If L1 is the line of intersection of the plane 2x – 2y + 3z

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 Multiple Choice QuestionsMultiple Choice Questions

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}

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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


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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


C.

132

L1 is parallel to i^j^k^2-231-11 = i^ + j^L2 is parallel to i^j^k^12-13-12 = 3i^ -5j^-7k^Also, L2 passes through 57,87,0So required plane is x-57y-87z1103-5-7 = 0 7x -7y + 8z + 3 = 0Now, perpendicular distance  = 3162 = 132


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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


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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


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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


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