Class 11 Mathematics Linear Inequalities MCQs Set 02

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
Answer: 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,∞)
Answer: d

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 the options
Answer: b

Question:

Answer: b

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 options
Answer: b

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 the options
Answer: 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 the options
Answer: a

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
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: 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 the options
Answer: b

Question:

Answer: d

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

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 the options
Answer: a

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

Question:

Answer: a

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 the options
Answer: c

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 options
Answer: a

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
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 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 options
Answer: b

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
Answer: c

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 the options
Answer: b

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
Answer: a

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

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)²
Answer: 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
Answer: 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 options
Answer: b

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 options
Answer: d

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
Answer: b

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
Answer: d

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 the options
Answer: d

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 the options
Answer: c

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 the options
Answer: c