The angle between the curves, y = x and y2 - x = 0 at the point (

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121.

The angle between the curves, y = x and y2 - x = 0 at the point (1, 1) is

  • π2

  • tan-143

  • π3

  • tan-134


D.

tan-134

Given curve are

             y = x2       ...(i)

and y2 - x = 0        ...(ii)

From Eq. (i),

               dydx = 2x dydx1, 1 = 2 = m1From Eq. (ii),  2y dydx - 1 = 0          dydx = 12y dydx1, 1 = 12 = m2Let θ be the angle between given curve. Then,tanθ = m1 - m21 + m1m2          = 2 - 121 + 2 . 12 = 322 = 34  θ = tan-134

 


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122.

If the distance between (2, 3) and (- 5, 2) is equal to the distance between (x, 2) and (1, 3), then the values of x are

  • - 6, 8

  • 6, 8

  • - 8, 6

  • - 7, 7


123.

The vertices of a triangle are A(3, 7), B (3, 4) and C (5, 4). The equation of the bisector of the angle ABC is

  • y = x + 1

  • y = x - 1

  • y = 3x - 5

  • y = x


124.

If the angle between a and c is 25°, the angle between b and c is 65° and a + b = c, then the angle between a and b is

  • 40°

  • 115°

  • 25°

  • 90°


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125.

The projection of the vector 2i + aj - k on the vector i - 2j + k is - 56. Then, the value of a is equal to

  • 1

  • 2

  • - 2

  • 3


126.

A unit vector in the XOY-plane that makes an angle 30° with the vector i + j and makes an angle 60° with i - j is

  • 146 + 2i - 6 - 2j

  • 126 - 2i + 6 + 2j

  • 146 - 2i + 6 + 2j

  • 146 + 2i + 6 - 2j


127.

The angle between the line r = (i + 2j + 3k) + λ(2i + 3j + 4k) and the plane r - (i + j - 2k) = 0 is

  • 60°

  • 30°

  • 90°


128.

The lines r = i + j - k + (3i - j) and r = 4j - k + µ (2i + 3k) intersect at the point

  • (0, 0, 0)

  • (0, 0, 1)

  • (0, - 4, - 1)

  • (4, 0, - 1)


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129.

An equation of the plane through the points (1, 0, 0) and (0, 2, 0) and at a distance 67 units from the origin is

  • 6x + 3y + z - 6 = 0

  • 6x + 3y + 2z - 6= 0

  • 6x + 3y + z + 6 = 0

  • 6x + 3y + 2z + 6 = 0


130.

The projection of a line segment on the axes are 9, 12 and 8. Then, the length of the line segment is

  • 15

  • 16

  • 17

  • 18


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