If the plane 2x - y + 2z = 3 = 0 has the distances 13 a

Subject

Mathematics

Class

JEE Class 12

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

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

     


Advertisement
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


Advertisement

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


D.

13

λ - 66 = 13, μ - 33 = 23λ = 8, μ = 5Thus, λ+ μ = 8 + 5 = 13


Advertisement
Advertisement
9.

The integral π6π3sec23csc43xdx =

  • 35/3 - 31/3

  • 37/6 - 35/6

  • 35/6 - 31/3

  • 34/3 - 31/3


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


Advertisement