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 longest side of a triangle is three times the shortest side and the third side is 2cm shorter than the longest side if the perimeter of the triangles at least 61cm, find the minimum length of the shortest side.
  • A
    61cm
  • B
    11cm
  • C
    9cm
    Correct
  • D
    16cm
2
Which of the following is correct ?
  • A
    If -4 \(<\) 7 , then 4 \(<\) - 7
  • B
    If -2 \(<\) 5 , then 2 \(>\) 5
  • C
    If 0 \(>\) -7 , then 0 \(<\) 7
    Correct
  • D
    If 8 \(>\) 1 , then -8 \(>\) -1
3
Solve the inequality \({\text{3 }}--{\text{ 2}}x{\text{ }} \leq {\text{ 9}}\)
  • A
    none of these.
  • B
    \({\text{x }} \leq {\text{ }} - {\text{ 3}}\)
  • C
    \({\text{x }} \geq {\text{ }} - {\text{ 6}}\)
  • D
    \({\text{x }} \geq {\text{ }} - {\text{ 3}}\)
    Correct
4
Given that x is an integer, find the values of x which satisfy both \({\text{2x }} + {\text{ 3 }} > {\text{ 7}}\)and \({\text{x }} + {\text{ 4 }} < {\text{ 1}}0\)
  • A
    3 , 4 , 5
    Correct
  • B
    3
  • C
    4
  • D
    4 , 5
5
The solution for the simultaneous linear inequalities \({\text{2x }}--{\text{ 3 }} \leq {\text{ 7}}\) and \(--{\text{ x }} \leq {\text{ 2}}\) is :
  • A
    \( - {\text{ 5 }} \leq {\text{ x }} \leq {\text{ }} - {\text{ 2}}\)
  • B
    \( - {\text{ 1 }} < {\text{ x }} \leq {\text{ 2}}\)
  • C
    \( - {\text{ 2}} \leq {\text{x}} \leq {\text{5}}\)
    Correct
  • D
    none of these
6
x = 4 , 5 and 6 are the solutions for :
  • A
    \({\text{x }} > {\text{ 4 and x }} < {\text{ 7}}\)
  • B
    \({\text{x }} \geq {\text{ 4 and}}{\text{x }} < {\text{ 7}}\)
    Correct
  • C
    \({\text{x }} \geq {\text{ 4 and x }} \leq {\text{ 7}}\)
  • D
    \({\text{x }} > {\text{ 4 and x }} > {\text{ 7}}\)
7
What are the integer values of x which satisfy the inequalities \({\text{x }} > {\text{ }} - {\text{ 2 and}}{\text{x }} \leq {\text{ 2}}\) ?
  • A
    1 , 2, 3, 4
  • B
    none of these
  • C
    - 1 , 0 , 1 , 2, 3
  • D
    - 1 ,0 ,1 , 2
    Correct
8
Given that x is an integer , find the values of x which satisfy the simultaneous linear inequalities \({\text{2 }} + {\text{ x }} < {\text{ 6 and}}{\text{2 }} - {\text{3x }} < {\text{ }} - {\text{ 1}}\).
  • A
    2 , 3, 4,
  • B
    1 , 2 , 3
  • C
    1 , 2, 3, 4.
  • D
    2 , 3
    Correct
9
Solve : \({\text{3}}0x{\text{ }} < {\text{ 2}}00\), when x is a natural number :
  • A
    {4,5,6,7,8,9}
  • B
    {1,2,3,4,5,6,7}
  • C
    {2,3,4,5,6}
  • D
    { 1,2,3,4,5,6}
    Correct
10
The solution set for : \({\text{3x }}--{\text{ 7 }} > {\text{x }} + {\text{ 3}}\).
  • A
    ( 5, \(\infty \))
    Correct
  • B
    (- 5 , \(\infty \) )
  • C
    ( -5 , 5 )
  • D
    none of these.
11
he solution set for \(\left( {{\text{ x }} + {\text{ 3 }}} \right){\text{ }} + {\text{ 4 }} > {\text{ }} - {\text{ 2x }} + {\text{ 5}}\):
  • A
    none of these
  • B
    ( - \(\infty \) , - 2 )
  • C
    ( 2 , \(\infty \) )
  • D
    ( - 2 , \(\infty \) )
    Correct
12
Solve the system of inequalities \({\text{2x }} + {\text{ 5 }} \leq {\text{ }}0{\text{ }},{\text{ x }}--{\text{ 3 }} \leq {\text{ }}0\)
  • A
    \( x ≥ {5 \over 2}\)
  • B
    \( x ≤ - {5 \over 2}\)
    Correct
  • C
    \( x ≥ - {5 \over 2}\)
  • D
    \( x ≤ {5 \over 2}\)
13
Solve the system of inequalities \({\text{x }}--{\text{ 2 }} > {\text{ }}0{\text{ }},{\text{ 3x }} < {\text{ 18}}\)
  • A
    \({\text{1 }} < {\text{ x }} < {\text{ 3}}\)
  • B
    \({\text{3 }} < {\text{x }} < {\text{ 17}}\)
  • C
    \({\text{3 }} < {\text{ x }} < {\text{ 18}}\)
  • D
    \({\text{2 }} < {\text{ x }} < {\text{ 6}}\)
    Correct
14
Solve the system of inequalities \({\text{4x }} + {\text{ 3 }} \geq {\text{ 2x }} + {\text{ 17 }},{\text{ 3x }}--{\text{ 5 }} < {\text{ }} - {\text{ 2}}\)
  • A
    \(( - {3 \over 2},{2 \over 5})\)
  • B
    ( -2 , 2 )
  • C
    no solution
    Correct
  • D
    \(( - 4,12)\)
15
Solve the system of inequalities \(\left( {{\text{x }} + {\text{ 5 }}} \right){\text{ }}--{\text{ 7 }}\left( {{\text{ x }}--{\text{ 2 }}} \right){\text{ }} \geq {\text{ 4x }} + {\text{ 9 }},{\text{ 2 }}\left( {{\text{ x }}--{\text{ 3 }}} \right){\text{ }}--{\text{ 7 }}\left( {{\text{ x }} + {\text{ 5 }}} \right){\text{ }} \leq {\text{ 3x }}--{\text{ 9}}\)
  • A
    \( - {\text{ 9}}/{\text{4 }} \leq {\text{ x }} \leq {\text{ 1}}\)
  • B
    \( - {\text{ 1 }} \leq {\text{ x }} \leq {\text{ 1}}\)
  • C
    \( - {\text{ 4 }} \leq {\text{ x }} \leq {\text{ 1}}\)
    Correct
  • D
    \( - {\text{ 4 }} \leq {\text{ x }} \leq {\text{ 4}}\)