The curve y = (λ + 1)x2 + 2 intersects the curve y = λx + 3 in

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

Advertisement

51.

The curve y = (λ + 1)x2 + 2 intersects the curve y = λx + 3 in exactly one point, if λ equals -

  • {–2, 2}

  • {1}

  • {-2}

  • {-2}


C.

{-2}

for point of intersection at exactly one point
λx + 3 = (λ + 1)x2 + 2
(λ + 1)x2 – λx – 1 = 0
Δ = 0
λ2 + 4(λ + 1) = 0
λ2 + 4λ + 4 = 0
(λ + 2)2 = 0 λ = – 2

143 Views

Advertisement
52.

If the curves y2 = 6x, 9x2 + by2 = 16 intersect each other at right angles, then the value of b is

  • 9/2

  • 6

  • 7/2

  • 4


53.

If L1 is the line of intersection of the plane 2x – 2y + 3z – 2 = 0, x – y + z + 1 = 0 and L2 is the line of intersection of the plane x + 2y – z – 3 = 0, 3x – y + 2z – 1 = 0, then the distance of the origin from the plane containing the lines L1
and L2 is :

  • 12

  • 142

  • 132

  • 122


54.

The equation of the plane through (1, 2,- 3) and (2,- 2, 1) and parallel to X-axis is

  • y - z + 1 = 0

  • y - z - 1 = 0

  • y + z - 1 = 0

  • y + z + 1 = 0


Advertisement
55.

Three lines are drawn from the origin O with direction cosines proportional to (L,-1, 1), (2,-3, 0) and (1, 0, 3). The three lines are

  • not coplanar

  • coplanar

  • perpendicular to each other

  • coincident


56.

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at

  • (1, 2, 5)

  • (2, 2, 2)

  • (2, 1, 5)

  • (1, 1, 6)


57.

Angle between the planes x + y + 2z = 6 and 2x - y + z = 9 is

  • π4

  • π6

  • π3

  • π2


58.

The value of λ for which the straight line x - λ3 = y - 12 + λ = z - 3- 1 may lie on the plane x - 2y = 0, is

  • 2

  • 0

  • - 12

  • there is no such λ


Advertisement
59.

In a triangle PQR, PQR, R = . If tanP2 and tanQ2 are roots of ax2 + bx + c = 0, where a 0, then which one is true?

  • c = a + b

  • a = b + c

  • b = a + c

  • b = c


60.

If C is the reflection of A (2, 4) in x-axis and B is the reflection of C in y-axis, then | AB | is

  • 20

  • 2√5

  • 4√5

  • 4


Advertisement