{"id":17466,"date":"2022-05-28T12:00:26","date_gmt":"2022-05-28T06:30:26","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=17466"},"modified":"2022-05-28T12:32:53","modified_gmt":"2022-05-28T07:02:53","slug":"mcq-questions-for-class-11-maths-chapter-6","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/mcq-questions-for-class-11-maths-chapter-6\/","title":{"rendered":"MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers"},"content":{"rendered":"

Students can access the NCERT MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 11 Maths with Answers<\/a> during preparation and score maximum marks in the exam. Students can download the Linear Inequalities Class 11 MCQs Questions with Answers from here and test their problem-solving skills. Clear all the fundamentals and prepare thoroughly for the exam taking help from Class 11 Maths Chapter 6 Linear Inequalities Objective Questions.<\/p>\n

Linear Inequalities Class 11 MCQs Questions with Answers<\/h2>\n

Students are advised to solve the Linear Inequalities Multiple Choice Questions of Class 11 Maths to know different concepts. Practicing the MCQ Questions on Linear Inequalities Class 11 with answers will boost your confidence thereby helping you score well in the exam.<\/p>\n

Explore numerous MCQ Questions of Linear Inequalities Class 11 with answers provided with detailed solutions by looking below.<\/p>\n

Question 1.
\nIf -2 < 2x – 1 < 2 then the value of x lies in the interval
\n(a) (1\/2, 3\/2)
\n(b) (-1\/2, 3\/2)
\n(c) (3\/2, 1\/2)
\n(d) (3\/2, -1\/2)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (-1\/2, 3\/2)
\nGiven, -2 < 2x – 1 < 2
\n\u21d2 -2 + 1 < 2x < 2 + 1
\n\u21d2 -1 < 2x < 3
\n\u21d2 -1\/2 < x < 3\/2
\n\u21d2 x \u2208 (-1\/2, 3\/2)<\/p>\n<\/details>\n

\n

Question 2.
\nIf x\u00b2 < -4 then the value of x is
\n(a) (-2, 2)
\n(b) (2, \u221e)
\n(c) (-2, \u221e)
\n(d) No solution<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) No solution
\nGiven, x\u00b2 < -4
\n\u21d2 x\u00b2 + 4 < 0
\nWhich is not possible.
\nSo, there is no solution.<\/p>\n<\/details>\n

\n

Question 3.
\nIf |x| < -5 then the value of x lies in the interval
\n(a) (-\u221e, -5)
\n(b) (\u221e, 5)
\n(c) (-5, \u221e)
\n(d) No Solution<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) No Solution
\nGiven, |x| < -5
\nNow, LHS \u2265 0 and RHS < 0
\nSince LHS is non-negative and RHS is negative
\nSo, |x| < -5 does not posses any solution<\/p>\n<\/details>\n

\n

Question 4.
\nThe graph of the inequations x \u2264 0 , y \u2264 0, and 2x + y + 6 \u2265 0 is
\n(a) exterior of a triangle
\n(b) a triangular region in the 3rd quadrant
\n(c) in the 1st quadrant
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) a triangular region in the 3rd quadrant
\nGiven inequalities x \u2265 0 , y \u2265 0 , 2x + y + 6 \u2265 0
\nNow take x = 0, y = 0 and 2x + y + 6 = 0
\nwhen x = 0, y = -6
\nwhen y = 0, x = -3
\nSo, the points are A(0, 0), B(0, -6) and C(-3, 0)
\n\"MCQ
\nSo, the graph of the inequations x \u2264 0 , y \u2264 0 , and 2x + y + 6 \u2265 0 is a triangular region in the 3rd quadrant.<\/p>\n<\/details>\n

\n

Question 5.
\nThe graph of the inequalities x \u2265 0, y \u2265 0, 2x + y + 6 \u2264 0 is
\n(a) a square
\n(b) a triangle
\n(c) { }
\n(d) none of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) { }
\nGiven inequalities x \u2265 0, y \u2265 0, 2x + y + 6 \u2264 0
\nNow take x = 0, y = 0 and 2x + y + 6 = 0
\nwhen x = 0, y = -6
\nwhen y = 0, x = -3
\nSo, the points are A(0, 0), B(0, -6) and C(-3, 0)
\n\"MCQ
\nSince region is outside from the line 2x + y + 6 = 0
\nSo, it does not represent any figure.<\/p>\n<\/details>\n

\n

Question 6.
\nSolve: 2x + 1 > 3
\n(a) [-1, \u221e]
\n(b) (1, \u221e)
\n(c) (\u221e, \u221e)
\n(d) (\u221e, 1)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (1, \u221e)
\nGiven, 2x + 1 > 3
\n\u21d2 2x > 3 – 1
\n\u21d2 2x > 2
\n\u21d2 x > 1
\n\u21d2 x \u2208 (1, \u221e)<\/p>\n<\/details>\n

\n

This program is a multi purpose inequality solver<\/a>.<\/p>\n

Question 7.
\nThe solution of the inequality 3(x – 2)\/5 \u2265 5(2 – x)\/3 is
\n(a) x \u2208 (2, \u221e)
\n(b) x \u2208 [-2, \u221e)
\n(c) x \u2208 [\u221e, 2)
\n(d) x \u2208 [2, \u221e)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) x \u2208 [2, \u221e)
\nGiven, 3(x – 2)\/5 \u2265 5(2 – x)\/3
\n\u21d2 3(x – 2) \u00d7 3 \u2265 5(2 – x) \u00d7 5
\n\u21d2 9(x – 2) \u2265 25(2 – x)
\n\u21d2 9x – 18 \u2265 50 – 25x
\n\u21d2 9x – 18 + 25x \u2265 50
\n\u21d2 34x – 18 \u2265 50
\n\u21d2 34x \u2265 50 + 18
\n\u21d2 34x \u2265 68
\n\u21d2 x \u2265 68\/34
\n\u21d2 x \u2265 2
\n\u21d2 x \u2208 [2, \u221e)<\/p>\n<\/details>\n

\n

Question 8.
\nSolve: 1 \u2264 |x – 1| \u2264 3
\n(a) [-2, 0]
\n(b) [2, 4]
\n(c) [-2, 0] \u222a [2, 4]
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) [-2, 0] \u222a [2, 4]
\nGiven, 1 \u2264 |x – 1| \u2264 3
\n\u21d2 -3 \u2264 (x – 1) \u2264 -1 or 1 \u2264 (x – 1) \u2264 3
\ni.e. the distance covered is between 1 unit to 3 units
\n\u21d2 -2 \u2264 x \u2264 0 or 2 \u2264 x \u2264 4
\nHence, the solution set of the given inequality is
\nx \u2208 [-2, 0] \u222a [2, 4]<\/p>\n<\/details>\n

\n

Question 9.
\nSolve: -1\/(|x| – 2) \u2265 1 where x \u2208 R, x \u2260 \u00b12
\n(a) (-2, -1)
\n(b) (-2, 2)
\n(c) (-2, -1) \u222a (1, 2)
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) (-2, -1) \u222a (1, 2)
\nGiven, -1\/(|x| – 2) \u2265 1
\n\u21d2 -1\/(|x| – 2) – 1 \u2265 0
\n\u21d2 {-1 – (|x| – 2)}\/(|x| – 2) \u2265 0
\n\u21d2 {1 – |x|}\/(|x| – 2) \u2265 0
\n\u21d2 -(|x| – 1)\/(|x| – 2) \u2265 0
\n\"MCQ
\nUsing number line rule:
\n1 \u2264 |x| < 2
\n\u21d2 x \u2208 (-2, -1) \u222a (1, 2)<\/p>\n<\/details>\n

\n

Question 10.
\nIf x\u00b2 < 4 then the value of x is
\n(a) (0, 2)
\n(b) (-2, 2)
\n(c) (-2, 0)
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (-2, 2)
\nGiven, x\u00b2 < 4
\n\u21d2 x\u00b2 – 4 < 0
\n\u21d2 (x – 2) \u00d7 (x + 2) < 0
\n\u21d2 -2 < x < 2
\n\u21d2 x \u2208 (-2, 2)<\/p>\n<\/details>\n

\n

Question 11.
\nSolve: 2x + 1 > 3
\n(a) [1, 1)
\n(b) (1, \u221e)
\n(c) (\u221e, \u221e)
\n(d) (\u221e, 1)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (1, \u221e)
\nGiven, 2x + 1 > 3
\n\u21d2 2x > 3 – 1
\n\u21d2 2x > 2
\n\u21d2 x > 1
\n\u21d2 x \u2208 (1, \u221e)<\/p>\n<\/details>\n

\n

Question 12.
\nIf a is an irrational number which is divisible by b then the number b
\n(a) must be rational
\n(b) must be irrational
\n(c) may be rational or irrational
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) must be irrational
\nIf a is an irrational number which is divisible by b then the number b must be irrational.
\nEx: Let the two irrational numbers are \u221a2 and \u221a3
\nNow, \u221a2\/\u221a3 = \u221a(2\/3)<\/p>\n<\/details>\n

\n

Question 13.
\nSum of two rational numbers is ______ number.
\n(a) rational
\n(b) irrational
\n(c) Integer
\n(d) Both 1, 2 and 3<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) rational
\nThe sum of two rational numbers is a rational number.
\nEx: Let two rational numbers are 1\/2 and 1\/3
\nNow, 1\/2 + 1\/3 = 5\/6 which is a rational number.<\/p>\n<\/details>\n

\n

Question 14.
\nIf |x| = -5 then the value of x lies in the interval
\n(a) (-5, \u221e)
\n(b) (5, \u221e)
\n(c) (\u221e, -5)
\n(d) No solution<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) No solution
\nGiven, |x| = -5
\nSince |x| is always positive or zero
\nSo, it can not be negative
\nHence, given inequality has no solution.<\/p>\n<\/details>\n

\n

Question 15.
\nThe value of x for which |x + 1| + \u221a(x – 1) = 0
\n(a) 0
\n(b) 1
\n(c) -1
\n(d) No value of x<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) No value of x
\nGiven, |x + 1| + \u221a(x – 1) = 0, where each term is non-negative.
\nSo, |x + 1| = 0 and \u221a(x – 1) = 0 should be zero simultaneously.
\ni.e. x = -1 and x = 1, which is not possible.
\nSo, there is no value of x for which each term is zero simultaneously.<\/p>\n<\/details>\n

\n

Question 16.
\nIf x\u00b2 < -4 then the value of x is
\n(a) (-2, 2)
\n(b) (2, \u221e)
\n(c) (-2, \u221e)
\n(d) No solution<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (d) No solution
\nGiven, x\u00b2 < -4
\n\u21d2 x\u00b2 + 4 < 0
\nWhich is not possible.
\nSo, there is no solution.<\/p>\n<\/details>\n

\n

Question 17.
\nThe solution of |2\/(x – 4)| > 1 where x \u2260 4 is
\n(a) (2, 6)
\n(b) (2, 4) \u222a (4, 6)
\n(c) (2, 4) \u222a (4, \u221e)
\n(d) (-\u221e, 4) \u222a (4, 6)<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) (2, 4) \u222a (4, 6)
\nGiven, |2\/(x – 4)| > 1
\n\u21d2 2\/|x – 4| > 1
\n\u21d2 2 > |x – 4|
\n\u21d2 |x – 4| < 2
\n\u21d2 -2 < x – 4 < 2
\n\u21d2 -2 + 4 < x < 2 + 4
\n\u21d2 2 < x < 6
\n\u21d2 x \u2208 (2, 6), where x \u2260 4
\n\u21d2 x \u2208 (2, 4) \u222a (4, 6)<\/p>\n<\/details>\n

\n

Question 18.
\nThe solution of the function f(x) = |x| > 0 is
\n(a) R
\n(b) R – {0}
\n(c) R – {1}
\n(d) R – {-1}<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (b) R – {0}
\nGiven, f(x) = |x| > 0
\nWe know that modulus is non negative quantity.
\nSo, x \u2208 R except that x = 0
\n\u21d2 x \u2208 R – {0}
\nThis is the required solution<\/p>\n<\/details>\n

\n

Question 19.
\nSolve: |x – 1| \u2264 5, |x| \u2265 2
\n(a) [2, 6]
\n(b) [-4, -2]
\n(c) [-4, -2] \u222a [2, 6]
\n(d) None of these<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (c) [-4, -2] \u222a [2, 6]
\nGiven, |x – 1| \u2264 5, |x| \u2265 2
\n\u21d2 -(5 \u2264 (x – 1) \u2264 5), (x \u2264 -2 or x \u2265 2)
\n\u21d2 -(4 \u2264 x \u2264 6), (x \u2264 -2 or x \u2265 2)
\nNow, required solution is
\nx \u2208 [-4, -2] \u222a [2, 6]<\/p>\n<\/details>\n

\n

Question 20.
\nThe solution of the 15 < 3(x – 2)\/5 < 0 is
\n(a) 27 < x < 2
\n(b) 27 < x < -2
\n(c) -27 < x < 2
\n(d) -27 < x < -2<\/p>\n

\nAnswer<\/span><\/summary>\n

Answer: (a) 27 < x < 2
\nGiven inequality is:
\n15 < 3(x – 2)\/5 < 0
\n\u21d2 15 \u00d7 5 < 3(x – 2) < 0 \u00d7 5
\n\u21d2 75 < 3(x – 2) < 0
\n\u21d2 75\/3 < x – 2 < 0
\n\u21d2 25 < x – 2 < 0
\n\u21d2 25 + 2 < x < 0 + 2
\n\u21d2 27 < x < 2<\/p>\n<\/details>\n

\n

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Students can access the NCERT MCQ Questions for Class 11 Maths Chapter 6 Linear Inequalities with Answers Pdf free download aids in your exam preparation and you can get a good hold of the chapter. Use MCQ Questions for Class 11 Maths with Answers during preparation and score maximum marks in the exam. Students can …<\/p>\n

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