MCQ Questions Chapter 6 Linear Inequalities Class 11 Mathematics

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 ax² + bx + c = 0 be reciprocal of a root of the equation a′ x² + 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

Question. If the product of the roots of the equation (a + 1)x² + (2a + 3)x + (3a + 4) = 0 is 2, then the sum of roots is
(a) 1
(b) -1
(c) 2
(d) -2

Question. The system y (x² + 7x + 12) = 1 and x + y = 6,y > 0 has
(a) no solution
(b) one solution
(c) two solutions
(d) more than 2 solutions

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

Question. If α, β and γ are the roots of the equation x³ – 7x – = 0, then 1/α⁴ +1/β⁴ + 1/γ⁴ is
(a) 7/3
(b) 3/7
(c) 4/7
(d) 7/4

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

Question. The least value of |a|for which tan q and cotq are roots of the equation x² + ax 2 +1 = 0, is
(a) 2
(b) 1
(c) 1/2
(d) 0

Question. The harmonic mean of the roots of the equation (5 + √2)x² – (4 + √5)x + 8 + 2√5 = 0 is
(a) 2
(b) 4
(c) 6
(d) 8

Question. If a + b + c = 0, then the roots of the equation 4ax² + 3bx + 2c= are
(a) equal
(b) imaginary
(c) real
(d) None of these

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

Question. If the roots of the equation qx² + px + q = 0 are complex, where pand qare real, then the roots of the equation qx² + 4qx + p= 0 are
(a) real and unequal
(b) real and equal
(c) imaginary
(d) None of these

Question. If x1 x² and  x3, and are distinct roots of the equation ax² + bx +c = 0, then
(a) a = b = 0, c ∈ R
(b) a = c = 0, b ∈ R
(c) b² – 4ac ≥ 0
(d) a = b = c = 0

Question. If 4x² + 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

Question. The minimum value of P = bcx + cay + abz, when xyz = abc, is
(a) 3abc
(b) 6abc
(c) abc
(d) 4abc

Question. Let f (x) = x² + 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

Question. If sin a, sin b and cos a are in GP, then roots of x² + 2xcotb + 1 = 0 are always
(a) real
(b) real and negative
(c) greater than one
(d) non-real

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

Question. If the roots of the equation x² + px + q = 0area andb and roots of the equation x²-xr+ s= 0 are α⁴ and β⁴ and , then the roots of the equation x² – 4qx +2q² = 0 are
(a) both negative
(b) both positive
(c) both real
(d) one negative and one positive

Question. If a > 0, b > 0, c > 0, then both the roots of the equation ax²+ bx+ c = 0
(a) are real and negative
(b) have negative real part
(c) are rational numbers
(d) None of these

Question. If (ax²+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

Question. If roots of the equation (a – b)x² + (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 

Question. Let a, b be the roots of x² – 2x cosΦ + 1 = 0, then the equation whose roots are ^αn and βⁿ  , is
(a) x² – 2xcosnΦ – 1 = 0
(b) x² – 2xcosnΦ + 1 = 0
(c) x² – 2xcosnΦ + 1 = 0
(d) x² + 2xcosnΦ – 1 = 0 

Question. If a and b are the roots of the equation ax²+ bx +c = 0, then the equation whose roots are α+1/β and β+1/α
(a) acx² + (a+c)bx +(a+c)² = 0
(b) abx² + (a+c)bx +(a+c)² = 0
(c) acx² + (a+c)cx +(a+c)² = 0
(d) None of the above

Question. (a² – 3a +2)x2 + (a² – 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

Question. If the equation x² + 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

Question. If atleast one root of the equation x³ + ax² + 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

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) x² – 2xcosnφ – 1 = 0
(b) x² – 2xcosnφ – 1 = 0
(c) x² – 2xcosnφ – 1 = 0
(d) x² – 2xcosnφ – 1 = 0

Question. If the roots of the equation ( p²+ q² )x² – 2q(p + r)x+ (q² + r²) = 0 be real and equal, then p, q and r will be in
(a) AP
(b) GP
(c) HP
(d) None of these

Question. If roots of the equation ax²+ 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

Question. If atleast one root of 2x² + 3x + 5 = 0 and ax² + 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

Question. If x² + 2ax + b ≥ c ∀ x ∈ R, then
(a) b – c ≥ a²
(b) c – a ≥ b²
(c) a – b ≥ c²
(d) None of these

Question. If a_i > 0 for i = 1, 2, …, n and a₁a₂…….a_n= 1, then minimum value of (1+a₁)(1+a₂)….(1+ a_n) is
(a) 2 ^n/2
(b) 2ⁿ
(c) 22ⁿ
(d) 1

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

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) a²k² + abk + ac< 0

Question. The values of a for which 2x² – 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

Question. If a and b (a < b) are the roots of the equation x² + 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 |

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

Question. If|x + 2|≤ 9, then
(a) x ∈ (-7, 11)
(b) x ∈ [-11, 7]
(c) x ∈ (-∞, -7) ∪ (11, ∞)
(d) x ∈ (-∞, -7) ∪ [11, ∞)

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

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]

Question. |2x -3|<|x + 5|,then x belongs to
(a) (-3, 5)
(b) (5, 9)
(c) (-2/3,8)
(d) (8,-2/3)

Question. (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

Question. x² – 3|x| + 2 < 0, then x belongs to
(a) (1, 2)
(b) (-2, -1)
(c) (-2, -1) ∪ (1, 2)
(d) (-3, 5)

Question. If x² + 6x – 27 > 0 and x² – 3x – 4 < 0, then
(a) x > 3
(b) x < 4
(c) 3 < x < 4
(d) x = 7/2

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

Question. If the equation 2x²+3x + 5λ = 0 and x² + 2x + 3λ = 0 have a common root, then l is equal to
(a) 0
(b) -1
(c) 0, -1
(d) 2, -1

Question. If roots of the equation ax² + 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

Question. If ab = 4(a, b∈R), then
(a) a + b ≤ 4
(b) a + b = 4
(c) a + b ≥ 4
(d) None of these

Question. log₂ (x² – 3x + 18 < 4 , then x belongs to
(a) (1, 2)
(b) (2, 16)
(c) (1, 16)
(d) None of these

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.