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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. |
The slope of the straight line joining the points `(sqrt(3),1)and(-3,-sqrt(3))` is -A. 1B. `sqrt(3)`C. `(1)/(sqrt(3))`D. `-(1)/(sqrt(3))` |
| Answer» Correct Answer - C | |
| 2. |
The straight line joining the points (3,-5 ) and (-3,-5) is parallel to the -A. y- axisB. x-axisC. line 3x+5y=0D. line 3x-5y=0 |
| Answer» Correct Answer - B | |
| 3. |
The inclination of the line joining the points `(3-sqrt(3))` and `(sqrt(3),-1)` is -A. `15^(@)`B. `30^(@)`C. `60^(@)`D. `120^(@)` |
| Answer» Correct Answer - A | |
| 4. |
The straight line joining the points (2,-4) and (2,6) makes an angle of `90^(@)` with the -A. y -axisB. x- axisC. line y=3xD. line x-3y=0 |
| Answer» Correct Answer - B | |
| 5. |
Find the angle between ` x+y=3` and the line joining points (1,1) and (-3,4)A. `tan^(-1)((3)/(7))`B. `pi-tan^(-1)((3)/(7))`C. `tan^(-1)((1)/(7))`D. `pi- tan^(-1)((1)/(7))` |
| Answer» Correct Answer - C | |
| 6. |
A line meets X-axis in A and Y-axis in B. If R (4,6) is point on the line such that AR:RB=3:2, then the equation of the line isA. y=x+10B. x+y+10=0C. x+y=10D. none of these |
| Answer» Correct Answer - C | |
| 7. |
The equation of the line having x- intercept =5/3, and perendicular to the join of (5,-2) and (-1,3) isA. 6x-5y=10B. 5x-6y=10C. 6x-5y+10=0D. none of these |
| Answer» Correct Answer - A | |
| 8. |
The value of k such that the lines `2x-3y+k=0,3x-4y-13=0` and `8x-11y-33=0` are concurrent isA. 7B. -7C. 5D. -5 |
| Answer» Correct Answer - B | |
| 9. |
A line passes through the point `(2,2)` and is perpendicular to the line `3x + y =3,` then its `y`-intercept isA. `(1)/(3)`B. `(2)/(3)`C. 1D. `(4)/(3)` |
| Answer» Correct Answer - D | |
| 10. |
The slope of the line 3x+2y=8 and its intercept on y- axis is -A. `(-(3)/(2))` and 4 unitsB. `((3)/(2))` and 8 unitsC. `((2)/(3))` and 4 unitsD. `(-(2)/(3))` and 8 units |
| Answer» Correct Answer - A | |
| 11. |
The equation of the line through `(4,1)`, whose x-intercept is double its `y-`intercepts on the axes isA. x+2y=6B. 2x+y=6C. x+2y+6=0D. none of these |
| Answer» Correct Answer - A | |
| 12. |
If the intercepts on the x- axis and y- axis of a line be (-4) and 6 respectively ,then the equation of the line will be-A. `3x-2y-12=0`B. `3x-2y+12=0`C. `3x+2y-12=0`D. `3x+2y+12=0` |
| Answer» Correct Answer - B | |
| 13. |
Find the equation of the straight line whose intercepts on X-axis andY-axis are respectively twice and thrice of those by the line `3x+4y=12.`A. 9x+8y=72B. 9x-8y=72C. 8x+9y=72D. 9y-8x=72 |
| Answer» Correct Answer - A | |
| 14. |
The equation of the line through `(1,2)`, which makes equal intercepts on the axes isA. x+y=1B. x+y=2C. x+y=4D. none of these |
| Answer» Correct Answer - D | |
| 15. |
If (2,3) is the midpoint of the portion of a line intercepted between the co-ordinate axes , then the equation of the line isA. 2x+3y=12B. 2x+3y+12=0C. 3x+2y=12D. none of these |
| Answer» Correct Answer - C | |
| 16. |
The equation of the line through (6,1) having x- and y-intercepts eaual in magnitude but opposite in sign isA. x-y=5B. y=x+5C. x+y=5D. none of these |
| Answer» Correct Answer - A | |
| 17. |
Find the equation of the straight line which passes through the point(-3, 8) and cuts off positive intercepts on the coordinate axes whose sum is7.A. 8x-3y=24B. 4x+3y=12C. `3x+8y=24`D. none of these |
| Answer» Correct Answer - B | |
| 18. |
The equation of a line which makes an angle of `45^(@)` with x-axis and cuts the y-axis at (0,3) is -A. y= x+3B. y=3C. x=3D. none of these |
| Answer» Correct Answer - A | |
| 19. |
The area (in square unit) of the triangle which the straight line 3x+4y-12=0 forms with the coordinate axes is -A. 4 sq . UnitsB. 5 sq .unitsC. 6 sq . UnitsD. `6(1)/(2)` sq . Units |
| Answer» Correct Answer - C | |
| 20. |
If a vertex of a triangle is `(1,1)`, and the middle points of two sides passingthrough it are `-2,3)`and `(5,2),`then findthe centroid and the incenter of the triangle.A. (5/3,3)B. (5/3,-3)C. (-5/3,3)D. (-5/3,-3) |
| Answer» Correct Answer - A | |
| 21. |
If B (1,3) is equidistant form A (6,1) and C (x,8) then : x =A. 3 or -5B. `-3 or 5 `C. `-3 or 5 `D. 3 or 5 |
| Answer» Correct Answer - B | |
| 22. |
Statement - I: Equation of bisectors of the angles between the liens x=0 and y=0 are `y=+-x` Statement - II : Equation of the bisectors of the angles between the lines `a_(1)x+b_(1)y+c_(1)=0anda_(2)x+b_(2)y+c_(2)=0` are `(a_(1)x+b_(1)y+c_(1))/(sqrt(a_(1)^(2)+b_(1)^(2)))=+-(a_(2)x+b_(2)y+c_(2))/(sqrt(a_(2)^(2)+b_(2)^(2)))` (Provided `a_(1)b_(2)nea_(2)b_(1)andc_(1),c_(2)gt0)`A. Statement -I is true , Statement -II is true and Statement - II is a correct explanation for Statement -I.B. Statement -I is true , Statement -II is true but Statement -II is not a correct explanation of Statement -I.C. Statement -I is true , Statement -II is false .D. Statement -I is false, Statement -II is true. |
| Answer» Correct Answer - A | |
| 23. |
If the point P(x, y) be equidistant from the points `A(a+b, a-b)` and `B(a-b, a+b)` thenA. ax=byB. bx=ayC. ax=-byD. bx=-ay |
| Answer» Correct Answer - B | |
| 24. |
If the points (-3,4), (-14,12) and (8,k) are collinear then :kA. -1B. -2C. -3D. -4 |
| Answer» Correct Answer - D | |
| 25. |
For what value of `k`are thepoints `(k ,2-2k),(-k+1,2k)a n d(-4-k ,6-2k)`collinear?A. `(1)/(2)`B. `-(1)/(2)`C. 1D. -1 |
| Answer» Correct Answer - D | |
| 26. |
Prove that the points (a+b+c),(b,c+a) and (c,a+b) are collinear.A. vertices of an equilateral triangleB. vertices of a right angled triangleC. concyclicD. collinear |
| Answer» Correct Answer - D | |
| 27. |
Points A (a,3) and C (5,b) are opposite vertices of a rectangle ABCD. If the other two vertices lie on the line y=2x +c which passes through the point (a,b), then : c=A. -7B. -4C. 0D. 7 |
| Answer» Correct Answer - A | |
| 28. |
The complete set of values of the parameter `alpha` so that the point `P(alpha, (1 +alpha^(2))^(-1))` does not lie outside the triangle formed by the lines `L_(1): 15y = x +1, L_(2) : 78y = 118 - 23x` and `L_(3):y +2 = 0` isA. `(0,5)`B. `[2,5]`C. `[1,5]`D. `[0,2]` |
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Answer» Correct Answer - C As `P(alpha,(1+alpha^(2))^(1-))` lie on `y = (1)/(1+x^(2))` which never intersect the line `y =-2` `:.` On solving `y = (1)/(1+x^(2))` with `L_(1)`, we get `P_(1) (2,(1)/(5))` (i) and the `L_(2)`, we get `P_(2)(5,(1)/(26))` (ii) `:.` From (i) and (ii), we get `2 le alpha le 5` |
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| 29. |
The number of points on the line `3x +4y = 5`, which are at a distance of `sec^(2)theta +2 cossec^(2) theta, theta in R`, from the point (1,3) isA. 1B. 2C. 3D. infinite |
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Answer» Correct Answer - B The perpendicular distance of (1,3) from the line `3x +4y =5` is 2 units while `sec^(2) theta +2 cosec^(2) theta` `= 3 +(tan theta -sqrt(2) cot theta)^(2) +2sqrt(2)` `ge 3 +2 sqrt(2)`. Evidently, there will be two such points on the line. |
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| 30. |
If the distance of a given point `(alpha,beta)` from each of two straight lines `y = mx` through the origin is d, then `(alpha gamma- beta x)^(2)` is equal toA. `x^(2) +y^(2)`B. `d^(2)(x^(2)+y^(2))`C. `d^(2)`D. none of these |
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Answer» Correct Answer - B Any line through (0,0) is `y = mx` By given condition `|(beta-m alpha)/(sqrt(1+m^(2)))| =d` `(beta = m alpha)^(2) = d^(2) (1+m^(2))` `(beta = (y//x)alpha^(2)) =d^(2) (1+(y^(2))/(x^(2)))` `rArr ((alpha y -beta x)/(x^(2)))^(2) = d^(2) (1+y^(2)//x^(2))` `rArr (alpha y - beta x)^(2) = d^(2) (x^(2) +y^(2))` |
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| 31. |
If a,b,c `gt` 0, then area of the triangle formed by the line ax+by+c=0 and coordinatte axes isA. `a^(2)/(2abc)`B. `b^(2)/(2abc)`C. `c^(2)/(2abc)`D. 0 |
| Answer» Correct Answer - C | |
| 32. |
A straight line passing through the point `A(-2,-3)` cuts lines `x +3y = 9` and `x +y +1 = 0` at B and C, respectively. If `AB. AC = 20`, then equation of the possible line isA. `x - y =1`B. `x - y +1 = 0`C. `3x -y +3 = 0`D. `3x -y = 3` |
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Answer» Correct Answer - A::C Any point on line through A is `(-2 +r cos theta, -3 +r sin theta)` `:. (-2+AB cos theta, -3 +AB sin theta)` lies on `x +3y = 9` `:. AB = (20)/((cos theta +3 sin theta))`, similarly `AC = (4)/((cos theta + sin theta))` `AB xx AC = 20` `:. 4 = cos^(2) theta +4 sin theta cos theta +3 sin^(2) theta` `:. 4 +4 tan^(2) theta = 1 +4 tan theta +3 tan^(2) theta` `:. tan^(2) theta - 4 tan theta +3 = 0` `:. tan theta = 1` or `tan theta = 3` `:.` Required lines are `y +3 =x +2` or `y +3 =3 (x+2)` |
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| 33. |
ABC is an equilateral triangle whose centroid is origin and base BC is along the line `11x +60y = 122`. ThenA. Area of the triangle is numerically equal to the perimeterB. Area of triangle is numerically double the perimeterC. Area of triangle is numerically three times the perimeterD. Area of triangle is numerically half of the perimeter |
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Answer» Correct Answer - A Let h be the length of the altitude from A, Distance from centroid to `BC = (h)/(3) = (122)/(sqrt(11^(2)+60^(2))) = (122)/(61) =2` `:. h = 6` is height of `DeltaABC` `:.` Area is `Delta = (h^(2))/(sqrt(3)) = 12 sqrt(3)` Primeter, `P = 3 xx (2h)/(sqrt(3)) = 12 sqrt(3)` |
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| 34. |
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. x+3y=21B. 2x=3y=7C. x+7y=31D. 2x+3y=21 |
| Answer» Correct Answer - C | |
| 35. |
if `(3,-4),(-6,5)` are the exterimities of the diagonal of the parallelogram and `(-2,-1)` is itts third vertex then find fourth vertex,A. (1,0)B. (-1,0)C. (0,1)D. (0,-1) |
| Answer» Correct Answer - B | |
| 36. |
The slope of the line which bisects the angles in the second and fourth quadrants isA. -1B. 0C. 1D. none of these |
| Answer» Correct Answer - A | |
| 37. |
If A (1,-2), B (-2,3) and C(2,-5) are the vertices of `Delta` ABC, then the equation of the median BE isA. 7x+13y+47=0B. 13x+7y+5=0C. 7x-13y+5=0D. none of these |
| Answer» Correct Answer - B | |
| 38. |
The condition for which the straight line ax+by+c=0 will be parallel to x - axis -A. `ane0,b=0`B. `a=0,bne0`C. `ane0,bne0,c=0`D. `ane0,b=0` |
| Answer» Correct Answer - B | |
| 39. |
The condition for which the straight line ax +by +c=0 will pass throught the origin is -A. `ane0,bne0`B. `a=0,bne0`C. `ane0,bne0,c=0`D. `bne0,c=0` |
| Answer» Correct Answer - C | |
| 40. |
If c is negative then the distance of the straight line `ax+by+c=0` from the origin is -A. `(c)/(sqrt(a^(2)+b^(2)))` uintB. `(-c)/(sqrt(a^(2)+b^(2)))` unitC. `(1)/(sqrt(b^(2)+b^(2)))` unitD. `(-1)/(sqrt(a^(2)+b^(2)))` unit |
| Answer» Correct Answer - B | |
| 41. |
The equations `ax+by+c=0` and `dx+ey+f=0` represent the same straight line if and only ifA. `(a)/(d)=(b)/(e)`B. c=fC. `(a)/(d)=(b)/(e)=(c)/(f)`D. a=d, b=e, c=f |
| Answer» Correct Answer - C | |
| 42. |
The lines `x+y-1=0,(m-1)x+(m^(2)-7)y-5=0and(m-2)x+(2m-5)y=0` are -A. concurrent for three values of mB. concurrent for one value of mC. concurrent for no value of mD. parallel for m=3 |
| Answer» Correct Answer - C,D | |
| 43. |
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 | |
| 44. |
The equation of the straight line cutting off an no intercept 8 on x-axis and making an angle of `60^@` with the positive direction of y -axis isA. x-` sqrt(3)`y=8B. x-`sqrt(3)` y=8C. y=`sqrt(3)`x+8D. none of these |
| Answer» Correct Answer - B | |
| 45. |
If the point `P(p,q)` is equidistant from the points `A(a+b,b-a)and B(a-b,a+b),` thenA. ax=byB. bx=ayC. ax=-byD. bx=-ay |
| Answer» Correct Answer - B | |
| 46. |
In relation to the line : 7(x-2) =5(y+3), the point (3,-2) lies onA. the lineB. origin side of the lineC. non-origin side of the lineD. none of these |
| Answer» Correct Answer - C | |
| 47. |
The points `(-a,-b)`, `(0,0)`. `(a,b)` and `(a^(2),a^(3))` areA. vertices of a rectangleB. vertices of a parallelogramC. collinearD. none of these |
| Answer» Correct Answer - C | |
| 48. |
The point which divides the join of (1,2) and(3,4) externally in theratio 1:1a. lies in the III quadrantb. lies in the II quadrantc. lies in the I quadrantd. cannot be foundA. lies in the third quadrantB. lies in the second quadrantC. lies in the first quadrantD. cnnont be found |
| Answer» Correct Answer - D | |
| 49. |
Prove that the line `y-x+2``=0`divides the join of points (3,-1) and (8,9) in the ratio 2:3.A. `2:3 `B. `3:2`C. `-2: 3`D. `-3:2` |
| Answer» Correct Answer - A | |
| 50. |
If the point (3,k) lies on the line passing through the points (-1,3) and (1,5) then :k=A. -1B. 3C. 7D. 2 |
| Answer» Correct Answer - C | |