Please refer to the MCQ Questions for Class 11 Linear Inequalities with Answers. The following Linear Inequalities Class 11 Mathematics MCQ Questions have been designed based on the latest syllabus and examination pattern for Class 11. Our experts have designed MCQ Questions for Class 11 Linear Inequalities with Answers for all chapters in your NCERT Class 11 Mathematics book. You can access all MCQs for Class 11 Mathematics

**Linear Inequalities Class 11 MCQ Questions with Answers**

See below Linear Inequalities Class 11 Mathematics MCQ Questions, solve the questions and compare your answers with the solutions provided below.

**Question. If x is real, then function (x-a)(x-b)/(x-c) will assume all real values, provided**

(a) a > b > c

(b) a ≤ b ≤ c

(c) a > c > b

(d) a ≤ c ≤ b

## Answer

D

**Question: If the equation ax2+2BX-3C=0 has non-real roots and (3/C/4)<(a+b )then c is**

(a) < 0

(b) > 0

(c) ≥ 0

(d) = 0

## Answer

A

**Question: If α and β are the roots of ax2+bx+c=0, then the equation ax ^{2}-bx(x-1)+c(x-1)^{2}=0 has roots**

(a) α/1-α, β/1-β/1-β

(b) 1- α/α, 1-β/β

(c) α/α+1,β/β+1

(d) α+1/α,β+1/β

## Answer

C

**Question: The root of the equation 2 (1+i)X2-4(2-i)X-5-3i=0 where i =√-1,which has greater modulus, is**

(a) 3- 5i/2

(b) 5- 3i/2

(c) 3+i/2

(d) 3i+1/2

## Answer

A

**Question: The value of a for which the equations x ^{3} +ax+1 =0 and x^{4}+ax^{2}+1=0have a common root, is**

(a) -2

(b) -1

(c) 1

(d) 2

## Answer

A

**Question: If α and β are the roots of the equation ax2+bx+c=0 such that β<α< 0, then the quadratic equation whose roots are|α |,| β|, is given by**

## Answer

C

**Question: Suppose the quadratic equations x ^{2}+px+q=0 and x^{2}+ rx+ s 2=0 are such that p, q, r are s real and pr =2(q+s). Then,**

(a) both the equations always have real roots

(b) at least one equation always has real roots

(c) both the equations always have non-real roots

(d) at least one equation always has real and equal roots

## Answer

B

**Question:The number of real solutions of the equation**

(9/10)^{x}=-3+x-x^{2}is

(a) none

(b) one

(c) two

(d) more than two

## Answer

A

**Question: **

(a) -q/p

(b) αβ

(c) -p/q

(d) ω

(ω and ω^{2} are complex cube roots of unity)

## Answer

A

**Question: If x = ^{2}+2^{2/3}+2^{1/3}, then the value of x^{3}-6x^{2}+6x is**

(a) 3

(b) 2

(c) 1

(d) -2

## Answer

B

**Question: In writing an equation of the form ax ^{2}+bx+c=0; the coefficient of x is written incorrectly and roots are found to be equal. Again, in writing the same equation the constant term is written incorrectly and it is found that one root is equal to those of the previous wrong equation while the other is double of it. If a and b be the roots of correct equation, then ( α-β)^{2} is equal to**

(a) 5

(b) 5 α β

(c) – 4 α β

(d) – 4

## Answer

B

**Question: Let a ≠ 0 and p (x ) be a polynomial of degree greater than 2. If p (x ) leaves remainders a and a – when divided, respectively, by x+ a x a and x-a, the remainder when p (x) is divided by x ^{2}-a^{2} is**

(a) 2x

(b) -2x

(c) x

(d) -x

## Answer

D

**Question: If the equation ax ^{2}+2bx+3c=0 and 3x^{2}+8x+15=0 have a common root, where a b c , and are the lengths of the sides of a ΔABC,then sin^{2}A+sin^{2}B+sin^{2} is equal to**

(a) 1

(b) 3/2

(c) √2

(d) 2

## Answer

D

**Question: If the roots of the equation ax ^{2}– bx+ c =0 are α and β,then the roots of the equation b^{2}cx^{2}x-ab^{2}x+a^{3}=0 are**

## Answer

B

**Question: If roots of x ^{2}-(a-3)x+a=0 are such that atleastone of them is greater than 2, then**

(a) a ∈[7 , 9]

(b) a∈ [7, ∞)

(c) a ∈ [ 9,∞)

(d) a ∈[7,9)

## Answer

C

**Question: If a b∈ R, a≠0 and the quadratic equation ax ^{2}-bx+1=0 bx 2 has imaginary roots, then (a+b+1) ) a is**

(a) positive

(b) negative

(c) zero b

(d) dependent on the sign of b

## Answer

A

**Question: If the roots of the quadratic equation (4p-p ^{2}-5)x^{2}-2p-1)x+3p=0 lie on either side of unity, then the number of integral values of p is**

(a) 1

(b) 2

(c) 3

(d) 4

## Answer

B

**Question: The range of a for which the equation x ^{2}+ax-4=0 has its smaller root in the interval (-1 ,2) is**

(a) ( -∞,-3 )

(b) ( 0, 3)

(c) ( 0, ∞,)

(d) (- ∞,-3 ) ∪(0,∞)

## Answer

A

**Question: If α and β are the roots of ax ^{2}+bx+c=0 0, then and α+h,β +h are the roots of px^{2}+qx+r=0, then**

(a) h=1/2(b/a-q/p)

(b) b

^{2}-4ac/a

^{2}=q

^{2}-4pr/p

^{2}

(c) a/p=b/q=c/r

(d) None of the above

## Answer

(A,B)

**Question.****Consider the inequality 40x + 20y ≤ 120, where x and y are whole numbers. Then, its solution set is**

(a) (0, 0), (5, 5), (1, 1), (2, 2), (3, 0)

(b) (0, 0), (0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6)

(c) (1, 0), (2, 0), (3, 0), (4, 0), (5, 0)

(d) None of the above

## Answer

B

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

(a) 70

(b) 50

(c) 74

(d) 48

## Answer

A

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

(a) 8

(b) 6

(c) 4

(d) 3

## Answer

C

**Question.****In drilling world’s deepest hole it was found that the temperature T in degree Celcius, x km below** **the earth’s surface was given by T = 30 + 25 (x − 3),** **3 ≤ x ≤ 15. At what depth will the temperature be** **between 155°C and 205°C?**

(a) 10 to 12 km

(b) 8 to 10 km

(c) 8 to 10 km

(d) 15 to 18 km

## Answer

B

**Question: All the values of m for which both the roots of the equation x ^{2}– 2mx+m^{2} -1 =0 are greater than –2 but less than 4, lie in the interval**

(a) – 2<m<0

(b) m > 3

(c) – 1 < m<3

(d) 1 < m<4

## Answer

C

**Question:**

(a) –2, –32

(b) –2, 3

(c) –6, 3

(d) –6, –32

## Answer

A

**Question: The equation x ^{2}+a^{2}x+b^{2}=0 has two roots each of which exceeds a numbe r c, then**

(a) a

^{4}>4b

^{2}

(b) c

^{2}+a

^{2}c+b

^{2}>0

(c) – a

^{2}/2>c

(d) None of these

## Answer

(A,B,C)

**Question: If c ≠ 0 and the equation p/2x= a/x+c +b/x-c has two equal roots, then p can be**

(a) (√a- √b)^{2}

(b) (√a+√b)^{2}

(c) a+ b

(d) a- b

## Answer

(A,B)

**Question. For what value of l the sum of the squares of the roots of x2 +(2+λ)x – 1/2(1+λ) =0 is minimum ?**

(a) 3/2

(b) 1

(c) 1/2

(d) 11/4

## Answer

C

**Question. If a and b are the roots of the equation x2 – x + 1 = 0, then a2009 + b2009 is equal to **

(a) -2

(b) -1

(c) 1

(d) 2

## Answer

C

**Question. If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c = 0,**

(a) greater than 4ab

(b) less than 4ab

(c) greater than -4ab

(d) less than -4ab

## Answer

C

**Question. Let p, q ∈ {1, 2, 3, 4}. The number of equations of the form px2 + qx + 2+1 = 0 having real roots, is**

(a) 15

(b) 9

(c) 7

(d) 8

## Answer

C

**Question. The least value of c is**

(a) 4

(b) 6

(c) 7

(d) 5

## Answer

B

**Question. If the equations x ^{2} + 2x + 3 = 0 and ax^{2} + bx + c = 0, a, b, c ÎR, 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. Let a and b be the roots of the equation ax ^{2} + bx^{2} + c = 0 and g, d be the roots of the equation px2 + qx^{2} + r = 0. If a, b, g and d are in GP, then**

(a) q

^{2}ac b

^{2}pr = 2

(b) qac = bpr

(c) c

^{2}pq= r2ab = 2

(d) p

^{2}ab = a

^{2}qr

## Answer

A

**Question. Let a, b and c be real numbers a ¹ 0. If a is a root of a2x2 + bx2 + c = 0, b is a root of a2x2 – bx – c = 0 and 0 < a < b, then the equation a2x2 + 2bx +2c = 0 has a root of g that always satisfies**

(a) ϒ=(α+β)/2

(b) ϒ=α+β/2

(c) ϒ=α

(d) (α<ϒ<β

## Answer

D

**Question. sin x + cos x = y ^{2} – y + α has no value of x for any y, if a belongs to**

(a) (0, 3)

(b) (- 3, 0)

(c) (-

**∞**, – 3)

(d) ( 3, ∞)

## Answer

D

**Question. If roots of x ^{2} – ax + b = 0 are prime numbers, then**

(a) b is a prime number

(b) a is a composite number

(c) 1 + a + b is a prime number

(d) None of the above

## Answer

D

**Question. The value of a for which the equations x ^{3} +ax +1 = 0 and x^{4} + ax^{2} +1 = 0 have a common root, is**

(a) -2

(b) -1

(c) 1

(d) 2

## Answer

A

**Question. The number of real solutions of the equation (9/10)x = 3 + x – x ^{2} is**

(a) none

(b) one

(c) two

(d) more than two

## Answer

A

**Question. Suppose the quadratic equations x3 + px + q = 0 and x2 + rx + s = 0 are such that p, q, r and s are real and pr = 2(q + s). Then,**

(a) both the equations always have real roots

(b) atleast one equation always has real roots

(c) both the equations always have non-real roots

(d) atleast one equation always has real and equal roots

## Answer

B

**Question. In writing an equation of the form ax ^{2} + bx + c = 0; the coefficient of x is written incorrectly and roots are found to be equal. Again, in writing the same equation the constant term is written incorrectly and it is found that one root is equal to those of the previous wrong equation while the other is double of it. If a and b be the roots of correct equation, then (a – b)^{2} is equal to**

(a) 5

(b) 5 αβ

(c) – 4 αβ

(d) – 4

## Answer

A

**Question. If the equation ax ^{2} +2bx + 3c = 0 and 3x^{2} +8x + 15 = 0 have a common root, where a, b and c are the lengths of the sides of a DABC, then A + sin 2B + sin2C is equal to**

(a) 1

(b) 3/2

(c) 2

(d) 2

## Answer

D

**Question. If x = 2 + 2 ^{2/3}+ 2^{1/ 3}, then the value of x^{3} – 6x^{2} + 6x is**

(a) 3

(b) 2

(c) 1

(d) -2

## Answer

B

**Question. Let a ¹ 0 and p(x) be a polynomial of degree greater than 2. If p(x) leaves remainders a and – a when divided, respectively, by x ^{2} + a^{2} and x – a, the remainder when p(x) is divided by x^{2} – a^{2} is**

(a) 2x

(b) -2x

(c) x

(d) -x

## Answer

D

**Question. If a, b∈R, a ≠ 0 and the quadratic equation ax ^{2} – bx + 1 = 0 has imaginary roots, then (a + b + 1) is**

(a) positive

(b) negative

(c) zero

(d) dependent on the sign of b

## Answer

**Question. If roots of x ^{2} -( a – 3)x + a = 0 are such that atleast one of them is greater than 2, then**

(a) a ∈ [7, 9]

(b) a ∈ [7, ∞)

(c) a ∈ [9, ∞)

(d) a ∈ [7, 9)

## Answer

**Question. All the values of m for which both the roots of the equation x2 – 2mx + m2 – 1 = 0 are greater than –2 but less than 4, lie in the interval**

(a) -2 < m < 0

(b) m > 3

(c) -1 < m < 3

(d) 1 < m < 4

## Answer

C

**Question. If the roots of the quadratic equation (4p – p ^{2} – 5x) – (2p – 1)x + 3p = 0 lie on either side of unity, then the number of integral values of p is**

(a) 1

(b) 2

(c) 3

(d) 4

## Answer

B

**Question. The range of a for which the equation x ^{2} + ax – 4 = 0 has its smaller root in the interval (-1, 2) is**

**(a) (-∞, – 3)**

(b) (0, 3)

(c) (0, ∞)

(d) (-∞, – 3) ∪ (0, ∞)

## Answer

**Question. For x ^{2} – (α + 3)|x|+ 4 = 0 to have real solutions, then the range of a is**

(a) (-∞, -7] ∪ [1, ∞)

(b) (-3, ∞)

(c) (-∞, -7]

(d) [1, ∞)

## Answer

D

**Question. Leta and b be the roots of the equation x ^{2 }– x + p = 0 and g, d be the roots of x^{2 }– 4x + q. If α, β, γ and d are in GP, then integral values of pand q are respectively**

(a) –2, –32

(b) –2, 3

(c) –6, 3

(d) –6, –32

## Answer

A

**Question. The least value of a is**

(a) 4

(b) 6

(c) 7

(d) 5

## Answer

D

**Question. If the equation ax ^{2} + 2bx – 3c = 0 has non-real roots and (3c / 4) < (a + b), then c is**

(a) < 0

(b) > 0

(c) ≥ 0

(d) = 0

## Answer

A

**Question. If a and b are the roots of the equation ax ^{2} + bx + c = 0 such that β < a < 0, then the quadratic equation whose roots are|a |,|β|, is given by**

(a) |a|x

^{2}| b |x + |c | = 0

(b) | ax

^{2}| – b |x+c| |c | = 0

(c) |a|x

^{2}-| b |x + |c | = 0

(d) |a|x

^{2}– b |x| + c = 0

## Answer

C

**Question. The least value of b is**

(a) 10

(b) 11

(c) 13

(d) 15

## Answer

B

**Question. Let a and b be real and z be a complex number. If z ^{2} + az + b = 0 has two distinct roots on the line Re ( z) = 1, then it is necessary that**

(a) b Î(-1, 0)

(b) |b | = 1

(c) b Î[1, ∞)

(d) b Î(0, 1)

## Answer

C

**Question. IQ of a person is given by the formula IQ = MA/CA x 100****where, MA is mental age and CA is chronological age. If 80 ≤ IQ ≤ 140 for a group of 12 years children, then the range of their mental age is**

(a) 9.8 ≤ MA ≤ 16.8

(b) 10 ≤ MA ≤ 16

(c) 9.6 ≤ MA ≤ 16.8

(d) 9.6 ≤ MA ≤ 16.6

## Answer

C

**Question. If 5–2x/3 ≤ x/6 – 5, then x ∈**

(a) [2, ∞)

(b) [–8, 8]

(c) [4, ∞)

(d) [8, ∞)

## Answer

D

**Question. Which of the following is the solution set of 3x – 7 > 5x – 1 ∀ x ∈ R?**

(a) (–∞, –3)

(b) (–∞, –3]

(c) (–3, ∞)

(d) (–3, 3)

## Answer

A

**Question. Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below. **

Codes

A B C D

(a) 4 2 3 1

(b) 4 3 2 1

(c) 1 2 3 4

(d) 1 3 2 4

## Answer

B

**Question. The graph of the inequality 40x + 20y ≤ 120, x ≥ 0, y ≥ 0 is **

## Answer

D

**Question.** The solution set is

## Answer

B

**Question.** The solution set of the inequality 4x + 3 < 6x + 7 is

(a) [−2, ∞)

(b) (−∞, −2)

(c) (−2, ∞)

(d) None of these

## Answer

C

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

(a) x Î(10,∞)

(b) xÎ[10,∞)

(c) xÎ(−∞,10]

(d) xÎ[−10,10)

## Answer

D

**Question.** The solution set of 5x − 3 < 7, where x is an integer is

(a) {……, − 1, 0, 1}

(b) {……, − 3, − 2, − 1}

(c) (− ∞, 2)

(d) None of these

## Answer

A

**Question.** If 3x + 8 > 2, then which of the following is true?

(a) x Î{−1, 0, 1, 2,K}, when x is an integer

(b) x Î[−2, ∞), when x is a real number

(c) Both (a) and (b)

(d) None of the above

## Answer

A

**Question.** The solution set of 3(1 − x) < 2 (x + 4) is

(a) [− 1, ∞)

(b) (− 1, ∞)

(c) (− ∞, − 1]

(d) (−∞, 1)

## Answer

B

**Question.****The set of real x satisfying the inequality**

(a) (−∞, 8)

(b) (8, ∞)

(c) [8, ∞)

(d) (−∞, 8]

## Answer

C

**Question.****The solution set of 5x − 3 ≥ 3x − 5 is**

(a) (− 1, ∞)

(b) (1, ∞)

(c) [− 1, ∞)

(d) None of these

## Answer

C

**Question.****Which of the following is the solution set of the**

(a) (4, ∞)

(b) (−∞, 4)

(c) [4, ∞)

(d) (−∞, 4]

## Answer

A

**Question.****If 3 ≤ 3 t − 18 ≤ 18, then which one of the following is true?**

(a) 15 ≤ 2 t + 1 ≤ 20

(b) 8 ≤ t < 12

(c) 8 ≤ t + 1 ≤ 13

(d) 21 ≤ 3 t ≤ 24

## Answer

C

**Question.****The solution set of 2 ≤ 3x − 4 ≤ 5 is**

(a) [2, 3]

(b) (2, 3)

(c) (2, ∞)

(d) (− ∞, 3)

## Answer

A

**Question.** The solution set of the inequality 6 ≤ −3(2x −4) < 12 is

(a) (0, 1]

(b) [0, 1)

(c) [0, 1]

(d) (0, ∞)

## Answer

A

**Question.** The graphical solution of the system of linear**inequalities, 3x + 4y ≥ 12, y ≥ 1 and x ≥ 0, is**

## Answer

C

**Case Based MCQs**

**Shweta was teaching “method to solve a linear inequality in one variable” to her daughter.Step I Collect all terms involving the variable (x) on one side and constant terms on other side with the help of above rules and then reduce it in the form ax < b or ax £ b or ax > b or ax ≥ b.Step II Divide this inequality by the coefficient of variable (x). This gives the solution set of given inequality.Step III Write the solution set.**

**Based on above information, answer the following questions.**

**Question.** The solution set of 24x < 100, when x is a natural number is

(a) {1, 2, 3, 4}

(b) (1, 4)

(c) [1, 4]

(d) None of these

## Answer

A

**Question.** The solution set of 24x < 100, when x is an integer is

(a) {…… − 4, − 3, − 2, − 1, 0, 1, 2, 3, 4}

(b) (−∞, 4]

(c) [4, ∞]

(d) None of the above

## Answer

A

**Question.** The solution set of − 5x + 25 > 0 is

(a) [5, ∞)

(b) (− ∞, 5]

(c) (5, ∞)

(d) (− ∞, 5)

## Answer

D

**Question.** The solution set of 3x − 5 < x + 7 is

(a) (6, ∞)

(b) [6, ∞)

(c) (− ∞, 6)

(d) (− ∞, 6]

## Answer

C

**Question.** The solution set of

(a) (− ∞, 6]

(b) (−∞, 6)

(c) [6, ∞)

(d) None of these

## Answer

B

**A manufacturing company produces certain goods. The company manager used to make a data record on daily basis about the cost and revenue of these goods separately. The cost and revenue function of a product are given by C(x) = 20x + 4000 and R(x) = 60x + 2000, respectively, where x is the number of goods produced and sold.**

**Based on above information, answer the following questions.**

**Question.****How many goods must be sold to realise some profit?**

(a) x < 50

(b) x > 50

(c) x ≥ 50

(d) x ≤ 50

## Answer

B

**Question.** If the cost and revenue functions of a product are given by C(x) = 3x + 400 and R(x) = 5x + 20 respectively, where x is the number of items produced by the manufacturer, then how many items must be sold to realise some profit?

(a) x £ 190

(b) x ≥ 190

(c) x < 190

(d) x > 190

## Answer

D

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

(a) x is always positive

(b) x is always negative

(c) x is real number

(d) None of these

## Answer

D

**Question.** The solution set of 3x − 5 < x + 7, when x is a whole number is given by

(a) {0, 1, 2, 3, 4, 5}

(b) (− ∞, 6)

(c) [0, 5]

(d) None of these

## Answer

A

**Question.** Graph of inequality x > 2 on the number line is represented by

## Answer

B

**ASSERTION – REASON TYPE QUESTIONS**

**(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.****(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion****(c) Assertion is correct, reason is incorrect****(d) Assertion is incorrect, reason is correct.**

**Question. Assertion : The inequality ax + by < 0 is strict inequality.****Reason : The inequality ax + b ≥ 0 is slack inequality. **

## Answer

B

**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 : Graph of linear inequality in one variable is a visual representation.****Reason : If a point satisfying the line ax + by = c, then it will lie in upper half plane.**

## Answer

C

**Question. Assertion : A line divides the cartesian plane in two part(s).****Reason : If a point P(α, β) on the line ax + by = c, then aα + bβ = c. **

## Answer

B

**Question. Assertion : Each part in which a line divides the cartesian plane, is known as half plane.****Reason : A point in the cartesian plane will either lie on a line or will lie in either of half plane I or II. **

## Answer

B