Please refer to MCQ Questions Chapter 6 Linear Inequalities Class 11 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 11 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 11 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 6 Linear Inequalities in Class 11 Mathematics provided below to get more marks in exams.

**Chapter 6 Linear Inequalities MCQ Questions**

Please refer to the following **Chapter 6 Linear Inequalities MCQ Questions Class 11 Mathematics** with solutions for all important topics in the chapter.

**MCQ Questions Answers for Chapter 6 Linear Inequalities Class 11 Mathematics**

**Question. If a root of the equation ax ^{2} + bx + c = 0 be reciprocal of a root of the equation a′ x^{2} + b′x + c′ = 0′ then**

(a) (cc′ – aa′ )^{2} = (ba′ – cb′)(ab′ – bc′)

(b) (bb′ – aa′ )

^{2}= (ca′ – bc′)(ab′ – bc′)

(c) (cc′ – aa′ )

^{2}= (ba′ + cb′)(ab′ + bc′)

(d) None of the above

## Answer

A

**Question. If the product of the roots of the equation (a + 1)x ^{2} + (2a + 3)x + (3a + 4) = 0 is 2, then the sum of roots is**

(a) 1

(b) -1

(c) 2

(d) -2

## Answer

B

**Question. The system y (x ^{2} + 7x + 12) = 1 and x + y = 6,y > 0 has**

(a) no solution

(b) one solution

(c) two solutions

(d) more than 2 solutions

## Answer

D

**Question. If [x] ^{2} = [x + 2], where [x] = the greatest integer less than or equal to x, then x must be such that**

(a) x = 2, -1

(b) [-1, 0) ∪ [2, 3)

(c) x ∈ [-1, 0)

(d) None of these

## Answer

B

**Question. If α, β and γ are the roots of the equation x ^{3} – 7x – = 0, then 1/α^{4} +1/β^{4} + 1/γ^{4} is**

(a) 7/3

(b) 3/7

(c) 4/7

(d) 7/4

## Answer

B

**Question. If the roots of the equation a/x-b + β/x-β = 1 be equal inmagnitude but opposite in sign, thena + b is equal to**

(a) 0

(b) 1

(c) 2

(d) None of these

## Answer

A

**Question. The least value of |a|for which tan q and cotq are roots of the equation x ^{2} + ax 2 +1 = 0, is**

(a) 2

(b) 1

(c) 1/2

(d) 0

## Answer

A

**Question. The harmonic mean of the roots of the equation (5 + √2)x ^{2} – (4 + √5)x + 8 + 2√5 = 0 is**

(a) 2

(b) 4

(c) 6

(d) 8

## Answer

B

**Question. If a + b + c = 0, then the roots of the equation 4ax ^{2} + 3bx + 2c= are**

(a) equal

(b) imaginary

(c) real

(d) None of these

## Answer

C

**Question. If a < b < c < d, then the roots of the equation (x – a)(x – c) + 2(x – b)(x – d) = 0 are**

(a) real and distinct

(b) real and equal

(c) imaginary

(d) None of these

## Answer

A

**Question. If the roots of the equation qx ^{2} + px + q = 0 are complex, where pand qare real, then the roots of the equation qx^{2} + 4qx + p= 0 are**

(a) real and unequal

(b) real and equal

(c) imaginary

(d) None of these

## Answer

A

**Question. If x1 x ^{2} and x3, and are distinct roots of the equation ax^{2} + bx +c = 0, then**

(a) a = b = 0, c ∈ R

(b) a = c = 0, b ∈ R

(c) b

^{2}– 4ac ≥ 0

(d) a = b = c = 0

## Answer

D

**Question. If 4x ^{2} + 2x + 2xy + my = 0 has two rational factors, then the values of m will be**

(a) – 6, – 2

(b) – 6, 2

(c) 6, – 2

(d) 6, 2

## Answer

C

**Question. The minimum value of P = bcx + cay + abz, when xyz = abc, is**

(a) 3abc

(b) 6abc

(c) abc

(d) 4abc

## Answer

A

**Question. Let f (x) = x ^{2} + ax + b; a, b∈ R.If f (1) + f (2) + f (3) = 0, then the roots of the equation f (x) = 0**

(a) are imaginary

(b) are real and equal

(c) are from the set {1, 2, 3}

(d) real and distinct

## Answer

D

**Question. If sin a, sin b and cos a are in GP, then roots of x ^{2} + 2xcotb + 1 = 0 are always**

(a) real

(b) real and negative

(c) greater than one

(d) non-real

## Answer

A

**Question. If a < b < c < d, then the roots of the equation (x – a)(x – c) + 2(x – b)(x – d) = 0 are**

(a) real and distinct

(b) real and equal

(c) imaginary

(d) None of these

## Answer

A

**Question. If the roots of the equation x ^{2} + px + q = 0area andb and roots of the equation x^{2}-xr+ s= 0 are α^{4} and β^{4} and , then the roots of the equation x^{2} – 4qx +2q^{2} = 0 are**

(a) both negative

(b) both positive

(c) both real

(d) one negative and one positive

## Answer

C

**Question. If a > 0, b > 0, c > 0, then both the roots of the equation ax ^{2}+ bx+ c = 0**

(a) are real and negative

(b) have negative real part

(c) are rational numbers

(d) None of these

## Answer

B

**Question. If (ax ^{2}+c) y (a’ x2 + c’ ) = 0 and x is a rational function of y and ac is negative, then**

(a) ac’ + a’c = 0

(b) a/a’ = c/c’

(c) a2 + c2 + 2 = a’2 + c’2

(d) aa’ + cc’ = 1

## Answer

B

**Question. If roots of the equation (a – b)x ^{2} + (c – a)x + (b – c) = 0 are equal, then a, b and c are in**

(a) AP

(b) HP

(c) GP

(d) None of these

## Answer

A

**Question. Let a, b be the roots of x ^{2} – 2x cosΦ + 1 = 0, then the equation whose roots are ^{α}n and β^{n} , is**

(a) x

^{2}– 2xcosnΦ – 1 = 0

(b) x

^{2}– 2xcosnΦ + 1 = 0

(c) x

^{2}– 2xcosnΦ + 1 = 0

(d) x

^{2}+ 2xcosnΦ – 1 = 0

## Answer

B

**Question. If a and b are the roots of the equation ax ^{2}+ bx +c = 0, then the equation whose roots are α+1/β and β+1/α**

(a) acx

^{2}+ (a+c)bx +(a+c)

^{2}= 0

(b) abx

^{2}+ (a+c)bx +(a+c)

^{2}= 0

(c) acx

^{2}+ (a+c)cx +(a+c)

^{2}= 0

(d) None of the above

## Answer

A

**Question. (a ^{2} – 3a +2)x2 + (a^{2} – 5a + 6)x + a -2 = r for three distinct values of x for some r ∈ R, if a + r is equal to**

(a) 1

(b) 2

(c) 3

(d) does not exist

## Answer

B

**Question. If the equation x ^{2} + 9y – 4x + 3 = 0 is satisfied values of x and y, then**

(a) 1 ≤ x ≤ 3

(b) 2 ≤ x ≤ 3

(c) -1/3 < y < 1

(d) 0 < y < 2/3

## Answer

A

**Question. If atleast one root of the equation x ^{3} + ax^{2} + bx + c = 0 remains unchanged, when a, b and c are decreased by one, then which one of the following is always a root of the given equation ?**

(a) 1

(b) -1

(c) ω, an imaginary cube root of unity

(d) i

## Answer

C

**Question. Let a, b be the roots of x2 – 2xcos φ + 1 = 0, then the equation whose roots are a n bn and , is**

(a) x^{2} – 2xcosnφ – 1 = 0

(b) x^{2} – 2xcosnφ – 1 = 0

(c) x^{2} – 2xcosnφ – 1 = 0

(d) x^{2} – 2xcosnφ – 1 = 0

## Answer

B

**Question. If the roots of the equation ( p ^{2}+ q^{2} )x^{2} – 2q(p + r)x+ (q^{2} + r^{2}) = 0 be real and equal, then p, q and r will be in**

(a) AP

(b) GP

(c) HP

(d) None of these

## Answer

B

**Question. If roots of the equation ax ^{2}+ bx+c = 0; (a, b, c ∈ N) are rational numbers, then which of the following cannot be true ?**

(a) All a , b and c are even

(b) All a , b and c are odd

(c) b is even while a and c are odd

(d) None of the above

## Answer

D

**Question. If atleast one root of 2x ^{2} + 3x + 5 = 0 and ax^{2} + bx + c = 0, a, b, c ∈ N is common, then the maximum value of a + b + c is**

(a) 10

(b) 0

(c) does not exist

(d) None of these

## Answer

C

**Question. If x ^{2} + 2ax + b ≥ c ∀ x ∈ R, then**

(a) b – c ≥ a

^{2}

(b) c – a ≥ b

^{2}

(c) a – b ≥ c

^{2}

(d) None of these

## Answer

A

**Question. If a _{i} > 0 for i = 1, 2, …, n and a_{1}a_{2}…….a_{n}= 1, then minimum value of (1+a_{1})(1+a_{2})….(1+ a_{n}) is**

(a) 2

^{n/2}

(b) 2

^{n}

(c) 22

^{n}

(d) 1

## Answer

B

**Question. For all x, x ax ( a) 2 + 2 + 10 – 3 > 0, then the interval in which a lies, is**

(a) a < – 5

(b) – 5 < a < 2

(c) a > 5

(d) 2 < a < 5

## Answer

B

**Question. If a and b be the roots of the quadratic equation ax2 + bx + c = 0 and k be a real number, then the condition, so that a < k < b is given by**

(a) ac > 0

(b) ak2 + bk c 2 + + = 0

(c) ac < 0

(d) a^{2}k^{2} + abk + ac< 0

## Answer

D

**Question. The values of a for which 2x ^{2} – 2(2a + 1)x + a(a + 1) = 0may have one root less than a and other root greater than a are given by**

(a) 1 > a > 0

(b) – 1 < a < 0

(c) a ≥ 0

(d) a > 0 or a < – 1

## Answer

D

**Question. If a and b (a < b) are the roots of the equation x ^{2} + bx + c = 0, where c < 0 < b, then**

(a) 0 < a < b

(b) a < 0 < b < |a |

(c) a < b < 0

(d) a < 0 < |a |< b |

## Answer

B

**Question. The solution set of 1 ≤|x – 2|≤ 3 is **

(a) (-1, 1) ∪ (3, 5]

(b) [-1, 1] ∪ [3, 5]

(c) [-1, 1] ∪ [3, 5)

(d) None of these

## 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 solution set of |x-2|-1 /|x-2|-2≤0 is**

(a) [0, 1] ∪ (3, 4)

(b) [0, 1] ∪ [3, 4]

(c) [0, 1] ∪ (3, 4)

(d) None of these

## Answer

B

**Question. The solution set of 1 ≤ |x – 2|≤ 3 is **

(a) [-1, 1] ∪ (3, 5)

(b) (-1, 1) ∪ [3, 5]

(c) [-1, 1] ∪ [3, 5]

(d) [-1, 2] ∪ [3, 5]

## Answer

C

**Question. |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. (x – 1)(x ^{2}– 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. x ^{2} – 3|x| + 2 < 0, then x belongs to**

(a) (1, 2)

(b) (-2, -1)

(c) (-2, -1) ∪ (1, 2)

(d) (-3, 5)

## Answer

C

**Question. If x ^{2} + 6x – 27 > 0 and x^{2} – 3x – 4 < 0, then**

(a) x > 3

(b) x < 4

(c) 3 < x < 4

(d) x = 7/2

## Answer

C

**Question. If a + b = 8, then ab is greatest when **

(a) a = 4, b = 4

(b) a = 3, b = 5

(c) a = 6, b = 2

(d) None of these

## Answer

A

**Question. If the equation 2x ^{2}+3x + 5λ = 0 and x^{2} + 2x + 3λ = 0 have a common root, then l is equal to**

(a) 0

(b) -1

(c) 0, -1

(d) 2, -1

## Answer

C

**Question. If roots of the equation ax ^{2} + bx + c = 0; (a, b, c ∈ N) are rational numbers, then which of the following cannot be true ?**

(a) All a , b and c are even

(b) All a , b and c are odd

(c) b is even while a and c are odd

(d) None of the above

## Answer

D

**Question. If ab = 4(a, b∈R), then**

(a) a + b ≤ 4

(b) a + b = 4

(c) a + b ≥ 4

(d) None of these

## Answer

C

**Question. log _{2} (x^{2} – 3x + 18 < 4 , then x belongs to**

(a) (1, 2)

(b) (2, 16)

(c) (1, 16)

(d) None of these

## Answer

A

We hope you liked the above provided **MCQ Questions Chapter 6 Linear Inequalities Class 11 Mathematics** with solutions. If you have any questions please ask us in the comments box below.