Q1.

On solving the inequalities 6x + y \(\geq\) 18, x + 4y \(\geq\) 12, 2x + y \(\geq\) 10, we get the following situation : 

  • (0, 18), (12, 0), (4, 2) & (2, 6)

  • (3, 0), (8, 0), (4, 2) & (7, 6)

  • (5, 0), (0, 10), (4, 2) & (7, 6)

  • (0, 18), (12, 0), (4, 2), (0, 0)  & (2, 6)

Solution:

NA

Q2.

The rules and regulations demand that the employer should employ not more than 5 experienced hands to 1 fresh one and this fact is represented by : (Taking experienced person as x and fresh person as y ) 

  • \(y\geq {x \over5}\)

  • \(5y \leq x\)

  • \(5y \geq x\)

  • None

Solution:

NA

Q3.

If a > 0 and b < 0, it follows that :

  • \( {1 \over a} > {1 \over b}\)

  • \( {1 \over a} < {1 \over b}\)

  • \( {1 \over a} = {1 \over b}\)

  • None of these 

Solution:

NA

Q4.

The solution of the inequality \({(5 - 2x) \over 3} \leq {x \over 6} - 5 \)  is 

  • \(x \geq 8\)

  •  \(x \leq 8\)

  • x = 8

  • None of these 

Solution:

NA

Q5.

The solution of the inequality 8x + 6 < 12x + 14 is 

  • (-2, 2)

  • (0, -2)

  • (2, \(\infty\))

  • (-2, \(\infty\))

Solution:

NA

Q6.

The common region in the graph of linear inequalities 2x + y \(\geq\) 18, x + y \(\geq\) 12 and 3x + 2y \(\leq\)  34 is 

  • unbounded 

  • infeasible 

  • feasible and bounded 

  • feasible and unbounded 

Solution:

NA

Q7.

On the average an experienced person does 7 units of work while a fresh one work 5 units of work daily but the employer has  to maintain an output of atleast 35 units of work per day. The situation can be expressed as :   

  •  7x + 5y < 35 

  •  7x + 5y \(\leq\) 35 

  •  7x + 5y > 35 

  •  7x + 5y \(\geq\) 35 

Solution:

NA

Q8.

Find the solution 

2x + 3y \(\leq\) 6,

3x - 2y \(\leq\) 6,

y \(\leq\) 1, x, y \(\geq\) 0

  • (0,0) , (2, 0), (30/13, 6/13), (3/2, 1), (0, 1)

  • (5,0) , (2, 0), (10/13, 6/13), (5/2, 1), (0, 1)

  • (0,7) , (3, 0), (30/15, 6/15), (3/5, 1), (0, 1)

  • None of these

Solution:

NA

Q9.

Find the solution 

2x + 4y \(\leq\) 8,

3x + y \(\leq\) 6,

x + y \(\leq\) 4, 

x \(\geq\) 0, y \(\geq\) 0

 

 

  • (6, 0), (2, 0), (10/5, 4/5), (8, 2) 

  • (0, 0), (2, 6), (8/5, 6/8)

  • (0, 0), (2, 0), (8/5, 6/5), (0, 2) 

  • None of these 

Solution:

NA

Q10.

Find the solution

x + 2y \(\geq\)10, x + y \(\geq\) 6, 

3x + y \(\geq\) 8, x \(\geq\) 0, y \(\geq\) 0 

  • (10, 0), (2, 4), (1, 5), (0, 8)

  • (0, 0), (8, 4), (1, 5), 

  • (10, 8), (2, 5), (1, 5), (0, 8)

  • None of these 

Solution:

NA