The objective function z = 4x1 + 5x2, subject to 2x1 + x2 &g

Subject

Mathematics

Class

JEE Class 12

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 Multiple Choice QuestionsMultiple Choice Questions

11.

If fx = x for  x 0= 0 for x > 0, then f(x) at x = 0 is

  • continuous but not differentiable

  • not continuous but differentiable

  • continuous and differentiable

  • not continuous and not differentiable


12.

The value of cos-1cotπ2 + cos-1sin2π3 is

  • 2π3

  • π3

  • π2

  • π


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13.

The objective function z = 4x1 + 5x2, subject to 2x1 + x2  7, 2x1 + 3x2  15, x2  3, x1x2  0 has minimum value at the point

  • on X-axis

  • on Y-axis

  • at the origin

  • on the line parallel to X-axis


A.

on X-axis

 Given objective function is minimise, z = 4x1 + 5x2

Subject to constraints, 2x1 + x2  7, 2x1 + 3x2  15, x2  3, x1x2  0

Table for line 2x1 + x2 = 7 is

x1 0 1 2 3
x2 7 5 3 1

Table for line 2x1 + 3x2 = 15 is

x1 0 3 6
x2 5 3 1

Now, the value of z at corner points are given below :

Corner points z = 4x1 + 5x2

A(3.5, 0) z = 4 x 3.5 + 5 x 0 = 14(minimum)
B(7.5, 0) z = 4 x 7.5 + 5 x 0 = 30
C(3, 3) z = 4 x 3 + 5 x 3 = 27
D(2, 3) z = 4 x 2 + 4 x 3 = 20

Hence, the minimum value of z is 14 at (3.5, 0) i.e. at X-axis.


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14.

01xtan-1xdx =

  • π4 + 12

  • π4 - 12

  • 12 - π4

  • - π4 - 12


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15.

If 19 - 16x2dx = αsin-1βx + c, then α + 1β =

  • 1

  • 712

  • 1912

  • 912


16.

The solution of the differential equation

dydx = tanyx + yx is

  • cosyx = cx

  • sinyx = cx

  • cosyx = cy

  • sinyx = cy


17.

If 0π2logcosxdx = π2log12, then 0π2logsecxdx =

  • π2log12

  • 1 - π2log12

  • 1 + π2log12

  • π2log2


18.

If the angle between the planes r . mi^ - j^ + 2k^ + 3 = 0 and r . 2i^ - mj^ - k^ - 5 = 0 is π3, then m =

  • 2

  • ± 3

  • 3

  • - 2


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19.

If the origin and the points P(2, 3, 4 ), Q(1, 2, 3) and R(x, y, z) are coplanar, then

  • x - 2y - z = 0

  • x + 2y + z = 0

  • x - 2y + z = 0

  • 2x - 2y + z = 0


20.

If lines represented by equation px2 - qy2 = 0 are distinct, then

  • pq > 0

  • pq < 0

  • pq = 0

  • p + q = 0


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