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
Answer
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
Answer
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
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 x3 – 7x – = 0, then 1/α4 +1/β4 + 1/γ4 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 x2 + 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)x2 – (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 4ax2 + 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 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
Answer
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
Answer
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
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) = 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
Answer
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
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 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
Answer
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
Answer
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
Answer
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
Answer
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
Answer
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
Answer
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
Answer
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
Answer
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
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) x2 – 2xcosnφ – 1 = 0
(b) x2 – 2xcosnφ – 1 = 0
(c) x2 – 2xcosnφ – 1 = 0
(d) x2 – 2xcosnφ – 1 = 0
Answer
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
Answer
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
Answer
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
Answer
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
Answer
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
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) a2k2 + abk + ac< 0
Answer
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
Answer
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 |
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)(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. x2 – 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 x2 + 6x – 27 > 0 and x2 – 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 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
Answer
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
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. log2 (x2 – 3x + 18 < 4 , then x belongs to
(a) (1, 2)
(b) (2, 16)
(c) (1, 16)
(d) None of these
Answer
A
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