Students can refer to the following MCQ Questions for Linear Inequalities Class 11 Maths MCQ Questions with Answers provided below based on the latest curriculum and examination pattern issued by CBSE and NCERT. Our teachers have provided here a collection of multiple choice questions for Linear Inequalities Class 11 covering all topics in your textbook so that students can assess themselves on all important topics and thoroughly prepare for their exams

## Linear Inequalities Class 11 Maths MCQ Questions with Answers

We have provided below Linear Inequalities Class 11 Maths MCQ Questions with answers which will help the students to go through the entire syllabus and practice multiple choice questions provided here with solutions. As Linear Inequalities MCQs in Class 11 pdf download can be really scoring for students, you should go through all problems provided below so that you are able to get more marks in your exams.

#### Linear Inequalities Class 11 Maths MCQ Questions

**Question. 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: 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: **

**Answer**

B

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

(a) 3abc

(b) 6abc

(c) abc

(d) 4abc

**Answer**

A

**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

**Answer**

A

**Question: 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: 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: 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: (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:**

**Answer**

D

**Question: 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:** **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:** **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:** **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

**Answer**

C

**Question:**

**Answer**

A

**Question: 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. 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. 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. 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

**Answer**

B

**Question. 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. 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. 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. 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. 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

**Answer**

B

**Question. 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. 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. 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. 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. 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. 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

**Answer**

B

**Question. 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. 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. 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. 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. 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

**Answer**

B

**Question. 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. 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. 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. 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. 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

**Answer**

D

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

(a) 0

(b) 2

(c) 1

(d) 4

## Answer

B

**Question. 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= 0

## Answer

A

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

(a) 2

(b) 2

(c) 1

(d) None of the above

## Answer

C

**Question. 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) 0

## Answer

A

**Question. 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)

**Answer**

D

Our teachers have developed really good **Multiple Choice Questions** covering all important topics in each chapter which are expected to come in upcoming tests and exams, as MCQs are coming in all exams now therefore practice them carefully to get full understanding of topics and get good marks. Download the latest questions with multiple choice answers for Class 11 Linear Inequalities in pdf or read online for free.

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