Linear Inequalities Test -1

Result

Linear Inequalities Test -1

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

The solution of $$2^{x}+2^{|x|}\geq 2\sqrt{2}$$ is

A
$$\left ( (-\infty ,log_{2}(\sqrt{2}+1)) \right )$$

B
$$(0,\infty )$$

C
$$\left ( \frac{1}{2}, log_{2}(\sqrt{2}-1) \right )$$

D
$$(-\infty , log_{2}(\sqrt{2}-1)]\cup [\frac{1}{2},\infty )$$

Solution
Question 2
1 / -0

The point (3, 2) is reflected in the y-axis and then moved a distance of 5 units towards the negative side of y-axis. The coordinates of the point thus obtained are

A
(-3, -3)

B
(3, 3)

C
(-3, 3)

D
(3, -3)
Question 3
1 / -0

The recommended daily calcium intake for a 20-year-old is 1,000 milligrams (mg). One cup of milk contains 299 mg of calcium and one cup of juice contains 261 mg of calcium. Which of the following inequalities represents the possible number of cups of milk m and cups of juice j a 20-year-old could drink in a day to meet or exceed the recommended daily calcium intake from these drinks alone?

A
$$\displaystyle 299m+261j\ge 1000$$

B
$$\displaystyle 299m+261j>1000$$

C
$$\displaystyle \frac { 299 }{ m } +\frac { 261 }{ j } \ge 1000$$

D
$$\displaystyle \frac { 299 }{ m } +\frac { 261 }{ j } >1000$$

Solution
Question 4
1 / -0

Which of the following is a correct graph of $$x>1, x<4$$?

A
Line A

B
Line B

C
Line C

D
Line D

E
Line E

Solution
Question 5
1 / -0

If $${ ax }^{ 2 }+\frac { b }{ x } \ge c\;\; \forall\; x\in R^{ + }$$ where $$a>0$$ and $$b>0$$ then

A
$${ 27ab }^{ 2 }\ge { 4c }^{ 3 }$$

B
$${ 27ab }^{ 3 }\ge { 4c }^{ 3 }$$

C
$${ 27a^{ 2 }b }^{ 2 }\ge { 4c }^{ 3 }$$

D
$${ 27a^3b }\ge { 4c }^{ 3 }$$

Solution
Question 6
1 / -0

If the system of inequalities $$y \ge 2x+1$$ and $$y > \dfrac{1}{2}x-1$$ is graphed in the $$xy$$-plane above, which quadrant contains no solutions to the system?

A
Quadrant II

B
Quadrant III

C
Quadrant IV

D
There are solutions in all four quadrants

Solution

given, $$y\geq 2x+1$$ and
$$y>\dfrac{1}{2}x-1$$

first, draw the graph for equations  $$y= 2x+1$$ and $$y=\dfrac{1}{2}x-1$$

for $$y= 2x+1$$
substitute y=0 we get, $$2x+1=0 \implies x=-0.5$$
substitute x=0 we get, $$y=1$$
therefore, $$y= 2x+1$$ line passes through (0.5,0) and (0,1) as shown in fig.
Hence,  $$y\geq 2x+1$$ includes the region above the line.

for $$y=\dfrac{1}{2}x-1$$
substitute y=0 we get, $$\dfrac{1}{2}x-1=0 \implies x=2$$
substitute x=0 we get, $$y=-1$$
therefore, $$y= 2x+1$$ line passes through (2,0) and (0,-1) as shown in fig.
Hence,  $$y>\dfrac{1}{2}x-1$$ includes the region above the line.

the intersection region is the shaded region as shown in above figure which includes I, II and III quadrants.
Therefore, quadrant IV has no solution
Question 7
1 / -0

$$y = {x^2} - 4x$$ Find the minimum value of y

A
-2

B
-4

C
4

D
5

Solution
Question 8
1 / -0

Graphical solution of $$2 x+y-2>0$$

A

B

C

D

Solution
Question 9
1 / -0

The solution set of the inequation $$| x - 1 | + | x - 2 | + | x - 3 | \geq 6 ,$$

A
$$[ 0,4 ]$$

B
$$( - \infty , - 2 ) \cup [ 4 , \infty )$$

C
$$( - \infty , 0 ] \cup [ 4 , \infty )$$

D
none of these

Solution
Question 10
1 / -0

If $$xy=2(x+y), x< y$$ and $$x, y \in N$$, number of solutions of the equation

A
Two

B
Three

C
No solutions

D
Infinitely many solutions

Solution