IIT - JEE Main Important Questions of Linear Programming | Zigya

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 Multiple Choice QuestionsMultiple Choice Questions

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1.

The line L1: y = x = 0 and L2: 2x + y = 0 intersect the line L3: y + 2 = 0 at P and Q respectively. The bisectorof the acute angle between L1 and L2 intersects L3 at R.
Statement-1: The ratio PR: RQ equals 2√2:√5
Statement-2: In any triangle, the bisector of an angle divides the triangle into two similar triangles.

  • Statement-1 is true, Statement-2 is true ; Statement-2 is correct explanation for Statement-1

  • Statement-1 is true, Statement-2 is true ; Statement-2 is not a correct explanation for Statement-1

  • Statement-1 is true, Statement-2 is false

  • Statement-1 is true, Statement-2 is false

241 Views

2.

If x is real, the maximum value of fraction numerator 3 straight x squared space plus 9 straight x space plus 17 over denominator 3 straight x squared space plus 9 straight x space plus 7 end fraction space is

  • 1/4

  • 41

  • 1

  • 1

131 Views

3.

The function straight f left parenthesis straight x right parenthesis space equals straight x over 2 space plus 2 over straight x has a local minimum at

  • x = 2

  • x = −2

  • x = 0

  • x = 0

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4.

For the LPP Min z = x1 + x2 such that inequalities 5x1 + 10x2 0, x1 + x2  1, x2  4 and x1, x2 > 0

  • There is a bounded solution

  • There is no solution

  • There are infinite solutions

  • None of these


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5.

The maximum value of z = 9x + 13y subject to 2x + 3y  18, 2x + y  10, x  0, y  0 is

  • 130

  • 81

  • 79

  • 99


6.

The maximum value of the objective function Z = 3x + 2y for linear constraints x + y  7, 2x + 3y  16, x2  0, y2  0 is

  • 16

  • 21

  • 25

  • 28


7.

A diet of a sick person must contain atleast 4000 unit of vitamins, 50 unit of proteins and 1400 calories. Two foods A and B are available at cost rs. 4 and rs. 3 per unit respectively. If one unit of A contains 200 unit of vitamins, 1 unit of protein and 40 calories, while one unit of food B contains 100 unit of vitamins, 2 unit of protein and 40 calories. Formulate the problem, so that the diet be cheapest

  • 200x + 100y  4000, x + 2y  5040x + 40y  1400, x  0 and y  0O. F z = 4x + 3y

  • 400x + 200y  100, x + 2y  5040x + 40y  1400, x  0 and y  0O. F z = 4x + 3y

  • 100x + 200y  4000, x + 2y  5040x + 40y  1400, x  0 and y  0O. F z = 4x + 3y

  • None of the above


8.

The constraints - x1 + x2  1, - x1 + 3x2  9, x1, x2 > 0 defines on

  • bounded feasible space

  • unbounded feasible space

  • both bounded and unbounded feasible space

  • None of the above


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9.

The objective function Z = x1 + x2, subject to the constraints are  x1 + x2  10, - 2x1 + 3x2  15, x1  6, x1x2  0 has maximum value of _ the feasible region.

  • at only one point

  • at only two points

  • at every point of the segment joining two points

  • at every point of the line joining two points equivalent to


10.

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


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