Linear Inequalities CBSE Questions & Answers

Linear Inequalities

This is Mathematics Class 11 Linear Inequalities CBSE Questions & Answers. There are 15 questions in this test with each question having around four answer choices.

Questions & Answers

1
The region of the XOY-plane represented by the inequalities \({\text{x }} \geq {\text{ 6 }},{\text{ y }} \geq {\text{ 2 }},{\text{ 2x }} + {\text{ y }} \leq {\text{ 1}}0\) is
  • A
    a polygon
  • B
    exterior of a triangle
  • C
    unbounded
  • D
    none of these
    Correct
2
\( - {\text{ 3x }} + {\text{ 17 }} < {\text{ }} - {\text{ 13}}\), then
  • A
    \(x \in (10,\infty )\)
    Correct
  • B
    \(x \in [10,\infty )\)
  • C
    none of these
  • D
    \(x \in ( - \infty ,10]\)
3
If x is a real number and \({\text{| x | }} < {\text{ 3}}\), then
  • A
    \( - {\text{ 3 }} \leq {\text{x }} \leq {\text{ 3}}\)
  • B
    \( - {\text{ 3 }} < {\text{ x }} < {\text{ 3}}\)
    Correct
  • C
    \({\text{x }} \geq {\text{ }} - {\text{3}}\)
  • D
    none of these
4
If \({\text{| x}}--{\text{1}}{\text{| }} > {\text{5}}\), then
  • A
    \(x \in [6,\infty )\)
  • B
    \(x \in (6,\infty )\)
  • C
    \(x \in \left( { - \infty , - 4} \right)\mathop \cup \nolimits^ (6,\infty ]\)
  • D
    \(x \in \left( { - \infty , - 4} \right)\mathop \cup \nolimits^ (6,\infty )\)
    Correct
5
If \({\text{|x}} + {\text{2|}} \leq {\text{9}}\), then
  • A
    none of these.
  • B
    x \(\in \) ( - 7 , 11 )
  • C
    \({\text{x }} \geq {\text{ 11}}\)
  • D
    x \(\in \) [ - 11 , 7 ]
    Correct
6
The graph of the inequations \({\text{x }} \geq {\text{ }}0{\text{ }},{\text{ y }} \geq {\text{ }}0{\text{ }},{\text{ 3x }} + {\text{ 4y }} \leq {\text{ 12}}\)is
  • A
    interior of a triangle including the points on the sides
    Correct
  • B
    none of these
  • C
    in the \({{\rm{2}}^{{\rm{nd}}}}\) quadrant
  • D
    exterior of a triangle
7
The region of XOY plane, which is represented by the inqualities \( - {\text{2 }} \leq {\text{ x }} \leq {\text{ 2 }},{\text{ }} - {\text{2 }} \leq {\text{ y }} \leq {\text{ 2}}\)is
  • A
    a square
    Correct
  • B
    none of these
  • C
    a triangle
  • D
    a circle
8
The graph of the inequalities \({\text{x }} \geq {\text{ }}0{\text{ }},{\text{ y }} \geq {\text{ }}0{\text{ }},{\text{ 2x }} + {\text{ y }} + {\text{ 6 }} \leq {\text{ }}0\) is
  • A
    a square
  • B
    none of these
  • C
    a triangle
  • D
    { }
    Correct
9
The graph of the inequalities \({\text{x }} \geq {\text{ }}0{\text{ }},{\text{ y }} \geq {\text{ }}0{\text{ }},{\text{ 2x }} + {\text{ y }} + {\text{ 6 }} \geq 0\) is
  • A
    none of these
  • B
    that line of the XOY plane which lies above the line 2x + y + 6 = 0
  • C
    that line of the XOY plane which lies below the line 2x + y + 6 = 0
  • D
    the \({{\rm{1}}^{{\rm{st}}}}\) quadrant
    Correct
10
If x and b are real numbers . If b \(>\) 0 and \({\text{|x|}} > b\), then
  • A
    none of these
  • B
    \(x \in ( - b,\infty )\)
  • C
    \(x \in ( - b,b)\)
    Correct
  • D
    \(x \in \left( { - \infty , - b} \right)\mathop \cup \nolimits^ (b,\infty )\)
11
The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then.
  • A
    breadth \(≥\) 20
    Correct
  • B
    breadth \(>\) 20
  • C
    length \(<\) 20
  • D
    length \(≤\) 20
12
The graph of the inequations \({\text{x }} \leq {\text{ }}0{\text{ }},{\text{ y }} \leq {\text{ }}0{\text{ }},{\text{ and 2x }} + {\text{ y }} + {\text{ 6 }} \geq 0\) is
  • A
    exterior of a triangle
  • B
    in the \({{\rm{1}}^{{\rm{st}}}}\) quadrant
  • C
    a triangular region in the \({{\rm{3}}^{{\rm{rd}}}}\) quadrant
    Correct
  • D
    none of these
13
The graph of the inequality xy \(≥\) 0 is
  • A
    set of all points in the \({{\rm{2}}^{{\rm{nd}}}}\) and \({{\rm{4}}^{{\rm{th}}}}\) quadrants
  • B
    none of these
  • C
    set of all points in the first and \({{\rm{3}}^{{\rm{rd}}}}\) quadrant including the points on the axis .
    Correct
  • D
    set of all points on the x axis and y axis
14
The graph of the inequality \({x^2} + {y^2} > 0\) is
  • A
    none of these
  • B
    set of all points in the XOY plane other than the origin
    Correct
  • C
    the plane XOY
  • D
    set of all points in the XOY plane other than those which lies on the axes
15
The solution set of the inequation 3x \(<\) 5 , when x is a natural number is
  • A
    { 1}
  • B
    { 1 , 5/3 }
  • C
    { 0 ,1 }
    Correct
  • D
    { }