Important Questions of Straight Lines Mathematics | Zigya

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11.

What is the equation of the straight line cutting off an intercept 2 from the negative direction of y-axis and inclined at 30° with the positive direction of x-axis ?

  • x - 23y - 32

  • x + 23y - 32 = 0

  • x + 3y - 23 = 0

  • x - 3y - 23 = 0


12.

What is the equation of the line passing through the point of intersection of the lines x + 2y - 3 = 0 and 2x - y + 5 = 0 and parallel to the line y - x + 10 = 0

  • 7x - 7y + 18 = 0

  • 5x - 7y + 18 = 0

  • 5x - 5y + 18 = 0

  • x - y + 5 = 0


13.

Consider the following statements :

  1. The length p of the perpendicular from the origin to the line ax + by = c satisfies the relation p2 = c2a2 + b2
  2. The length p of the perpendicular from the origin to the line xa + yb = 1 satisfies the relation 1p2 = 1a2 + 1b2
  3. The length p of the perpendicular from the origin to the line y = mx + c satisfies the relation 1p2 = 1 + m2 + c2c2

Which of the above is/are correct ?

  • 1, 2 and 3

  • 1 only

  • 1 and 2 only

  • 2 only


14.

What is the equation of the straight line passing through the point (2, 3) and making an intercept on the positive y-axis equal to twice its intercept on the positive x-axis ?

  • 2x + y = 5

  • 2x + y = 7

  • x + 2y = 7

  • 2x - y = 1


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15.

The perpendiculars that fall from any point of the straight line 2x + 11y = 5 upon the two straight lines 24x + 7y = 20 and 4x - 3y = 2 are :

  • 2 and 4 respectively

  • 11 and 5 respectively

  • Equal to each other

  • Not equal to each other


16.

The equation of the line, when the portion of it intercepted between the axes is divided by the point(2, 3) in the ratio of 3 : 2, is

  • Either x + y = 4 or 9x + y = 12

  • Either x + y = 5 or 4x + 9y = 30

  • Either x + y = 4 or x + 9y = 12

  • Either x + y = 5 or 9x + 4y = 30


17.

What is the distance between the straight lines 3x + 4y = 9 and 6x + 8y = 15 ? 

  • 32

  • 310

  • x2 + y2 + z2 + 4x - 6y - 8z = 4

  • x2 + y2 + z2 + 4x + 6y + 8z = 4


18.

Which one of the following is correct in respect of the cube roots of unity ?

  • They are collinear

  • They lie on a circle of radius 3

  • They form an equilateral triangle

  • None of the above


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19.

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation π6 and π3 respectively. What is the height of the hill ?

  • 2h

  • 3h2

  • h

  • h2


20.

Consider the following statements :

1. The distance between the lines y = mx + c1 and y = mx + c2 is c1 - c21 + m22. The distance between the lines ax + by + c1 = 0 and ax + by + c2 = 0 is c1 - c2a2 + b23. The distance between the lines x = c1 and x = c2 is c1 - c2Which of the above statements are correct ?

  • 1 and 2 only

  • 2 and 3 only

  • 1 and 3 only

  • 1, 2 and 3


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