) then the locus of the moving point P such that 2 PA = 3PB isA. `5x^(2)+5y^(2)`+72x+54y+225=0B. `5x^(2)+5y^(2)`-72x-54y+225=0C. `5x^(2)+5y^(2)`-72x+54y+225=0D. none of these |
| Answer» Correct Answer - C | |
| 58. |
The equation of the locus of the point whose distance from the x-axis is twice that of from the y-axis is :A. y=xB. y=2xC. x=yD. x=2y |
| Answer» Correct Answer - D | |
| 59. |
If `P= (1,0);Q=(-1.0) & R= (2,0)` are three given points, then the locus of the points S satisfying the relation, `SQ^2 + SR^2 =2SP^2` is -A. a line || to X-axisB. a line || to Y-axisC. circle with centre at originD. none of these |
| Answer» Correct Answer - B | |
| 60. |
If the coordinates of the points A,B,C be `(-1,5),(0,0)` and `(2,2)` respectively, and D be the middle point of BC, then the equation of the perpendicular drawn from B to the line AD isA. `x +2y = 0`B. `2x +y = 0`C. `x - 2y = 0`D. `2x - y = 0` |
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Answer» Correct Answer - C Here `D(1,1)` therefore equation of line AD is given by `2x + y -3 = 0`. Thus the line perpendicular to AD is `x - 2y +k = 0` and its passes through B, so `k = 0`. Hence required equation is `x - 2y = 0`. |
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| 61. |
Two lines are drawn through (3,4), each of which makes angle of `45^(@)` with the line `x-y = 2`. Then area of the triangle formed by these lines isA. 9B. `9//2`C. 2D. `2//9` |
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Answer» Correct Answer - B The equation of lines are `y - y_(1) = (m +- tan alpha)/(1 +- m tan alpha) (x-x_(1))` `rArr y - 4 =(1+- tan 45^(@))/(1+-tan 45^(@)) (x-x_(1))` `rArr y - 4 = (1+-1)/(1+-1) (x-3)` `rArr y = 4` or `x = 3` Hence, the lines which make the triangle are `x - y = 2, x = 3` and `y = 4`. THe intersection points of these lines are `(6,4),(3,1)` and (3,4). `:. Delta =(1)/(2) |6(-3)+3(0)+3(3)| =(9)/(2)` |
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| 62. |
The line `y = 2x +4` is shifted 2 units along `+y` axis, keeping parallel to itself and then 1 unit along `+x` axis direction in the same manner, then equation of the line in its new position is,A. `y = 2x +6`B. `y = 2x +5`C. `y = 2x +4`D. none of these |
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Answer» Correct Answer - C Any point `(x_(1),y_(1))` after shifting 2 units along `+y` axis becomes `(x_(1),y_(1)+2)` and after shifting along `+x` axis it will be `(x_(1)+1, y_(1)+2)`, which satisfy the same equation. |
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| 63. |
If the transversal `y = m_(r)x: r = 1,2,3` cut off equal intercepts on the transversal `x +y = 1` then `1 +m_(1),1 +m_(2),1+m_(3)` are inA. A.P.B. G.P.C. H.P.D. None of these |
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Answer» Correct Answer - C Solving `y = m_(r)x` and `x+y = 1`, we get `x = (1)/(1+m_(r))` and `y = (m_(r))/(1+m_(r))`. Thus the points of intersection of the three lines on the transversal are `P ((1)/(1+m_(1)),(m_(1))/(1+m_(1))), Q ((1)/(1+m_(2)),(m_(2))/(1+m_(2)))` and `R((1)/(1+m_(3)),(m_(3))/(1+m_(3)))` According to question `PQ = QR` `((1)/(1+m_(1))-(1)/(1+m_(2)))^(2)+((m_(1))/(1+m_(1))-(m_(2))/(1+m_(2)))^(2)` `= ((1)/(1+m_(2))-(1)/(1+m_(3)))^(2) +((m_(2))/(1+m_(2))-(m_(3))/(1+m_(3)))^(2)` `rArr (m_(2)-m_(1))/(1+m_(1)) = (m_(3)-m_(2))/(1+m_(3))` `rArr (1+m_(2))/(1+m_(1)) - 1 = 1 -(1+m_(2))/(1+m_(3))` `rArr (1+m_(2))/(1+m_(1)) +(1+m_(2))/(1+m_(3)) =2` `rArr 1+m_(2) =(2(1+m_(1))(1+m_(3)))/((1+m_(1))+(1+m_(3)))` `rArr 1+m_(1), 1 +m_(2), 1 +m_(3)` are in H.P. |
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| 64. |
Let `P S`be the median of thetriangle with vertices `P(2,2),Q(6,-1)a n dR(7,3)`Then equation of theline passing through `(1,-1)`and parallel to `P S`is`2x-9y-7=0``2x-9y-11=0``2x+9y-11=0``2x+9y+7=0`A. 2x-9y-7=0B. 2x-9y-11=0C. 2x+9y-11=0D. 2x+9y-7=0 |
| Answer» Correct Answer - D | |
| 65. |
The triangle with vertices (0,0), (2,0) and (0,3) isA. acute-angledB. isoscelesC. right-angledD. equilateral |
| Answer» Correct Answer - C | |
| 66. |
A triangle with vertices `(4, 0), (-1,-1), (3,5)`, isA. isosceles and right- angledB. isosceles but not right -angledC. right-angled but not isoscelesD. neither isosceles nor right -angled |
| Answer» Correct Answer - A | |
| 67. |
If `P_(1) "and" P_(2)` are the lenghts of perpendiculars from origin to the lines x. sec a+y . Csc a=2a and x.cos `alpha`+y. sin `alpha` =a cos 2 `alpha`,A. `4 sin^(2) 4 alpha`B. 4 `cos^(2) 4 alpha`C. 4 `csc^(2) 4 alpha`D. 4 `sec^(2) 4 alpha` |
| Answer» Correct Answer - C | |
| 68. |
If `A(-1, 3), B(1, -1)`and `C(5, 1)`are thevertices of a triangle `A B C`, find thelength of the median through `A`.A. 5B. 4C. 1D. 3 |
| Answer» Correct Answer - A | |
| 69. |
The points (3,3), (h,0) and (0,k) are collinear ifA. `(1)/(h)+(1)/(k)+=(1)/(3)`B. `(1)/(h)-(1)/(k)=(1)/(3)`C. `(1)/(k)-(1)/(h)=(1)/(3)`D. `(1)/(h)=(1)/(k)` |
| Answer» Correct Answer - A | |
| 70. |
If (-4,5) is a vertex of a square and one of its diagonal is 7x-y+8-0.Find the equation of other diagonalA. 7x-y+23=0B. x+7y=31C. x-7y=31D. none of these |
| Answer» Correct Answer - B | |
| 71. |
The length of perpendicular from the point ( ` a cos prop, a sin prop`) upon the striaght line y = x ` tan prop +c ` (where c gt 0) isA. cB. c. `sin^(2) alpha`C. c.cos `alpha`D. c.`sec^(2) alpha` |
| Answer» Correct Answer - C | |
| 72. |
A rectangle has two opposite vertices at the points (1,2) and (5,5). If the other vertices lie on the line x=3, then their coordinates areA. (3,-1), (3,-6)B. (3,1), (3,5)C. (3,2), (3,6)D. (3,1) ,(3,6) |
| Answer» Correct Answer - D | |
| 73. |
The equation to the sides of a triangle are `x-3y=0,4x+3y=5 and 3x+y=0` . The line `3x-4y=0` does not pass through the -A. incentre of the triangleB. centroid of the triangleC. circumcentre of the triangleD. orthocentre of the triangle |
| Answer» Correct Answer - A,B,C | |
| 74. |
State which of the following is the perpendicular distance of the line `3x-4y-5=0` from the origin ?A. 1 unitB. `(1)/(5)` unitC. 2 unitD. `(2)/(5)` unit |
| Answer» Correct Answer - A | |
| 75. |
A variable line L is drawn through O(0, 0) to meet lines L1: 2x + 3y = 5 and L2: 2x + 3y = 10 at point P and Q, respectively. A point R is taken on L such that 2OP.OQ = OR.OP + OR.OQ. Locus of R isA. `9x +6y = 20`B. `6x - 9y = 20`C. `6x +9y = 20`D. none of these |
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Answer» Correct Answer - C Let the line L be `(x)/(cos theta) =(y)/(sin theta)` Then `OP = (5)/(2cos theta +3 sin theta)` and `OQ = (10)/(2cos theta +3 sin theta)` and let `OR = r` Then according to condition `20 = 6r cos theta +9r sin theta` `:.` locus is `6x +9y = 20` |
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| 76. |
If the line passing through (2,3) and (5,k) has slope (5/3), then : k=A. -1B. 0C. 8D. 2 |
| Answer» Correct Answer - C | |
| 77. |
Let A,B,C be angles of triangles with vertex `A -= (4,-1)` and internal angular bisectors of angles B and C be `x - 1 = 0` and `x - y - 1 = 0` respectively. If A,B,C are angles of triangle at vertices A,B,C respectively then `cot ((B)/(2))cot .((C)/(2)) =`A. 2B. 3C. 4D. 6 |
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Answer» Correct Answer - D Angle between `x -1 =0` and BC is `(B)/(2) rArr tan.(B)/(2) =(1)/(2)` Angle between `x -y -1 =0` and BC is `(C )/(2) rArr tan.(C )/(2) =(1)/(3)` `rArr cot.(B)/(2) cot.(C )/(2) =6` |
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| 78. |
If `P(1,2)Q(4,6),R(5,7),`and `S(a , b)`are the vertices of a parallelogram `P Q R S ,`then`a=2,b=4`(b) `a=3,b=4``a=2,b=3`(d) `a=1orb=-1`A. a=2, b=4B. a=3, b=4C. a=2,b=3D. a=3, b=5 |
| Answer» Correct Answer - C | |
| 79. |
Which of the following is the perpendicular distance of the straight line `12x-5y-3=0` from the point (2,-1) ?A. `(3)/(13)` unitB. 3 unitC. 2 unitD. `(29)/(13)` unit |
| Answer» Correct Answer - C | |
| 80. |
State which of the following is the distance between the parallel line `3x-4y+1=0and6x-8y+9=0` ?A. `(7)/(10)` unitB. `(8)/(5)` unitC. `(4)/(5)` unitD. `(7)/(5)` unit |
| Answer» Correct Answer - A | |
| 81. |
The equation of the straight line px+qy +r=0 is reducible to the form `(x)/(a)+(y)/(b) =1` when -A. `pne0,qne0,rne0`B. `pne0,qne0`C. `pne0,rne0`D. `rne0` |
| Answer» Correct Answer - A | |
| 82. |
The perpendicular distance of the straight line `6x-8y=25` from the point (-1,-4) is -A. `(1)/(2)` unitsB. `(1)/(4)` unitsC. 1 unitD. 2 units |
| Answer» Correct Answer - A | |
| 83. |
The distance of the mid point of the line joining the points `(a sin theta, 0)and (0, a cos theta)` from the origin isA. aB. `(a)/(2) (sin theta+cos theta)`C. a`(sin theta+cos theta)`D. `(a)/(2)` |
| Answer» Correct Answer - D | |
| 84. |
The distance of the mid point of the line joining the points `(a sin theta, 0)and (0, a cos theta)` from the origin isA. `(a)/(2)`B. `(a)/(2) (sin theta+cos theta)`C. a`(sin theta+cos theta)`D. a |
| Answer» Correct Answer - A | |
| 85. |
A line passes through (2,2) and is perpendicular to the line `3x+y=3`, isA. 43833B. 43864C. 1D. 43924 |
| Answer» Correct Answer - D | |
| 86. |
Diagonals of a parallelogram PQRS must be aA. rectangleB. squareC. cyclic quadrilateralD. rhombus |
| Answer» Correct Answer - D | |
| 87. |
A square of area 25 sq.units is formed by taking two sides as `3x + 4y = k_1 and 3x + 4y = k_2` then `|k_1-k_2|=`A. 5B. 1C. 25D. 20 |
| Answer» Correct Answer - C | |
| 88. |
The straight line `a_(1)x+b_(1)y+c_(1)=0 anda_(2)x+b_(2)y+c_(2)=0` are parallel to each other if -A. `(a_(1))/(a_(2))ne(b_(1))/(b_(2))`B. `(a_(1))/(b_(1))ne(b_(2))/(a_(2))`C. `(a_(1))/(a_(2))=(b_(1))/(b_(2))`D. `(a_(1))/(b_(1))=(b_(2))/(a_(2))` |
| Answer» Correct Answer - C | |
| 89. |
A point of the X-axis which is at a unit distance from the line 5x+12y=12 isA. (1/5,0)B. (5,0)C. (17,0)D. none of these |
| Answer» Correct Answer - B | |
| 90. |
The distance of the straight line a(x-a)+b(y-b)=0 from the origin is -A. `sqrt(a^(2)+b^(2))` unitB. a unitC. b unitD. none of these |
| Answer» Correct Answer - A | |
| 91. |
If the perpendicular distance of the straight line 3x-4y=0 from the point (a,0) is `(6)/(5)` unit then the value of a is-A. `+-1`B. `+-(1)/(2)`C. `+-2`D. `+-(1)/(3)` |
| Answer» Correct Answer - C | |
| 92. |
If the straight lines `2x-3y+5=0andpx+2y=6` be parallel to each other , state which of the following is the value of p ,A. `(4)/(3)`B. `(3)/(4)`C. `-(4)/(3)`D. `-(3)/(4)` |
| Answer» Correct Answer - C | |
| 93. |
If the perpendicular distance of the line (x/a)+(y/b)=1 from the origin is `p//sqrt(2)` show that `a^(2),p^(2),b^(2)` are in Harmonic Progression.A. A.P.B. G.P.C. H.P.D. none of these |
| Answer» Correct Answer - C | |
| 94. |
Find the orthocentre of the triangle whosevertices are `(0,0),(3,0),`and `(0,4)dot`A. `((3)/(4),2)`B. (0,0)C. `(1,(4)/(3))`D. `(2,(3)/(2))` |
| Answer» Correct Answer - B | |
| 95. |
If the length of the perpendicular to a line L from the origin is 8 and the perpendicular makes an angle of `60^(@)` with the X-axis then the equation of line L isA. x+`ysqrt(3)`=16B. `xsqrt(3)`+y=16C. x-`ysqrt(3)`+16=0D. none of these |
| Answer» Correct Answer - A | |
| 96. |
If the length of the perpendicular to a line L from the origin si `5sqrt(2)` and the perperdicular to a makes an angle of `135^(@)` with the X-axis then the equation of line L isA. x+y+10=0B. x-y-10=0C. y=x+10D. none of these |
| Answer» Correct Answer - C | |
| 97. |
92. Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x2-9y2 +30 = 0 (b) 4x2-9y2-30 = 0 c) 9x2-4)/2-30=0 (d) none of theseA. `4x^(2) - 9y^(2) +30 = 0`B. `4x^(2) - 9y^(2) - 30 = 0`C. `9x^(2) - 4y^(2) - 30 = 0`D. none of these |
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Answer» Correct Answer - C We have Area `(DeltaOPQ) = (1)/(2) |quad{:(0,0,1),(a,(2a)/(3),1),(b,(-2b)/(3),1):}|=5` (Given) `rArr (4ab)/(3) = +-10` So `4ab = +- 30` (i) Also `2h = a+b` (ii) and `2k = (2a-2b)/(3)`or `a - b =3k` (iii) As `4ab = (a+b)^(2) -(a-b)^(2)` `rArr +- 30 = 4h^(2) - 9k^(2)` [Using (i),(ii) and (iii)] So required locus can be `4x^(2) - 9y^(2) = +30`. |
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| 98. |
If the point (1,1) lies on the line passing through the points (a,0) and (0,b) then : `(1)/(a)+(1)/(b)`=A. -1B. 0C. 1D. `(1)/(ab)` |
| Answer» Correct Answer - C | |
| 99. |
Ifa,b,c are in A.P., a,x,b,are in G.P and b,y,c are also in G.P then the point (x,y) lies onA. a lineB. a circleC. an ellipseD. a hyperbola |
| Answer» Correct Answer - B | |
| 100. |
If a+b+c=0 then the line 3ax+by+2c=0 passes through the fixed pointA. `(2,(2)/(3))`B. `((2)/(3),2)`C. `(2,(2)/(3))`D. `((2)/(3),(2)/(3))` |
| Answer» Correct Answer - B | |