# MCQs for Mathematics Class 11 with Answers Chapter 6 Linear Inequalities

Students of class 11 Mathematics should refer to MCQ Questions Class 11 Mathematics Linear Inequalities with answers provided here which is an important chapter in Class 11 Mathematics NCERT textbook. These MCQ for Class 11 Mathematics with Answers have been prepared based on the latest CBSE and NCERT syllabus and examination guidelines for Class 11 Mathematics. The following MCQs can help you to practice and get better marks in the upcoming class 11 Mathematics examination

**Chapter 6 Linear Inequalities MCQ with Answers Class 11 Mathematics**

MCQ Questions Class 11 Mathematics Linear Inequalities with answers provided below have been prepared by expert teachers of grade 11. These objective questions with solutions are expected to come in the upcoming Standard 11 examinations. Learn the below provided MCQ questions to get better marks in examinations.

**Question. The cost and revenue functions of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of items produced and sold. How many items must be sold to realise some profit? **

(a) Less than 40

(b) More than 50

(c) Less than 50

(d) Exactly 50

**Answer**

B

**Question: The quadratic equations x ^{2}-6x+a=0 and x^{2}-cx+6=0 have one root in common. The other roots of the first and second equations are integers in the ratio 4 3: . Then, the common root is **

(a) 2

(b) 1

(c) 4

(d) 3

**Answer**

A

**Question: If α and β are the roots of the equation x ^{2}-x+1=0, then a 2009+ β^{2009} is equal to**

(a) -2

(b) -1

(c) 1

(d) 2

**Answer**

C

**Question: If the equations x ^{2}+2x+3=0 and ax^{2}+bx+c=0, a,bc∈R,Î have a common root, then a: b: c is**

(a) 1 : 2 : 3

(b) 3 : 2 : 1

(c) 1 : 3 : 2

(d) 3 : 1 : 2

**Answer**

A

**Question: If the roots of the equation bx ^{2}+cx+a=0 be imaginary, then for all real values of x, the expression 3b^{2}x^{2}+6bcx+2c^{2} **

(a) greater than 4ab

(b) less than 4ab

(c) greater than -4ab

(d) less than -4ab

**Answer**

C

**Question: If the roots of the quadratic equation x ^{2}+px+q=0 are tan 30° and tan 15°, then the value of 2+q-p is**

(a) 3

(b) 0

(c) 1

(d) 2

**Answer**

A

**Question: All the values of m for which both roots of the equation x ^{2}-2mx+m^{2}-1=0 are greater than -2**

**but less than 4 lie in the interval**

(a) m > 3

(b) -1 <m<3

(c) 1 < m<4

(d) – 2<m<0

**Answer**

B

**Question: If the difference between the roots of the equation x ^{2}+ax+1=0 is less than √5, then the set of possible values of a is **

(a) (-3 3,)

(b) (-3,∞)

(c) (3,∞)

(d) (-∞,-3)

**Answer**

A

**Question: The value of a for which the sum of the squares of the roots of the equation x ^{2}-(a-2)x-a-1=0 the least value is **

(a) 2

(b) 3

(c) 0

(d) 1

**Answer**

D

**Question: If the cube roots of unity are 1,ω and ω ^{2},, then the roots of the equation (x -1)^{3}+8=0, are **

**Answer**

B

**Question: If both the roots of the quadratic equation x ^{2}-2kx+k^{2}-5=0 are less than 5, than k lies in the interval **

(a) [4, 5]

(b) (-∞,4)

(c) (6 ,∞)

(d) (5, 6]

**Answer**

B

**Question: If the roots of the equation x ^{2}-bx+c=0 be two consecutive integers, then b^{2}-4c equals **

(a) 1

(b) 2

(c) 3

(d) -2

**Answer**

A

**Question:**

(a) equal to α

(b) greater than or equal to α

(c) smaller than α

(d) greater than α

**Answer**

C

**Question: If one root of the equation x ^{2}+px+12=0 is 4, while the equation x^{2}+ px+q=0 has equal roots, then the value of q is **

(a) 49/4

(b) 12

(c) 3

(d) 4

**Answer**

A

**Question: If (1 – p) is a root of quadratic equation x ^{2}+px+(1-_{p})=0,then its roots are **

(a) 0, 1

(b) – 1, 1

(c) 0, -1

(d) – 1, 2

**Answer**

C

**Question: If the sum of the roots of the quadratic equation ax ^{2}+bx+c=0 is equal to the sum of the squares of their reciprocals, then a/c, b/a, and c/b are in**

(a) arithmetic progression

(b) geometric progression

(c) harmonic progression

(d) arithmetico-geometric progression

**Answer**

C

**Question: Let two numbers have arithmetic mean 9 and geometric mean 4. Then, these numbers are the roots of the quadratic equation **

(a) x^{2}+18x+16=0

(b) x^{2}-18x+16=0

(c) x^{2}+18x-16=0

(d) x^{2}-18x-16=0

**Answer**

B

**Question: The value of a for which one root of the quadratic equation (a ^{2}-5a+3) x^{2}+3a-1)x+2 is twice as large as the other, is **

(a) 2/3

(b) -2/3

(c) 1/3

(d) -1/3

**Answer**

A

**Question:**

**Answer**

B

**Question: The number of the real solutions of the equation x ^{2}-3|x|+2=0 is**

(a) 2

(b) 4

(c) 1

(d) 3

**Answer**

B

**Question. If 3x – 7 < 5 + x, 11 – 5 x ≤ 1, then x ∈ **

(a) [2, 6]

(b) [–2, 6]

(c) [2, 6)

(d) (–2, 6)

**Answer**

C

**Question. If 7x + 3 < 5x + 9 then x ∈ **

(a) (–∞, 3]

(b) (–∞, ∞)

(c) (–∞, 3)

(d) [3, ∞)

**Answer**

C

**Question. If −5 ≤ 5 – 3x/2 ≤ 8, then x ∈ **

(a) [-11/3 , 5]

(b) [–5, 5]

(c) [-11/3, ∞]

(d) (– ∞, ∞)

**Answer**

A

**Question. If 1 ≤ |x –2| ≤ 3, then x ∈ **

(a) [–1, 5]

(b) [–1, 1] ∪ [3, 5]

(c) (–1, 0) ∪ (2, 5)

(d) (–1, 5)

**Answer**

B

**Question. Solution of |x2 – 10| ≤ 6 is **

(a) (2, 4)

(b) (– 4, – 2)

(c) (– 4, – 2) ∪ (2, 4)

(d) [– 4, – 2] ∪ [2, 4]

**Answer**

D

**Question. If |2x – 3| < |x + 5|, then x belongs to **

(a) (–3, 5)

(b) (5, 9)

(c) (-2/3 ,8)

(d) (-8, 2/3)

**Answer**

C

**Question. (i) x ≥ 2**

(ii) y ≥ 3

(iii) 5x + 4y ≤ 40

(iv) 8x + 3y ≤ 10

(v) x ≤ 0

(a) (i), (ii) and (iv)

(b) (i), (ii) and (iii)

(c) only (iii) and (iv)

(d) (ii), (iii) and (v)

**Answer**

B

**Question. If the expression (mx – 1 + 1/x) is always nonnegative, then the minimum value of m must be **

(a) -1/2

(b) 0

(c) 1/4

(d) 1/2

**Answer**

C

**Question. Solution of l1 + 3/xl > 2 is **

(a) (0, 3]

(b) [–1, 0)

(c) (–1, 0) ∪ (0, 3)

(d) None of these

**Answer**

C

**Question. If (x – 1)(x2 – 5x + 7) < (x – 1), then x belongs to **

(a) (1, 2) ∪ (3, ∞)

(b) (2, 3)

(c) (–∞, 1) ∪ (2, 3)

(d) None of these

**Answer**

C

**Question. If 4x + 3 < 6x + 7, then x ∈ **

(a) (2, ∞)

(b) (–2, ∞)

(c) (–∞, 2)

(d) (– ∞, ∞)

**Answer**

B

**Question. If |x + 2| ≤ 9, then **

(a) x ∈(–7, 11)

(b) x ∈[–11, 7]

(c) x ∈(– ∞, –7) ∪ (11, ∞)

(d) x ∈(– ∞, –7) ∪ [11, ∞)

**Answer**

B

**Question. The inequality representing the following graph is: **

(a) |x| < 5

(b) |x| ≤ 5

(c) |x| > 5

(d) |x| ≥ 5

**Answer**

A

**Question. If x – 2/x + 5 > 2 , then x ∈ **

(a) (–12, 5)

(b) (–12, –5)

(c) (–5, 12)

(d) (5, 12)

**Answer**

B

**Question. Solution of (x – 1)2(x + 4) < 0 is **

(a) (– ∞, 1)

(b) (–∞, –4)

(c) (– 1, 4)

(d) (1, 4)

**Answer**

B

**Question. Which of the following statements is correct? **

(a) If x > y and b < 0, then bx < by

(b) If x > y, then x > 0 and y < 0

(c) If xy < 0, then x > 0 and y > 0

(d) All of these

**Answer**

A

**Question. (i) x + 2y ≤ 8 **

(ii) x ≥ 0, y ≥ 0

(iii) x ≤ 0, y ≤ 0

(iv) 2x + y ≤ 8

(v) 4x + 5y ≥ 40

(a) (i), (iii) and (v)

(b) (i), (iv) and (v)

(c) (i), (iii) and (iv)

(d) (i), (ii) and (iv)

**Answer**

D

**Question. Solution of | 3x + 2 | < 1 is **

(a) [-1, -1/3]

(b) {-1/3 , -1}

(c) (-1, – 1/3)

(d) None of these

**Answer**

C

**Question. Solution of |x+ 1/x | > 2 is **

(a) R – {0}

(b) R – {–1, 0, 1}

(c) R – {1}

(d) R – {–1, 1}

**Answer**

B

**Question. The marks obtained by a student of Class XI in first and second terminal examination are 62 and 48, respectively. Find the minimum marks he should get in the annual examination to have an average of at least 60 marks. **

(a) 50

(b) 60

(c) 70

(d) 80

**Answer**

C

**Question. The length of a rectangle is three times the breadth. If the minimum perimeter of the rectangle is 160 cm, then **

(a) breadth > 20 cm

(b) length < 20 cm

(c) breadth ≥ 20 cm

(d) length ≤ 20 cm

**Answer**

C

**Question. Solution of |3 – x| = 3 – x is **

(a) x < 3

(b) x > 3

(c) x ≥ 3

(d) x ≤ 3

**Answer**

D

**Question. Solution of 2x – 1 = | x + 7| is **

(a) – 2

(b) 8

(c) – 2, 8

(d) None of these

**Answer**

B

**Question. Solution of 2x-3/3x – 5 ≥ 3 is **

(a) [1,12/7]

(b) (5/3 , 12/7]

(c) (–∞ , 5/3)

(d) [2/7, ∞)

**Answer**

B

**Question. Solution of |x+ 1/x | < 4 is **

(a) (2 − 3, 2 + 3)∪(−2 − 3,− 2 + 3)

(b) R − (2 − 3, 2 + 3)

(c) R − (−2 − 3, − 2 + 3)

(d) none of these

**Answer**

A

**Question. Solution of |x – 1| ≥ | x – 3| is **

(a) x ≤ 2

(b) x ≥ 2

(c) [1, 3]

(d) None of these

**Answer**

B

**Question. The set of values of x which satisfy the inequations 5x + 2 < 3x + 8 and x + 2/x – 1 < 4 is **

(a) (– ∞, 1)

(b) (2, 3)

(c) (– ∞, 3)

(d) (– ∞, 1) ∪ (2, 3)

**Answer**

D

**Question. Solution of 0 < |3x + 1| < 1/3 is **

(a) (-4/9 , 2/9)

(b) [-4/9 , -2/9]

(c) (-4/9 , -2/9) – {-1/3}

(d) [-4/9 , -2/9] – {-1/3}

**Answer**

C

**Question. Find all pairs of consecutive odd natural numbers, both of which are larger than 10, such that their sum is less than 40. **

(a) (11, 13), (13, 15), (15, 17), (17, 19)

(b) (11, 13), (13, 15), (15, 17)

(c) (21, 23), (23, 25), (25, 27), (27, 29)

(d) (15, 17), (17, 19), (19, 21), (21, 23)

**Answer**

A

**Question. Solutions of the inequalities comprising a system in variable x are represented on number lines as given below, then 36 **

(a) x ∈(– ∞, –4] ∪ [3, ∞)

(b) x ∈ [–3, 1]

(c) x ∈(– ∞, –4) ∪ [3, ∞)

(d) x ∈ [–4, 3]

**Answer**

B

**Question. If –3x + 17 < –13, then **

(a) x ∈ (10, ∞)

(b) x ∈ [10, ∞)

(c) x ∈ (–∞, 10)

(d) x ∈ [–10, 10)

**Answer**

A

**Question. If |x + 3| ≥10, then **

(a) x ∈(–13, 7]

(b) x ∈(–13, 7)

(c) x ∈(– ∞, –13] ∪ [7, ∞)

(d) x ∈(– ∞, –13) ∪[7, ∞)

**Answer**

C

**Question. Solution of x – 7/x +3 > 2 is **

(a) (– 3, ∞)

(b) (– ∞, –13)

(c) (– 13, –3)

(d) (– 13, 3)

**Answer**

C

**Question. If lx -2 l/x – 2 ≥ 0 then x ∈ **

(a) [2, ∞)

(b) (2, ∞)

(c) (–∞, 2)

(d) (–∞, 2]

**Answer**

B

**Question. x and b are real numbers. If b > 0 and |x| > b, then **

(a) x ∈(–b, ∞)

(b) x ∈(– ∞, b)

(c) x ∈(–b, b)

(d) x ∈(– ∞, –b) ∪ (b, ∞)

**Answer**

D

**Question. If |3 – 4x| ≥ 9, then x ∈ **

(a) (–∞, –3) ∪ (3, ∞)

(b) (−∞ , -3/2] ∪ (3 , ∞)

(c) (−∞ ,-3/2] ∪ (0 , ∞)

(d) (−∞ ,-3/2] ∪ [3 , ∞)

**Answer**

D

**Question. The inequality 2/x < 3 is true, when x belongs to **

(a) [2/3 , ∞)

(b) (–∞ , 2/3)

(c) (–∞ ,0) ∪(2/3,∞)

(d) None of these

**Answer**

C

**Question. If |x – 1| > 5, then **

(a) x ∈(–4, 6)

(b) x ∈[–4, 6]

(c) x ∈(– ∞, –4) ∪ (6, ∞)

(d) x ∈(– ∞, –4) ∪ [6, ∞)

**Answer**

C

**Question. If –8 ≤ 5x – 3 < 7, then x ∈ **

(a) (–1, 2)

(b) [–1, 2)

(c) [–2, ∞)

(d) [–2, 0)

**Answer**

B

**Assertion & Reasoning Based **

**(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.****(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.****(c) Assertion is correct statement but Reason is wrong statement.****(d) Assertion is wrong statement but Reason is correct statement.**

**Question. Assertion : If –5 ≤ 2x + 9 ≤ 2, then x ∈ [–7, –3.5]. ****Reason : The graphical representation of –5 ≤ 2x + 9 ≤ 2 is**

**Answer**

A

**Question. Assertion : |3x – 5| > 9 ⇒ x∈ (– ∞ , -4/3)∪ (14/3 , ∞) . ****Reason : The region containing all the solutions of an inequality is called the solution region.**

**Answer**

B

**Question. Assertion : If 11x – 9 ≤ 68, then x ∈ (–∞, 7). ****Reason : If an inequality consist of signs ≤ or ≥, then the point on the line are also included in the solution region.**

**Answer**

D

**Question. Assertion : If x ≥ – 3, then x + 5 ≥ 2. ****Reason : Same number can be added to both sides of the inequality without changing the sign of inequality.**

**Answer**

A

**Question. Assertion : If a < b, c < 0, then a/c < b/c . ****Reason : If both sides are divided by the same negative quantity, then the inequality is reversed.**

**Answer**

D

We hope the above MCQ Questions Class 11 Mathematics Linear Inequalities with answers based on the latest syllabus and examination guidelines issued by CBSE, NCERT and KVS are really useful for you. Linear Inequalities is an important chapter in Class 11 as it provides very strong understanding about this topic. Students should go through the answers provided for the MCQs after they have themselves solved the questions. All MCQs have been provided with four options for the students to solve. These questions are really useful for benefit of class 11 students. Please go through these and let us know if you have any feedback in the comments section.