# 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

A

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

B

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

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

B

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

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

A

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

A

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

B

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

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

A

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

A

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

D

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

C

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

A

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

D

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

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

A

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

C

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

B

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

B

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

A

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

B

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

A

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

B

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

A

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

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

B

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

B

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

D

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

C

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

A

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

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

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) a2k2 + abk + ac< 0

D

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

D

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 |

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

B

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

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

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]

C

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

C

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

C

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

C

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

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

A

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

C

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

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

C

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