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 x ^{2}-3x+4/x^{2}+3x+4 x will be**

(a) 2, 1,

(b) 5.1/5

(c) 7,1/7

(d) None of these

**Answer**

C

**Question 2: If x is real, then expression x+2/2x ^{2}+3x+6 takes all values in the interval**

(a) (1/13,1/3)

(b) [-1/13,1/3]

(c) (-1/3,1/13)

(d) None of these

**Answer**

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) a≤ c ≤b **Answer**

D

**Question 4: (a ^{2}-3a-2)x^{2}+(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 5. If one root of the equation x ^{2} + 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

**Answer**

A

**Question 6: log2 (x ^{2}-3x+18)<4, ) then x belongs to**

(a) (1, 2)

(b) (2,16)

(c) (1,16)

(d) None of these

**Answer**

A

**Question 7: The minimum value of P= bcx+ cay+ abz , when xyz = abc, is**

(a) 3abc

(b) 6abc

(c) abc

(d) 4abc **Answer**

**Question: If the equation x ^{2}+9y^{2}-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

**Click for Answer**

A

**Question 8: If roots of x ^{2}-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 x ^{2} correctly as 6 and 1 respectively the correct roots are **

(a) 3, 2

(b) 3, 2

(c) 6, 1

(d) 6, 1

**Answer**

D

**Question 10. If sin ., sin / and cos . are in GP, then roots of x ^{2} + 2xcot β/ + 1 = 0 are always A**

(a) real

(b) real and negative

(c) greater than one

(d) non-real

**Answer**

**Question 11. If the roots of the equationx x ^{2} + 2ax + b = 0 are real and distinct and they differ by atmost 2m, then b lies in the interval **

(a) (a

^{2}– m

^{2}, a

^{2})

(b) [a

^{2}– m

^{2}, a

^{2})

(c) (a

^{2}, m

^{2}+ a

^{2})

(d) None of the above

**Click for Answer**

B

**Question 12: Let p q,∈{1,2,3,4}. The number of equations of the form px ^{2}+ qx+1 =0 having real roots, is**

(a) 15

(b) 9

(c) 7

(d) 8

**Answer**

C

**Question 13:** **sin x+cos x=y ^{2}-y+a has no value of x for any y, if a belongs to**

(a) ( 0,√3)

(b) (-√3,0)

(c) (-∞,-√3)

(d) (√3,∞)

**Answer**

D

**Question 14:** **If the roots of ax ^{2}+bx+c=0 area α,β and the roots of Ax^{2}+ Bx+ C=0 are α-k, β-k, then B^{2}-4AC/b^{2}-4ac is equal to**

(a) 0

(b) 1

(c) (A/a)

^{2}

(d) (a/A)

^{2 }

**Answer**

C

**Question 15:** **For what value of λ the sum of the squares of the roots of x ^{2}+(2+λ) x-1/2 (1+λ)=0 is minimum ?**

(a) 3/2

(b) 1

(c) 1/2

(d) 11/4

**Click for Answer**

C

**Question 16. If (2x ^{2} – 3x +1) (2x^{2} + 5x+ 1) = 9x^{2} , then equation has **

(a) four real roots

(b) two real and two imaginary roots

(c) four imaginary roots

(d) None of the above

**Answer**

A

**Question 17. The roots of ax ^{2} + 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

(d) None of the above

**Answer**

B

**Question 18. The number of real solutions of the equation **

|x^{2} + 4x + 3| + 2x + 5 = 0 are

(a) 1

(b) 2

(c) 3

(d) 4**Answer**

B

**Question 19. If a + b + c 0, then the roots of the equation 4ax ^{2} + 3bx + 2c =0 are **

(a) equal

(b) imaginary

(c) real

(d) None of these

**Answer**

C

**Question 20. Conditions on a and b for whichx x ^{2} -ax – b^{2} is less than zero for atleast one positive x, are **

(a) a > 3, b< 0

(b) a > 3, b> 0

(c) a, b εR

(d) None of these

**Answer**

C

**Question 21. If ax ^{2}+ bx^{2} + 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

**Click for Answer**

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**

x^{2} (sinα . 2)x (1+ sinα.) = 0 has roots, whose sum of square is least, is

(a) π /4

(b) π/3

(c) π/2

(d) π/6**Answer**

C

**Question 23. If x ^{2} + 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

(d) 6, 2

**Answer**

C

**Question 24. If the roots of the equation qx ^{2} + px + = 0 are complex, where pand qare real, then the roots of the equation x^{2} – 4qx + p2 = 0 are **

(a) real and unequal

(b) real and equal

(c) imaginary

(d) None of these

**Answer**

A

**Question 25. The number of values of the triplet (a, b, c) for which, acos ^{2}x + bsin^{2}x +C = 0 is satisfied by all real x, is **

(a) 0

(b) 2

(c) 3

(d) infinite

**Answer**

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 + (a^{2}-b) = 0

(b) (a^{2}-b) x^{2} – 2ax + 1 =0

(c) (a^{2}-b) x^{2} – 2bx + 1 =0

(d) None of the above

**Click for Answer**

B

**Question 27. If px ^{2} + x+ 1 is a factor of the expression ax^{3} + bx + c , then **

(a)a

^{2}+ c

^{2}= – ab

(b)a

^{2}– c

^{2}= – ab

(c)a

^{2}– c

^{2}= ab

(d) None of these

**Answer**

C

**Question 28. The number of real roots of the equation ****e ^{sin x} – e^{-sin x} 4 0are**

(a) 1

(b) 2

(c) infinite

(d) None of these

**Answer**

D

**Question 29. The roots of the equationx x ^{4} 8x^{2} 9 = 0 are **

(a) ± 1, ± i

(b) ± 3, ± i

(c) ± 2 , ± i

(d) None of these

**Answer**

B

**Question 30. If 2 + i√3 is a root of the equation x ^{2} + px + q = 0, where p and q are real, then ( p, q) is equal to **

(a) ( 4, 7)

(b) (4, 7)

(c) (4, 7)

(d) ( 4, 7)

**Answer**

A

**Question 31. If tan A and tan B are the roots of the quadratic equation x ^{2} – px + q = 0, then the value of sin2 (A+B )is **

(a) p2 / p2 + q

^{2}

(b) p2 / (p + q)

^{2}

(c) 1 – p/(1-q)

^{2}(d) None of these

**Click for Answer**

D

**Question 32. If the roots of a x b x c 1 = 0 are α _{1}β_{1} and those of a_{1}x_{2} + b_{1}x_{1} + c_{1} = 0 are α1β1 and those of a2x2 + b2x + c2 = 0 such that . α1.α2 = β1β2 =1, then **

(a) a

_{1}/a

_{2}= b

_{1}/b

_{2}= c

_{1}/c

_{2}

(b) a

_{1}/ c

_{2}= b

_{1}/b

_{2}= c

_{1}/a

_{2}

(c) a1 a2 = b1b2 = c1 c2

(d) None of these

**Answer**

B

**Question 33. The number of real roots of 3 ^{2×2} 7x + 7 = 9 is **

(a) 0

(b) 2

(c) 1

(d) 4Answer

B

**Question 34. If sin . and cos . are the roots of the equation **

ax^{2} + bx + c = 0, then

(a)a^{2} – b^{2} + 2ac=0

(b) (a c)^{2} = b^{2} + c^{2}

(c)a^{2} + b^{2} – 2ac= 0

(d) a^{2} + b^{2} + 2ac= 0Answer

A

**Question 35. If |x ^{2} | |x| – 2 = 0, then the value of x is equal to **

(a) 2

(b) 2

(c) 1

(d) None of the aboveAnswer

C

**Question 36. The least value of| | a for which tan = and cot= are roots of the equation x ^{2 }+ ax+ 1 =0, is **

(a) 2

(b) 1

(c) 1/2

(d) 0Answer

A

**Question 37. If x ^{2} 3x + 2 be a factor of x^{4} – px^{2} + q , then ( p, q) is equal to **

(a) (3, 4)

(b) (4, 5)

(c) (4, 3)

(d) (5, 4)

**Click for Answer**

D

**Question 38. The value of a for which2 2x ^{2} – 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 < 0

**Answer**

B

**Question 39. If c <d, x ^{2} + (c + d)x + cd <, 0 then x ε **

(a) (d, c]

(b) (d, c)

(c) R

(d) S

**Answer**

B

**Question 40. If x ^{2} + ax + 1 is a factor of ax^{3} + 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) None of these

**Answer**

D

**Question 41. If the difference of the roots of the equation x ^{2} – Px + 8 = 0 is 2, then the value of P is **

(a) ±4

(b) ±6

(c) ±5

(d) None of these

**Answer**

B

**Question 42. If the sum of the squares of the roots of the equation x ^{2}-( a -2) x – (a +1)0 is least, then the value of a is **

(a) 1

(b) 1

(c) 2

(d) 2

**Click for Answer**

B

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### Frequently Asked Question (FAQs)

## How many MCQ questions are there in Class 11 Chapter 6 Mathematics?

In Class 11 Chapter 6 Mathematics, we have provided 42 Important MCQ Questions, But in the future, we will add more MCQs so that you can get good marks in the Class 11 exam.

## Can we score good marks in Class 11 Mathematics with the help of Linear Inequalities MCQ Questions?

Yes, MCQ Question is one of the best strategies to make your preparation better for the CBSE Board Exam. It also helps to know the student’s basic understanding of each Chapter. So, You can score good marks in the Class 9 Mathematics exam.