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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 the equation `ax^2+by^2+cx+cy=0` represents a pair of straight lines , thenA. `a+b=0`B. `b+c=0`C. `c+a=0`D. `a+b=c` |
| Answer» Correct Answer - A | |
| 52. |
The square of the distance between the origin and the point of intersection of the lines given by `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0`, isA. `(c(a+b)+f^(2)+g^(2))/(ab-h^(2))`B. `(c(a+b)-f^(2)-g^(2))/(h^(2)-ab)`C. `(c(a+b)-f^(2)-g^(2))/(ab-h^(2))`D. none of these |
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Answer» Correct Answer - C Let `f(x,y)=ax^(2)+2hxy+by^(2)+2gx+2fy+c.` The point of intersection of the lines given by `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` is obtained by solving `(delf)/(delx)=0` and `(delf)/(dely)=0` i.e. `ax+hy+g=0 and hx+by+f=0` The coordinates of the point of intersection are `P((hf-bg)/(ab-h^(2)),(hg-af)/(ab-h^(2)))` `therefore" Distance between the origin and the point P is given by "` `OP=sqrt(((hf-bg)^(2)+(hg-af)^(2))/((ab-h^(2))^(2)))` `=sqrt((f^(2)(h^(2)+a^(2))+g^(2)(h^(2)+b^(2))-2fgh(a+b))/((ab-h^(2))_(2)))` `=sqrt((f^(2)(h^(2)+a)+g^(2)(h^(2)+b^(2))-(a+b)(af^(2)+bg^(2)+ch^(2)-abc))/((ab-h^(2))^(2)))` `" "[because abc+2fgh-af^(2)-hg^(2)-ch^(2)=0]` `=sqrt((ac(ab-h^(2))+bc(ab-h^(2))-f^(2)(ab-h^(2))-g^(2)(ab-h^(2)))/((ab-h^(2))^(2)))` `=sqrt((c(a+b)-f^(2)-g^(2))/((ab-h^(2))))` Hence, `OP^(2)=(c(a+b)-f^(2)-g^(2))/((ab-h^(2)))` |
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| 53. |
The combined equation of the pair of lines through the origin and perpendicular to the pair of lines given by `ax^(2)+2hxy+by^(2)=0`, isA. `ax^(2)-2hxy+by^(2)=0`B. `bx^(2)+2hxy+ay^(2)=0`C. `bx^(2)-2hxy+ay^(2)=0`D. `bx^(2)+2hxy-ay^(2)=0` |
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Answer» Correct Answer - C Let `y=m_(1)x and y=m_(2)x` be the lines represented by `ax^(2)+2hxy+by^(2)=0`. Then, `m_(1)+m_(2)=-(2h)/(b) and m_(1)m_(2)=(a)/(b)" …(i)"` The equation of the lines passing through the origin and perpendicular to `y=m_(1)x and y=m_(2)x` respectively are `m_(1)y+x=0 and m_(2)y+x=0` The combined equation of these lines is `(m_(1)y+x)(x_(2)y+x)=0` `rArr" "m_(1)m_(2)y^(2)+xy(m_(1)+m_(2))+x^(2)=0` `rArr" "(a)/(b)y^(2)-(2h)/(b)xy+x^(2)=0` `rArr" "ay^(2)-2hxy+bx^(2)=0` NOTE- The equation of the pair of lines through the origin and perpendicular to the pair of lines given by `ax^(2)+2hxy+by^(2)=0` can be obtained by interchanging the coefficients of `x^(2)` and `y^(2)` and changing the sign of the term containing xy. |
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| 54. |
The equation `x^(3)+ax^(2)y+bxy^(2)+y^(3)=0` represents three straight lines, two of which are perpendicular, then the equation of the third line, isA. `y=ax`B. `y=bx`C. `y=x`D. `y=-x` |
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Answer» Correct Answer - C Let `y=m_(1) x, y=m_(2)x and y=m_(3)x` be the lines represented by the given equation. Then, `x^(3)+ax^(2)y+bxy^(2)+y^(3)=(y-x_(1)x)(y-m_(2)x)(y-m_(3)x)` `rArr" "m_(1)+m_(2)+m_(3)=-a` `m_(1)m_(2)+m_(2)m_(3)+m_(3)m_(1)=b` and, `m_(1)m_(2)m_(3)=-1` Let `y=m_(1)x and y =m_(2)x` be perpendicular lines. Then, `m_(1)m_(2)=-1` `therefore" "m_(3)=1" "[because m_(1)m_(2)m_(3)=-1]` Thus, the third line is `y=m_(3)x` i.e., y = x. |
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| 55. |
The value of `lambda` for which the lines joining the point of intersection of curves `C_(1)` and `C_(2)` to the origin are equally inclined to the axis of x. `C_(1):lambdax^(2)+3y^(2)-2lambdaxy+9x=0, C_(2):3x^(2)-4y^(2)+8xy-3x=0`A. `lambda=(4)/(3)`B. `lambda=12`C. `lambda=1`D. none of these |
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Answer» Correct Answer - B The combined equation of the striaght lines joining the origin to the points of intersecton of `C_(1)` and `C_(2)` is a homogeneous equation and is given by `lambdax^(2)+3y^(3)-2lambdaxy+3(3x^(2)-4y^(2)+8xy)=0` `or, (lambda+9)x^(2)+2xy(12-lambda)-9y^(2)=0`. Lines given by this equation are equally inclined with X-axis. `therefore" Sum of their slopes = 0 "` `rArr" "(-2(12-lambda))/(-9)=0" "[becausem_(1)+m_(2)=-(2h)/(b)]` `rArr" "lambda=12` |
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| 56. |
If the lines represented by the equation `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` are equidistant from the origin, thenA. `f^(4)-g^(4)=c(bf^(2)-ag^(2))`B. `f^(4)-g^(4)=c(af^(2)-bg^(2))`C. `f^(4)-g^(4)=c(ag^(2)-bf^(2))`D. none of these |
| Answer» Correct Answer - A | |
| 57. |
The combined equation of the pair of lines through the point (1, 0) and perpendicular to the lines represented by `2x^(2)-xy-y^(2)=0`, isA. `2x^(2)-xy-y^(2)-x+y-1=0`B. `2y^(2)+xy-x^(2)+2x-y-1=0`C. `2y^(2)+xy-x^(2)-x-xy+2=0`D. none of these |
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Answer» Correct Answer - B The combined equation of the pair of lines through the origin and perpendicular to the lines given by `2x^(2)-xy-y^(2)=0 ` is `2y^(2)+xy-x^(2)=0`. Shifting the origin at (1, 0), the equations of the required lines are `2y^(2)+(x-1)y-(x-1)^(2)=0` or, `2y^(2)+xy-x^(2)+2x-y-1=0` |
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| 58. |
If the lines given by `ax^(2)+2hxy+by^(2)=0` are equally inclined to the lines given by `ax^(2)+2hxy+by^(2)+lambda(x^(2)+y^(2))=0`, thenA. `lambda` is any real numberB. `lambda=2`C. `lambda=1`D. none of these |
| Answer» Correct Answer - A | |
| 59. |
If the slope of one line is double the slope of another line and thecombined equation of the pair of lines is `((x^2)/a)+((2x y)/h)+((y^2)/b)=0`, then find the ratio `a b: h^2dot` |
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Answer» Correct Answer - `9 : 8` If m and 2m are the slopes , then `m+2m=-(2//h)/(1//h)=-(2b)/(h)` and `mxx2m=(1//a)/(1//b)=(b)/(a)` Eliminating m, we get `2(-(2b)/(3h))^(2)=(b)/(a)` or `(ab)/(h^(2))=(9)/(8)` |
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| 60. |
The combined equation of the pair of the straight lines through the point (1, 0) and parallel to thelines represented by `2x^(2)-xy-y^(2)=0` isA. `2x^(2)-xy-2y^(2)+4x-y=6`B. `2x^(2)-xy-y^(2)-4x+y+2=0`C. `2x^(2)-xy-y^(2)-4x-y+2=0`D. none of these |
| Answer» Correct Answer - C | |
| 61. |
Combined equation of pair of lines, both passing through (0,1), and each making an angle of `60^(@)` with X-axis isA. `x^(2)-3(y-1)^(2)=0`B. `3x^(2)-y^(2)=0`C. `(y-1)^(2)-3x^(2)=0`D. `x^(2)+3y^(2)=0` |
| Answer» Correct Answer - C | |
| 62. |
If the coordinate axes are the bisectors of the angles between the pair of lines `ax^(2)+2hxy+by^(2)=0`, thenA. `a+b=0`B. `h=0`C. `h ne 0, a+b=0`D. `a+b ne 0` |
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Answer» Correct Answer - B The combined equation of the angle bisectors of lines given by `ax^(2)+2hxy+by^(2)=0`, is `(x^(2)-y^(2))/(a-b)=(xy)/(h)` `rArr" "(a-b)xy=(x^(2)-y^(2))h" …(i)"` It is given that the coordinate axes are the bisectors of the angles between the lines given by `ax^(2)+2hxy+by^(2)=0`. So, their combined equation is `xy=0" ...(ii)"` From (i) and (ii), we get `h=0, a-b ne0` |
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| 63. |
Combined equation of pair of lines, through (1,2) and parallel to co-ordinate axes isA. `xy-2x-y+2=0`B. `xy+2x-y+2=0`C. `xy+2x+y+2=0`D. `xy+2x+y-2=0` |
| Answer» Correct Answer - A | |
| 64. |
If two lines `ax^(2)+2hxy+by^(2)=0` are equally inclined with co-ordinate axes, thenA. `h=0` and `ablt0`B. `a=b`C. `a=+-b`D. `a^(2)+b^(2)=0` |
| Answer» Correct Answer - C | |
| 65. |
Combined equation of pair of lines, both passing through (1,0), and each makingk an angle of `30^(@)` with X-axis, isA. `(x-1)^(2)-3y^(2)=0`B. `x^(2)-3y^(2)=0`C. `x^(2)-3(y-1)^(2)=0`D. `3x(x-1)^(2)-y^(2)=0` |
| Answer» Correct Answer - A | |
| 66. |
If two lines represented by `x^2(tan^2theta+cos^2theta)-2xytantheta+y^2sin^2theta=0` make angles `alpha, beta` with x-axis thenA. 4B. 3C. 2D. none of these |
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Answer» Correct Answer - C Let `m_(1)` and `m_(2)` be the slopes of the lines given by `x^(2)(tan^(2)theta+cos^(2)theta)-2xy tan theta +y^(2)sin^(2)theta=0`. Then, `m_(1)+m_(2)=(2tan theta)/(sin^(2)theta)=2sec theta" cosec "theta` and `m_(1)m_(2)=(tan^(2)theta+cos^(2)theta)/(sin^(2)theta)=sec^(2)theta+cot^(2)theta` `therefore" "m_(1)-m_(2)=sqrt((m_(1)+m_(2))^(2)-4m_(1)m_(2))` `rArr" "m_(1)-m_(2)=sqrt(4sec^(2)theta" cosec"^(2)theta-4(sec^(2)theta+cot^(2)theta))` `rArr" "m_(1)-m_(2)=sqrt(4sec^(2)theta(1+cot^(2)theta)-4(sec^(2)theta+cot^(2)theta))` `rArr" "m_(1)-m_(2)=2sqrt(sec^(2)thetacot^(2)theta-cot^(2)theta)` `rArr" "m_(1)-m_(2)=2sqrt(cot^(2)theta(sec^(2)theta-1))=2` |
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| 67. |
Joint equation of two lines through (-2,3) parallel to bisectors of angles between co-ordinate axes isA. `x^(2)+y^(2)+4x+6y-5=0`B. `x^(2)-y^(2)+4x+6y-5=0`C. `x^(2)-y^(2)-4x-6y+5=0`D. `x^(2)-y^(2)-4x-6y-5=0` |
| Answer» Correct Answer - B | |
| 68. |
If the equation `2x^(2)+lambdaxy+2y^(2)=0` represents a pair of real and distinct lines, thenA. `lambda in (-4, 4)`B. `lambda in R`C. `lambda in (-oo,-4)uu(4,oo)`D. `lambda = 4, -4` |
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Answer» Correct Answer - C The equation `2x^(2)+lambdaxy+2y^(2)=0` will represent a pair of real and distinct lines, if `((lambda)/(2))^(2)-2xx2gt0" "["Using : h"^(2) gt ab]` `rArr" "lambda^(2)-16gt0 rArr lambda in (-oo,-4)uu(4,oo)` |
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| 69. |
If the slope of one of the lines represented by `ax^(2)+2hxy+by^(2)=0` is the square of the other , then `(a+b)/(h)+(8h^(2))/(ab)=`A. 4B. -6C. 6D. -4 |
| Answer» Correct Answer - C | |
| 70. |
Joint equation of lines, through the origin, making an equalateral triangle with line `y=2` isA. `3x^(2)-y^(2)=0`B. `x^(2)-3y^(2)=0`C. `sqrt(3)x^(2)-y^(2)=0`D. `x^(2)+3y^(2)=1` |
| Answer» Correct Answer - A | |
| 71. |
If the pair of lines represented by `ax^(2)+2hxy+by^(2)=0, b ne 0`, are such that the sum of the slopes of the lines is three times the product of their slopes, thenA. `3b+2h=0`B. `3a+2h=0`C. `2a+3h=0`D. none of these |
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Answer» Correct Answer - B Let `y=m_(1)x and y=m_(2)x` be the lines represented by `ax^(2)+2hxy+by^(2)=0`. Then, `m_(1)+m_(2)=-(2h)/(b) and m_(1)m_(2)=(a)/(b)` It is given that `m_(1)+m_(2)=3m_(1)m_(2)rArr-(2h)/(b)=(3a)/(b) rArr 2h+3a=0` |
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| 72. |
If `h^(2)=ab` then slopes of lines `ax^(2)+2hxy+by^(2)=0` are in the ratioA. `1:2`B. `2:1`C. `2:3`D. `1:1` |
| Answer» Correct Answer - D | |
| 73. |
If the slopes of the lines given by `ax^(2)+2hxy+by^(2)=0` are in the ratio `3:1`, then `h^(2)=`A. `(ab)/(3)`B. `(4ab)/(3)`C. `(4a)/(3b)`D. none of these |
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Answer» Correct Answer - B Let `y=m_(1)x and y=m_(2)x` be the lines represented by the given equation. Then, `m_(1)+m_(2)=-(2h)/(b)and m_(1)m_(2)=(a)/(b)` We have, `m_(1):m_(2)=3:1rArrm_(1)=3m_(2)` `therefore" "m_(1)+m_(2)=-(2h)/(b)and m_(1)m_(2)=(a)/(b)` `rArr" "4m_(2)=-(2h)/(b) and 3m_(2)^(2)=(a)/(b)` `rArr" "m_(2)=-(h)/(2b)and 3m_(2)^(2)=(a)/(b)` `rArr" "3(-(h)/(2b))^(2)=(a)/(b)rArr h^(2)=(4ab)/(3)` |
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| 74. |
If the equation `2x^2 + 2hxy + 6y^2-4x + 5y-6 = 0` represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal toA. 2B. 4C. `sqrt7`D. 0 |
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Answer» Correct Answer - B The x-coordinates of the points of intersection of the pair of lines by `2x^(2)+2hxy+6y^(2)-4x+5y-6=0` and x-axis are roots of the equation `2x^(2)-4x-6=0` or, `x^(2)-2x-3=0` `rArr" "(x-3)(x+1)=0 rArr x=-1, 3` Hence, required length `=|x_(1)-x_(2)|=4.` |
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| 75. |
If the equation `2x^(2)+2hxy +6y^(2) - 4x +5y -6 = 0` represents a pair of straight lines, then the length of intercept on the x-axis cut by the lines is equal toA. 2B. 4C. `sqrt(7)`D. 0 |
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Answer» Correct Answer - B Put `y = 0 rArr 2x^(2) -4x -6 = 0 rArr x^(2) -2x -3 =0` `rArr (x-3) (x+1) =0` `:.` Length of intercept `= 13 -(-1)|=4` units |
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| 76. |
Joint equation of two lines through the origin each making angle of `30^(@)` with line `x+y=0`, isA. `x^(2)-4xy+y^(2)=0`B. `x^(2)+4xy+y^(2)=0`C. `x^(2)-4xy-y^(2)=0`D. `x^(2)+4xy-y^(2)=0` |
| Answer» Correct Answer - B | |
| 77. |
If slopes of lines `ax^(2)+2hxy+by^(2)=0` differ by k then `(h^(2)-ab):b^(2)=`A. `4k^(2)`B. `4:k^(2)`C. `k^(2):4`D. `k^(2)+4` |
| Answer» Correct Answer - C | |
| 78. |
The equation `3x^(2)+2hxy+3y^(2)=0` represents a pair of straight lines passing through the origin. The two lines areA. real and distinct if `h^(2) gt 3`B. real and distinct if `h^(2) gt 9`C. real and coincident if `h^(2)=3`D. real and coincident if `h^(2) gt3` |
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Answer» Correct Answer - B The equation `ax^(2)+2hxy+by^(2)=0` represents a pair of real and distinct lines if `h^(2)gtab`. The given equation will represent a pair of real and distinct lines if `h^(2) gt 9[ because a=3, b=3]` |
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| 79. |
If `ax^(2)+2hxy+by^(2)+2gx+2fy+c=0` represents parallel straight lines, thenA. `hf=bg`B. `h^(2)=bc`C. `a^(2)f=b^(2)g`D. none of these |
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Answer» Correct Answer - A The given equation represents a pair of parallel straight lines, if `h^(2)=ab and bg^(2)=af^(2)`. Now, `bg^(2)=af^(2)` `rArr" "abf^(2)=b^(2)g^(2)" [Multiplying both side by b]"` `rArr" "h^(2)f^(2)=b^(2)g^(2)" "[because h^(2)=ab]` `rArr" "hf=bg` |
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| 80. |
The image of the pair of lines respresented by `ax^2 + 2hxy + by^2 = 0` by the line mirror `y = 0` is:(A) `ax^2-2hxy+by^2=0`(b) `bx^2-2hxy+ay^2=0`(c) `bx^2+2hxy+ay^2=0`(d) `ax^2-2hxy-by^2=0`A. `ax^(2)-2hxy+by^(2)=0`B. `bx^(2)+2hxy+ay^(2)=0`C. `bx^(2)-2hxy+ay^(2)=0`D. none of these |
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Answer» Correct Answer - A Let `y=m_(1) x, y=m_(2)x` be the lines represented by `ax^(2)+2hxy+by^(2)=0`. Then, `m_(1)+m_(2)=-(2h)/(b) and m_(1)m_(2)=(a)/(b)` Clearly, if `y=m_(1)x` makes an angle `theta_(1)` with y = 0 (x-axis), then its image in line mirror y - 0 makes an angle `-0_(1)` with x-axis. So, its equation is `y=tan(-theta_(1))x or y=-(tan theta_(1))x or y=-x_(1)x`. Similarly, equation of the image of `y-m_(2) x` in `y-0` is `y=-m_(2)x` Therefore, the combined equation of the images is `(y+x_(1)x)(y+m_(2)x)=0` `rArr" "y^(2)+xy(m_(1)+m_(2))+m_(1)m_(2)x^(2)=0` `rArr" "y^(2)-(2h)/(b)xy+(a)/(b)x^(2)=0" [Using (i) ]"` `by^(2)-2hxy+ax^(2)=0` |
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| 81. |
The pairs of straight lines `ax^(2)-2hxy-ay^(2)=0` and `hx^(2)-2axy-gy^(2)=0` are such thatA. one pair bisects the angle between the other pairB. the lines of one pair are equally inclined to the lines of the other pairC. the lines of each pair are perpendicular to other pairD. all of these |
| Answer» Correct Answer - D | |
| 82. |
Slopes of lines `6x^(2)-xy-2y^(2)=0` differ byA. 2B. 7C. `(-2)/7`D. `7/2` |
| Answer» Correct Answer - D | |
| 83. |
If the pairs of straight lines `ax^(2)+2hxy-ay^(2)=0` and `bx^(2)+2gxy-by^(2)=0` be such that each bisects the angles between the other, thenA. `hg+ab=0`B. `ah+bg=0`C. `h^(2)-ab=0`D. `ag+bh=0` |
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Answer» Correct Answer - A Since each pair of lines bisects the angles between the other. So, the equation of the bisectors of the angles bectween the lines given by `ax^(2)+2hxy-ay^(2)=0` is `bx^(2)+2gxy-by^(2)=0` The equation of the bisectors of the angles between the lines given by `ax^(2)+2hxy-ay^(2)=0` is `(x^(2)-y^(2))/(a-(-a))=(xy)/(h)rArr hx^(2)-2axy-hy^(2)=0" (ii)"` Since (i) and (ii) represent the same pair of straight lines. `therefore" "(b)/(h)=(g)/(-a)=(-b)/(-h)rArr -ab=ghrArr ab+gh=0` |
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| 84. |
The equation of the straigh lines through the point `(x_(1),y_(1))` and parallel to the lines given by `ax^(2)+2xy+ay^(2)=0`, isA. `a(y-y_(1))^(2)+2h(x-x_(1))(y-y_(1))+b(x-x_(1))^(2)=0`B. `a(y-y_(1))^(2)-2h(x-x_(1))(y-y_(1))+b(x-x_(1))^(2)=0`C. `b(y-y_(1))^(2)+2h(x-x_(1))(y-y_(1))+a(x-x_(1))^(2)=0`D. none of these |
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Answer» Correct Answer - C Shifing the origin at `(x_(1),y_(1))` the equation of the requried lines are given by `a(x-x_(1))^(2)+2h(x-x_(1))(y-y_(1))+b(y-y_(1))^(2)=0` |
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| 85. |
If the equation `x^(2)-y^(2)-x-lamday-2=0` represents a pair of lines then `lamda=`A. 3,-3B. `-3,1`C. 3,1D. `-1,1` |
| Answer» Correct Answer - A | |
| 86. |
If pairs of lines `3x^(2)-2pxy-3y^(2)=0` and `5x^(2)-2qxy-5y^(2)=0` are such that each pair bisects then angle between the other pair then `pq=`A. -1B. -3C. -5D. -15 |
| Answer» Correct Answer - D | |
| 87. |
If one of the two lines `6x^(2)+xy-y^(2)=0` coincides with one of the two lines `3x^(2)-axy+y^(2)=0` tenA. `a^(2)-3a+28=0`B. `2a^(2)-a-28=0`C. `2a^(2)-15a+28=0`D. None of these |
| Answer» Correct Answer - B | |
| 88. |
The lines `y = mx` bisects the angle between the lines `ax^(2) +2hxy +by^(2) = 0` ifA. `h(m^(2)-1)+m(b-a)=0`B. `h(m^(2)-1)+m(a-b)=0`C. `h(m^(2)+1)+m(a-b)=0`D. None of these |
| Answer» Correct Answer - B | |
| 89. |
Orthocentre of the triangle formed by the pair of lines `xy=0` and the lines `2x+3y+4=0` isA. `(2,3)`B. `(3,2)`C. `(0,0)`D. `(4,-4)` |
| Answer» Correct Answer - C | |
| 90. |
The centroid of the triangle whose three sides are given by the combined equation `(x^(2)+7xt+2y^(2))(y-1)=0`, isA. `(2/3,0)`B. `(7/3,2/3)`C. `(-7/3,2/3)`D. None of these |
| Answer» Correct Answer - C | |
| 91. |
If the pair of lines `ax^2-2xy+by^2=0` and bx^2-2xy+ay^2=0` be such that each pair bisects the angle between the other pair , then |a-b| equals to |
| Answer» Correct Answer - C | |
| 92. |
The combined equation of the lines `L_(1)` and `L_(2)` is `2x^(2)+6xy+y^(2)=0` and that lines `L_(3)` and `L_(4)` is `4x^(2)+18xy+y^(2)=0`. If the angle between `L_(1)` and `L_(4)` be `alpha`, then the angle between `L_(2)` and `L_(3)` will beA. `(pi)/2-alpha`B. `(pi)/4+alpha`C. `2alpha`D. `alpha` |
| Answer» Correct Answer - D | |
| 93. |
If sum of slopes of the lines `x^(2)-2xy tan A-y^(2)=0` si 4, then: `/_a=`A. `0^(@)`B. `45^(@)`C. `60^(@)`D. `tan^(-1)(-2)` |
| Answer» Correct Answer - D | |
| 94. |
The pair equation of the lines passing through the origin and having slopes 3 and `-(1)/(3)`, isA. `3y^(2)+8xy-3x^(2)=0`B. `3x^(2)+8xy+3y^(2)=0`C. `3y^(2)-8xy-3x^(2)=0`D. `3x^(2)+8xy-3y^(2)=0` |
| Answer» Correct Answer - A | |
| 95. |
If `(a,a^(2))` falls inside the angle made by the lines `y=(x)/(2), x gt 0 and y=3x, x gt 0`, then a belongs to the intervalA. `(0,1/2)`B. `(3,oo)`C. `(1/2,3)`D. `(-3,-1/2)` |
| Answer» Correct Answer - C | |
| 96. |
Joint equation of pair of lines through `(3,-2)` and parallel to `x^2-4xy+3y^2=0` isA. `x^(2)-4y+3y^(2)+14x+24y+45=0`B. `x^(2)-4xy+3y^(2)-14x-24y+45=0`C. `x^(2)-4xy+3y^(2)-14x-24y+45=0`D. `x^(2)-4xy+3y^(2)-14x+24y+45=0` |
| Answer» Correct Answer - D | |
| 97. |
Find the angle between the lines represented by `x^2+2x ysectheta+y^2=0`A. `2 theta`B. `theta`C. `(theta)/2`D. `(theta)/4` |
| Answer» Correct Answer - B | |
| 98. |
If the two lines `2x^(2)-3xy+y^(2)=0` makes anlges `alpha` and `beta` with X-axis then `: csc^(2) alpha+csc^(2)beta=`A. 2B. `7//2`C. `15//4`D. `13//4` |
| Answer» Correct Answer - D | |
| 99. |
If the acute alngles betwene the pairs of lines `3x^(2)+7xy+4y^(2)=0` and `6x^(2)-5xy+y^(2)=0` are `theta_(1)` and `theta_(2)` thenA. `theta_(1)-theta_(2)`B. `theta_(1)=2theta_(2)`C. `theta_(2)-2theta_(1)`D. None of these |
| Answer» Correct Answer - A | |
| 100. |
If the angle between the two lines represented by `2x^(2)+5xy+3y^(2)+6x+7y+4=0` is `tan^(-1)(m)`, then m is equal toA. `1/5`B. `1`C. `7/5`D. `7` |
| Answer» Correct Answer - A | |