The point where the line x - 12 = y 

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

241.

Joint equation of pair of lines through (3, - 2) and parallel to x2 - 4xy + 3y2 = 0 is

  • x2 + 3y2 - 4xy - 14x + 24y + 45 = 0

  • x2 + 3y2 + 4xy - 14x + 24y + 45 = 0

  • x2 + 3y2 + 4xy - 14x + 24y - 45 = 0

  • x2 + 3y2 + 4xy - 14x - 24y - 45 = 0


242.

Equation of the plane passing through (- 2, 2, 2) and (2, - 2, - 2) and perpendicular to the plane 9x - 13y - 3z = 0 is

  • 5x + 3y + 2z = 0

  • 5x - 3y + 2z = 0

  • 5x - 3y - 2z = 0

  • 5x + 3y - 2z = 0


243.

If 'f' is the angle between the lines ax2 + 2hxy + by2 = 0, then angle between x2 + 2xy secθ + y2 = 0 is

  • θ

  • 2θ

  • θ2

  • 3θ


244.

The equation of the plane which passes through (2, - 3, 1) and is normal to the line joining the points (3, 4, - 1) and (2, - 1, 5), is given by

  • x + 5y - 6z + 19 = 0

  • x - 5y + 6z - 19 = 0

  • x + 5y + 6z + 19 = 0

  • x - 5y - 6z - 19 = 0


Advertisement
245.

The angle between the lines x2 - xy - 6y2 - 7x + 31y - 18 = 0 is

  • π4

  • π6

  • π2

  • π3


246.

The equation of the lines passing through the origin and having slopes 3 and - 13, is

  • 3y2 + 8xy - 3x2 = 0

  • 3x2 + 8xy + 3y2 = 0

  • 3y2 - 8xy - 3x2 = 0

  • 3x2 + 8xy - 3y2 = 0


Advertisement

247.

The point where the line x - 12 = y - 2- 3 = z + 34 meets the plane 2x + 4y - z = 1, is

  • (3, - 1, 1)

  • (3, 1, 1)

  • (1, 1, 3)

  • (1, 3, 1)


A.

(3, - 1, 1)

Let point be (a, b, c), then

2a + 4b - c = 1           ...(i)

and a = 2k + 1, b = - 3k + 2 and c = 4k - 3

          [where k is constant]
On substituting these values in Eq. (i), we get

2(2k + 1) + 4 (- 3k + 2) - (4k - 3)= 1

                                            k = 1

Hence, required point is (3, - 1, 1).


Advertisement
248.

A vector vis equally inclined to the x-axis, y-axis and z-axis respectively, its direction cosines are

  • < 13, 13, 13 >

  • < - 13, - 13, - 13 >

  • < 13, 13, 13 > or < - 13, - 13, - 13 >

  • None of the above


Advertisement
249.

A plane meets the axes in A, B and C such that centroid of the ABC is (1, 2, 3). The equation of the plane is

  • x + y/2 + z/3 = 1

  • x/3 + y/6 + z/9 = 1

  • x + 2y + 3z = 1

  • None of these


250.

If α, β and γ are the angles which a half ray makes with the positive direction of the axes, then sin2α + sin2β + sin2γ is equal to

  • 1

  • 2

  • 0

  • - 1


Advertisement