Linear Programming Test

Result

Linear Programming Test - 26

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Weekly Quiz Competition

Question 1
1 / -0

The taxi fare in a city is as follows. For the first km the fare is $$Rs.10$$ and subsequent distance is $$Rs.6 / km.$$ Taking the distance covered as $$x \ km$$ and fare as $$Rs\ y$$ ,write a linear equation.

A
$$y=4+6x$$

B
$$y=4+5x$$

C
$$y=3+6x$$

D
$$y=3+5x$$

Solution

First $$km$$ fare =$$Rs.10$$
Subsequent distance fare=$$Rs\ 6/km$$

Then fare $$x\ km$$ of distance
$$y=(x-1) \times 6+10$$
$$y=6x-6+10$$

$$y=6x+4$$

$$A$$ is correct
Question 2
1 / -0

The inequalities $$f(-1)\le -4,f(1) \le 0$$ & $$f(3) \le 5$$ are known to hold for $$f(x)=ax^{2}+bx+c$$ then the least value of $$'a'$$ is:

A
$$-1/4$$

B
$$-1/3$$

C
$$1/4$$

D
$$1/8$$

Solution
Question 3
1 / -0

The feasible region for anLPP is shown shaded in the figure. Find the maximum value of the objective function $$z=11x+7y$$.

A
35

B
47

C
21

D
14

Solution

the cover point of feasible
$$(0,3)$$, $$(0,5)$$, $$(3,2)$$
$$\rightarrow$$
$$Z(0,3)=21$$
$$Z(0,5)=35$$
$$Z(3,2)=47$$ = max value of $$Z$$
Question 4
1 / -0

Shade region is represented by

A
$$2x+5y \ge 80,x+y \le 20, x \ge 0,y \le 0$$

B
$$2x+5y \ge 80,x+y \ge 20, x \ge 0,y \ge 0$$

C
$$2x+5y \le 80,x+y \le 20, x \ge 0,y \ge 0$$

D
$$2x+5y \le 80,x+y \le 20, x \ge 0,y \le 0$$

Solution
Question 5
1 / -0

The maximum value of $$P=3x+4y$$ subject to the constraints $$x +y \le 40,x+2y \le 60,x \ge 0$$ and $$y \ge 0$$ is

A
$$120$$

B
$$140$$

C
$$100$$

D
$$160$$

Solution
Question 6
1 / -0

The problem associated with $$ LPP$$ is

A
single objective function

B
Double objective function

C
No any objective function

D
None

Solution

The problem associated with LLP is single objective.
Question 7
1 / -0

The maximum value of $$4x+5y$$ subject to the constraints $$x+y \le 20,x+2y \le 35,x-3y \le 12$$ is

A
$$84$$

B
$$95$$

C
$$100$$

D
$$96$$

Solution
Question 8
1 / -0

A_____ in a table represents a relationship among a set of values.

A
Column

B
Key

C
Row

D
Entry

Solution
Question 9
1 / -0

If $$x$$ is any real number, then which of the following is correct?

A
$$\dfrac { x ^ { 2 } } { 1 + x ^ { 4 } } \geq \dfrac { 1 } { 2 }$$

B
$$\dfrac { x ^ { 2 } } { 1 + x ^ { 4 } } \geq \dfrac { 1 } { 4 }$$

C
$$\dfrac { x ^ { 2 } } { 1 + x ^ { 4 } } \leq \dfrac { 1 } { 2 }$$

D
none of these

Solution

We know that $$(x-\dfrac{1}{x})^{2}\geq 0$$

$$x^{2}+\dfrac{1}{x^{2}}-2\geq 0$$

$$x^{2}+\dfrac{1}{x^{2}}\geq 2$$

$$0 < \dfrac{1}{x^{2}+\dfrac{1}{x^{2}}}\leq \dfrac{1}{2}$$

$$0 \leq \dfrac{x^{2}}{x^{4}+1}\leq \dfrac{1}{2}$$ ($$\because x^{2}$$ and $$x^{4}$$ are positive or zero)

$$\dfrac{x^{2}}{x^{4}+1}\in [0,\dfrac{1}{2}]$$
Question 10
1 / -0

The shape of the region determined by $$ 2x+6y \geq 12, 3x +2y \geq 6, x+y \leq 8, x \geq 0, y \geq 0$$

A
a triangle

B
a quadrilateral

C
a pentagon

D
a hexagon

Solution