# Linear Inequalities MCQ Class 11 Mathematics

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-}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: 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

## 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 tan A and tan B are the roots of the quadratic equation x ^{2}-px+q=0 then the value of sin^{2} (A+B) is**

## Answer

D

**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) x^{2}-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: The value of a, 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(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:**

## Answer

B

**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

## Answer

C

**Question: If X denotes the set of real number p for which the equation x ^{2}= 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)

## Answer

C

**Question: If ax ^{2}+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

## Answer

B

**Question: Conditions on a and b for which 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 ∈ R

(d) None of these

## Answer

C

**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 value of a for which 2x ^{2}-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

## Answer

B

**Question: Find all values of p, so that 6 lies between the roots of the equationx ^{2}+2(p-3)x+9=0**

(a)(-∞,3/4)

(b)(-∞,3/4)

(c) (3/4∞)

(d) None of thes

## Answer

B

**Question: **

## Answer

B

**Question:**

## Answer

A

**Question: **

## Answer

D

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

(a) (-d,-c)

(b) (-d,-c)

(c) R

(d) S

## Answer

B

**Question: **

## Answer

B

**Question:**

(a) (2,∞)

(b) (1, 2)

(c) (-2,-1)

(d) None of these

## Answer

A

**Question: **

## Answer

B

**Question: If x ^{2}+x+ |x|+1≤ 0, then x lies in**

(a) (0,∞)

(b) (-∞,0)

(c) R

(d) Φ

## Answer

D

**Question:**

## Answer

C

**Question: If (ax ^{2}+c) y+(a’x^{2}+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) a

^{2}+c

^{2}=a

^{‘2}+c

^{‘2}

(d) aa’+cc’=1

## Answer

B

**Question: If the roots of the equation (p ^{2}+q^{2})x^{2}-2q(p+r)x+(q^{2}+r^{2})=0 be in real and equal, then p q r , and will be in**

(a) AP

(b) GP

(c) HP

(d) None of these

## Answer

B

**Question: If roots of the equation (a-b)x ^{2}+(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

## Answer

A

**Question: If a >0, b>0,c>0, then both the roots of the equation ax ^{2}+ bx+c = 0**

(a) are real and negative

(b) have negative real part

(c) are rational numbers

(d) None of these

## Answer

B

**Question:**

## Answer

B

**Question: If roots of the equation ax ^{2}+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

## Answer

D

**Question: **

## Answer

D

**Question: Let α,β be the roots of x ^{2}-2x cos Φ+1then the equation whose roots are a^{n }and β^{n} , is**

(a) x

^{2}-2x cos nΦ-1=0

(b) x

^{2}-2x cos nΦ +1=0

(c) x

^{2}-2x sin nΦ+1=0

(d) x

^{2}+2x sin nΦ-1=0

## Answer

B

**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 x^{2}+(a+c) bx+(a+c)^{2}=0

(b) abx^{2}+ (a+ c) bx+(a+c)^{2}=0

(c) ac x^{2}+ (a+ b) cx +(a+c)^{2}=0

(d) None of the above

## Answer

A

**Question: Let α and α ^{2}be the roots of x^{2}+x+1=0, then the equation whose roots are α^{31} and α ^{62} , is**

(a) x

^{2-}x+1=0

(b) x

^{2}+x-1=0

(c) x

^{2}+x+1=0

(d) x

^{60}+x

^{30}+1=0

## Answer

C

**Question: If at least one root of the equation x ^{3}+ax^{2}+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

## Answer

C

**Question: If the equation 2x ^{2}+3x+5λ=0 and x^{2}+2x+3λ=0 have a common root, then λ is equal to**

(a) 0

(b) -1

(c) 0, -1

(d) 2, -1,

## Answer

C

**Question: If each pair of the equation**

## Answer

A

**Question: If at least one root of 2x ^{2}+3x+5=0 and ax^{2}+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

## Answer

C

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