Please refer to Chapter 6 Linear Inequalities MCQ Class 11 Mathematics with answers below. These multiple-choice questions have been prepared based on the latest NCERT book for Class 11 Mathematics. Students should refer to MCQ Questions for Class 11 Mathematics with Answers to score more marks in Grade 11 Mathematics exams. Students should read the chapter Linear Inequalities and then attempt the following objective questions.

MCQ Questions Class 11 Mathematics Chapter 6 Linear Inequalities

The Linear Inequalities MCQ Class 11 Mathematics provided below covers all important topics given in this chapter. These MCQs will help you to properly prepare for exams.

Question: If the roots of the equation x2+2ax+ b= 0 are real and distinct and they differ by atmost 2m, then b lies in the interval
(a)(-a^2-m²,a²)
(b)(a²-m²,a²)
(c)(a²,m²+a²)
(d) None of the above 

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

Question:The number of values of the triplet (a, b, c) for which,acos² x+ bsin²x+c=0 is satisfied by all real x, is
(a) 0
(b) 2
(c) 3
(d) infinite 

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

Question: If a and b are rational and b 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 

Question: The value of a, 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 

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

Question:

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

Question: If X denotes the set of real number p for which the equation x²= p (x+p) has its roots greater than p, then X is equal to
(a)(-2,-1/2)
(b)(-1/2,1/4)
(c) Φ
(d) (-∞,0)

Question: If ax²+bx+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 

Question: Conditions on a and b for which 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 ∈ R
(d) None of these 

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

Question: The value of a for which 2x²-2(2a+1) x+a (a+1)=0  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

Question: Find all values of p, so that 6 lies between the roots of the equationx²+2(p-3)x+9=0
(a)(-∞,3/4)
(b)(-∞,3/4)
(c) (3/4∞)
(d) None of thes 

Question:

Question:

Question:

Question: If c< d, x²+(c+d) x +cd <0, then x
(a) (-d,-c)
(b) (-d,-c)
(c) R
(d) S 

Question:

Question:

(a) (2,∞)
(b) (1, 2)
(c) (-2,-1)
(d) None of these

Question:

Question: If x²+x+ |x|+1≤ 0, then x lies in
(a) (0,∞)
(b) (-∞,0)
(c) R
(d) Φ 

Question:

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=a^‘2+c^‘2 
(d) aa’+cc’=1   

Question: If the roots of the equation (p²+q²)x²-2q(p+r)x+(q²+r²)=0 be in real and equal, then p q r , and will be in
(a) AP
(b) GP
(c) HP
(d) None of these 

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 

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 

Question:

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 are c even
(b) All a b, and c are odd
(c) b is even while a and c are odd
(d) None of the above

Question:

Question: Let α,β be the roots of x²-2x cos Φ+1then the equation whose roots are aⁿ and βⁿ , is
(a) x²-2x cos nΦ-1=0
(b) x²-2x cos nΦ +1=0
(c) x²-2x sin nΦ+1=0 
(d) x²+2x sin nΦ-1=0 

Question: If  α  and β are the roots of the equation ax2+bx+c=0,  then the equation whose roots are a+1/β and β+1/α,, is
(a) ac x²+(a+c) bx+(a+c)²=0
(b) abx²+ (a+ c) bx+(a+c)²=0 
(c) ac x²+ (a+ b) cx +(a+c)²=0
(d) None of the above

Question: Let α and α²be the roots of x²+x+1=0,  then the equation whose roots are α³¹ and α ⁶² , is
(a) x^2-x+1=0
 (b) x²+x-1=0
(c) x²+x+1=0
(d) x ⁶⁰+x³⁰+1=0

Question: If at least one root of the equation x³+ax²+bx+c=0 ax 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) w, an imaginary cube root of unity
(d) i 

Question: If the equation 2x²+3x+5λ=0 and x²+2x+3λ=0 have a common root, then λ is equal to
(a) 0
(b) -1
(c) 0, -1
(d) 2, -1, 

Question: If each pair of the equation

Question: If at least 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 

We hope you liked the above Linear Inequalities MCQ Class 11 Mathematics. In case you have any questions please put them in the comments box below and our teachers will provide you a response