The distance of the point having position vector - i^&n

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

1.

The sum of the real roots of the equation x- 6- 12- 3xx - 3- 32xx + 2 = 0, is equal to

  • 0

  • 6

  • - 4

  • 1


2.

The tangent and normal to the ellipse 3x2 + 5y2 = 32 at the point P(2, 2) meet the x-axis at Q and R, respectively .Then the area (in sq. units) of the triangle PQR is :

  • 6815

  • 163

  • 143

  • 3415


3.

If cos-1x - cos-1y2 = α, where - 1  x  1- 2  y  2, x  y2 then for all x, y, 4x2 - 4xycosα + y2 is equal to

  • 4sin2α

  • 2sin2α

  • 4cos2α +2x2y2

  • 4sin2α - 2x2y2


4.

A spherical iron ball of radius 10cm is coated with a layer of ice of uniform thickness that melts a rate of 50cm3/min When the thickness of the ice 5cm, then the rate at which the thickness (in cm/min) of the ice decreases, is :

  • 56π

  • 118π

  • 19π

  • 136π

     


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5.

If x5e- x2dx = g(x)e- 2 + c, where c is a constant of interation then g(- 1) is equal to :

  • - 1

  • 1

  • 12

  • - 52


6.

The area (in sq.units ) of the region bounded by the curves y = 2x and y = x + 1,in the first quadrant is:

  • 32 - 1loge2

  • loge2 +32

  • 12

  • 32


7.

Let y = y(x) be the solution of the differential equation dydx + ytanx = 2x +x2tanx, x  - π2, π2 such that if y(0) = 1, then

  • y'π4 - y'- π4 = π - 2

  • yπ4 - y- π4 = 2

  • yπ4 + y- π4 = π22 + 2

  • y'π4 + y'- π4 = - 2


8.

If the plane 2x - y + 2z = 3 = 0 has the distances 13 and 23 units from the planes 4x - 2y + 4z + λ = 0  and 2x - y + 2z + μ, respectively then the maximum value of λ + μ

  • 5

  • 15

  • 9

  • 13


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9.

The integral π6π3sec23csc43xdx =

  • 35/3 - 31/3

  • 37/6 - 35/6

  • 35/6 - 31/3

  • 34/3 - 31/3


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10.

The distance of the point having position vector - i^ + 2j^ + 6k^ from the straight line passing  through the point (2, 3, - 4) and parallel to the vector 6i^ + 3j^ - 4k^ is :

  • 213

  • 7

  • 6

  • 43


B.

7

AP = 3, 1, - 10

AB = 6161 = 61PQ2 = AP2 - AQ2         = 110 - 61 = 49 PQ = 7


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