The angle between lines joining origin and intersection points of

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

The number of times the digit 5 will be written when listing the integers from 1 to 1000, is

  • 271

  • 272

  • 300

  • None of these


12.

The equation of the common tangent touching the circle (x - 3)2 + y2 = 9 and parabola y = 4x above the x-axis is

  • √3y = 3x + 1

  • √3y = -( x + 3 )

  • √3y = x + 3

  • √3y = -( 3x + 1 )


13.

The equation of the tangents to the ellipse 4x2 + 3y2 = 5 which are parallel to the line y = 3x + 7 are

  • y = 3x ± 1553

  • y = 3x ± 15512

  • y = 3x ± 9512

  • None of these


14.

The radius of the circle passing through the foci of the ellipse x216 + y29 = 1 and having its centre (0, 3) is

  • 4

  • 3

  • 12

  • 7/2


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15.

If the foot of the perpendicular from the origin to a straight line is at the point (3 - 4). Then, the equation of the line is

  • 3x - 4y = 25

  • 3x - 4y + 25 = 0

  • 4x + 3y - 25 = 0

  • 4x - 3y + 25 = 0


16.

If the arithmetic mean of a and b is an + bnan - 1 + bn - 1, then the value of n is

  • - 1

  • 0

  • 1

  • None of the above


17.

The expression tan2α + cot2α is

  •  2

  •  2

  •  - 2

  • None of these


18.

Locus of centroid of triangle whose vertices are acost, asint bsint, - bcost and (1, 0) where t is a parameter is

  • (3x - 1)2 + (3y)2 = a2 - b2

  • (3x - 1)2 + (3y)2 = a2 + b2

  • (3x + 1)2 + (3y)2 = a2 + b2

  • (3x + 1)2 + (3y)2 = a2 - b2


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19.

The equation 3sin2x + 10cosx - 6 is satisfied, if

  • x =  ± cos-113

  • x = 2 ± cos-113

  • x =  ± cos-116

  • x = 2 ± cos-116


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20.

The angle between lines joining origin and intersection points of line 2x + y = 1 and curve 3x2 + 4yx - 4x + 1= 0 is

  • π2

  • π3

  • π4

  • π6


A.

π2

The equation of required line is,

3x2 + 4xy - 4x(2x + y) + (2x + y)2 = 0

 3x2 + 4xy - 8x2 - 4xy + 4x2 + y2 + 4xy = 0                                          - x2 + y2 +4xy = 0

Since, (coefficient of x2) + (coefficient of y2)

                 - 1 + 1 = 0

  Lines are mutually perpendicular. 

i.e. Angle between line is π2


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