# Class 11 Mathematics Chapter 6 Linear Inequalities MCQ Questions with Answer

Linear Inequalities Class 11 MCQ is one of the best strategies to prepare for the CBSE Class 11 Board exam. If you want to complete a grasp concept or work on one’s score, there is no method except constant practice. Students can improve their speed and accuracy by doing more Linear Inequalities class 11 MCQ which will help them all through their board test.

## Linear Inequalities Class 11 MCQ Questions with Answer

Class 11 Math MCQ with answers are given here to Chapter 6 Linear Inequalities. These MCQs are based on the latest CBSE board syllabus and relate to the latest Class 11 Mathematics syllabus. By Solving these Class 11 MCQs, you will be able to analyze all of the concepts quickly in the Chapter and get ready for the Class 11 Annual exam.

Learn Linear Inequalities Class 11 MCQ with answers pdf free download according to the latest CBSE and NCERT syllabus. Students should prepare for the examination by solving CBSE Class 11 Linear Inequalities MCQ with answers given below.

Question 1: If x is real, then the maximum and minimum values of the expression x2-3x+4/x2+3x+4 x will be
(a) 2, 1,
(b) 5.1/5
(c) 7,1/7

C

Question 2: If x is real, then expression x+2/2x2+3x+6 takes all values in the interval
(a) (1/13,1/3)
(b) [-1/13,1/3]
(c) (-1/3,1/13)

B

Question 3: 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

Question 4: (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

B

Question 5. If one root of the equation x2 + px + 12 = 0 is 4, while the equation x + px + q = 0 has equal roots, then the value of qis
(a) 49/4
(b) 4/49
(c) 4
(d) None of these

A

Question 6: log2 (x2-3x+18)<4, ) then x belongs to
(a) (1, 2)
(b) (2,16)
(c) (1,16)

A

Question 7: The minimum value of P= bcx+ cay+ abz , when xyz = abc, is
(a) 3abc
(b) 6abc
(c) abc

Question: If the equation x2+9y2-4x+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 8: If roots of x2-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 9. Two students while solving a quadratic equation in x, one copied the constant term incorrectly and got the roots 3 and 2. The other copied the constant term coefficient of x2 correctly as 6 and 1 respectively the correct roots are
(a) 3,  2
(b)  3, 2
(c)  6, 1

D

Question 10. If sin ., sin / and cos . are in GP, then roots of x2  + 2xcot β/ + 1 = 0 are always    A
(a) real
(b) real and negative
(c) greater than one

Question 11. If the roots of the equationx x2 + 2ax + b = 0 are real and distinct and they differ by atmost 2m, then b lies in the interval
(a) (a2 – m2 , a2 )
(b) [a2 – m2 , a2 )
(c) (a2 , m2 + a2 )
(d) None of the above

B

Question 12: Let p q,∈{1,2,3,4}. The number of equations of the form px2+ qx+1 =0 having real roots, is
(a) 15
(b) 9
(c) 7

C

Question 13: sin x+cos x=y2-y+a has no value of x for any y, if a belongs to
(a) ( 0,√3)
(b) (-√3,0)
(c) (-∞,-√3)

D

Question 14: If the roots of ax2+bx+c=0 area α,β and the roots of Ax2+ Bx+ C=0 are α-k, β-k, then B2-4AC/b2-4ac is equal to
(a) 0
(b) 1
(c) (A/a)2

C

Question 15: For what value of λ 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

C

Question 16. If (2x2 – 3x +1) (2x2 + 5x+ 1) = 9x2 , then equation has
(a) four real roots
(b) two real and two imaginary roots
(c) four imaginary roots

A

Question 17. The roots of ax2 + bx + c = 0, where a 0 and coefficients are real, non-real complex and a + c
b, then
(a) 4a + c > 2b
(b) 4a + c < 2b
(c) 4a + c = 2b

B

Question 18. The number of real solutions of the equation
|x2 + 4x + 3| + 2x + 5 = 0 are
(a) 1
(b) 2
(c) 3

B

Question 19. If a + b + c  0, then the roots of the equation 4ax2 + 3bx + 2c =0 are
(a) equal
(b) imaginary
(c) real

C

Question 20. Conditions on a and b for whichx x2 -ax – b2 is less than zero for atleast one positive x, are
(a) a > 3, b< 0
(b) a > 3, b> 0
(c) a, b εR

C

Question 21. If ax2+ bx2 + 6 = 0 does not have two distinct real roots, then the least value of 3a + b is
(a) 2
(b)  2
(c) 1
(d)  1

B

Whoever needs to take the CBSE Class 11 Board Exam should look at this MCQ. To the Students who will show up in CBSE Class 11 Mathematics Board Exams, It is suggested to practice more and more questions. Aside from the sample paper you more likely had solved. These Linear Inequalities Class 11 MCQ are ready by the subject specialists themselves.

Question 22. The value of ., for which the equation
x2  (sinα .  2)x  (1+ sinα.) = 0 has roots, whose sum of square is least, is
(a) π /4
(b) π/3
(c) π/2

C

Question 23. If x2 + 2x + 2xy + my  3 = 0 has two rational factors, then the values of m will be
(a)  6,  2
(b)  6, 2
(c) 6,  2

C

Question 24. If the roots of the equation qx2 + px + = 0 are complex, where pand qare real, then the roots of the equation x2 – 4qx + p2 = 0 are
(a) real and unequal
(b) real and equal
(c) imaginary

A

Question 25. The number of values of the triplet (a, b, c) for which, acos2x + bsin2x +C = 0 is satisfied by all real x, is
(a) 0
(b) 2
(c) 3

D

Question 26. If aandb are rational andb is not a perfect square, then the quadratic equation with rational coefficients whose one root is
1 /a +√b , is
(a)x2 – 2ax + (a2-b) = 0
(b) (a2-b) x2 – 2ax + 1 =0
(c) (a2-b) x2 – 2bx + 1 =0
(d) None of the above

B

Question 27. If px2 + x+ 1 is a factor of the expression ax3 + bx + c , then
(a)a2 + c2 = – ab
(b)a2 – c2 = – ab
(c)a2 – c2 =  ab

C

Question 28. The number of real roots of the equation
esin x – e-sin x 4 0are
(a) 1
(b) 2
(c) infinite

D

Question 29. The roots of the equationx x4 8x2  9 = 0 are
(a) ± 1, ± i
(b) ± 3, ± i
(c) ± 2 , ± i

B

Question 30. If 2 + i√3 is a root of the equation x2 + px + q = 0, where p and q are real, then ( p, q) is equal to
(a) ( 4, 7)
(b) (4,  7)
(c) (4, 7)

A

Question 31. If tan A and tan B are the roots of the quadratic equation x2 – px + q = 0, then the value of sin2 (A+B )is
(a)  p2 / p2 + q2
(b) p2 / (p + q)2
(c) 1 – p/(1-q)2
(d) None of these

D

Question 32. If the roots of a x b x c 1 = 0 are α1β1  and those of  a1x2 + b1x1 + c1 = 0  are α1β1 and those of a2x2 + b2x + c2 = 0 such that . α1.α2 = β1β2 =1,  then
(a) a1 /a2 = b1/b2 = c1/c2
(b) a1 / c2 = b1/b2 =  c1/a2
(c) a1 a2 = b1b2 = c1 c2

B

Question 33. The number of real roots of 32×2  7x + 7 = 9 is
(a) 0
(b) 2
(c) 1

B

Question 34. If sin . and cos . are the roots of the equation
ax2 + bx + c = 0, then
(a)a2 – b2 + 2ac=0
(b) (a  c)2 = b2 + c2
(c)a2 + b2 – 2ac= 0
(d) a2 + b2 + 2ac= 0Answer

A

Question 35. If |x2 | |x| – 2 = 0, then the value of x is equal to
(a) 2
(b)  2
(c) 1

C

Question 36. The least value of| | a for which tan = and cot= are roots of the equation x+ ax+ 1 =0, is
(a) 2
(b) 1
(c) 1/2

A

Question 37. If x2  3x + 2 be a factor of x4 – px2 + q , then ( p, q) is equal to
(a) (3, 4)
(b) (4, 5)
(c) (4, 3)
(d) (5, 4)

D

Question 38. The value of a for which2 2x2 – 2(2a+1)x + a(a+1) may have one root less than a and other root greater than a, is
(a) 1<a<0
(b) a > 0 or a < 1
(c) a ≥ 0 (d) 1/2 < a < 0Answer

B

Question 39. If c <d, x2 + (c + d)x + cd <, 0 then x ε
(a) (d,  c]
(b) (d,  c)
(c) R

B

Question 40. If x2 + ax + 1 is a factor of ax3 + bx + c  , then
(a) b + a + a = a = c 2 0,
(b) b  a + a = a = c 2 0,
(c) b + a  a = a = 2 0, 0

D

Question 41. If the difference of the roots of the equation x2 – Px + 8 = 0 is 2, then the value of P is
(a) ±4
(b) ±6
(c) ±5

B

Question 42. If the sum of the squares of the roots of the equation x2-( a -2) x – (a +1)0 is least, then the value of a is
(a) 1
(b) 1
(c) 2
(d) 2

B

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