# MCQ Questions for Class 11 Linear Inequalities with Answers

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

A

Question:

B

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

A

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: 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
(d) None of these

C

Question: 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)
(d) None of these

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

D

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:

D

Question: 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
(d) 8

C

Question: 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) (√3,∞)

D

Question: 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
(d) (a/A)

C

Question: 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:

A

Question: 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

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 x2 correctly as 6 and 1 respectively the correct roots are
(a) 3,  2
(b)  3, 2
(c)  6, 1
(d) 6, 1

D

Question. 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
(d) non-real

Question. 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. 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
(d) π/6

C

Question. 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
(d) 6, 2

C

Question. 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
(d) None of these

A

Question. 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) infinite

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 + (a2-b) = 0
(b) (a2-b) x2 – 2ax + 1 =0
(c) (a2-b) x2 – 2bx + 1 =0
(d) None of the above

B

Question. 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
(d) None of the above

A

Question. 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
(d) None of the above

B

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

B

Question. If a + b + c  0, then the roots of the equation 4ax2 + 3bx + 2c =0 are
(a) equal
(b) imaginary
(c) real
(d) None of these

C

Question. 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
(d) None of these

C

Question. 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

Question. 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 < 0

B

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

B

Question. 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) None of these

D

Question. 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
(d) None of these

B

Question. 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

Question. 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
(d) None of these

C

Question. The number of real roots of the equation
esin x – e-sin x 4 0are
(a) 1
(b) 2
(c) infinite
(d) None of these

D

Question. The roots of the equationx x4 8x2  9 = 0 are
(a) ± 1, ± i
(b) ± 3, ± i
(c) ± 2 , ± i
(d) None of these

B

Question. 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)
(d) ( 4, 7)

A

Question. 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. 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
(d) None of these

B

Question. The number of real roots of 32×2  7x + 7 = 9 is
(a) 0
(b) 2
(c) 1
(d) 4

B

Question. 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= 0

A

Question. If |x2 | |x| – 2 = 0, then the value of x is equal to
(a) 2
(b)  2
(c) 1
(d) None of the above

C

Question. The least value of| | a for which tan = and cot= are roots of the equation x2 + ax+ 1 =0, is
(a) 2
(b) 1
(c) 1/2
(d) 0

A

Question. 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

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.

The above NCERT based MCQs for Class 11 Linear Inequalities have been designed by our teachers in such a way that it will help you a lot to gain an understanding of each topic. These CBSE NCERT Class 11 Linear Inequalities Multiple Choice Questions have been developed and are available free for benefit of Class 11 students.

a) Linear Inequalities Class 11 Maths MCQ Questions will help the kids to strengthen concepts and improve marks in tests and exams.

b) Multiple Choice Questions for Linear Inequalities Class 11 have proven to further enhance the understanding and question solving skills.

c) Regular reading topic wise questions with choices will for sure develop very good hold over each chapter which will help in exam preparations.

d) It will be easy to revise all Linear Inequalities chapters and faster revisions prior to class tests and exams.

Free Printable MCQs in PDF of CBSE Class 11 Linear Inequalities are designed by our school teachers and provide best study material as per CBSE NCERT standards.

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The MCQs for Class 11 Linear Inequalities with Answers have been developed based on current NCERT textbook issued by CBSE.

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MCQs cover the topics of all chapters given in NCERT Book for Class 11 Linear Inequalities.

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