Class 11 Mathematics Linear Inequalities MCQs Set 03

Question: Solution of |x+1/x| > 2 is
(a) R – {0}
(b) R – {–1, 0, 1}
(c) R – {1}
(d) R – {–1, 1}
Answer: b

Question: The values of ‘a’ for which (a²-1)x²+2(a-1)x+2 is positive for any x, are
(a) a ≥ 1
(b) a ≤1
(c) a > - 3
(d) a < - 3 or a > 1 
Answer: d

Question: The solution set of 2x- 1/3 ≥(3x-2/4) -(2-x/5) is
(a) (4,∞) 
(b) [4 ,∞ ) 
(c) [ -4,4] 
(d) (-∞,2] 
Answer: d

Question: If α and β (α <β ) are the roots of the equation x²+bx+c=0 where c <0 <b, then
(a) 0 <α <β
(b) α<0<β <|α|
(c) a<β < 0
(d) a<0<|α|<β|
Answer: b

Question: For all x,x2+2ax+(10-3a)>0, then the interval in which a lies, is
(a) a < - 5
(b) - 5<a<2 
(c) a > 5
(d) 2<a < 5 
Answer: b

Question: If the roots of the equation x²-2ax+a²+a-3=0 are real and less than 3
(a) a < 2
(b) 2≤ a ≤3 
(c) 3< a ≤ 4
(d) a > 4
Answer: a

Question: The solution set of 1≤|x-2|≤3 is
(a) [ -1,1 ] ∪( 3,5 ) 
(b) (-1 1)∪ [3,5 ]
(c) [ -1, 1] ∪ [3, 5] 
(d) [ -1,2] ∪ [3,5] 
Answer: c

Question: If ab=4 (a,b∈R⁺)then
(a) a+ b ≤ 4
(b) a+ b =4
(c) a+ b ≥ 4
(d) None of these 
Answer: c

Question: If α and β be the roots of the quadratic equation ax²+ bx+ c=0 and k be a real number, then the condition, so that α <k<β is given by
(a) ac > 0
(b) ak²+bk+c=0 
(c) ac < 0
(d) a²k²+abk+ac<0 
Answer: d

Question: x and b are real numbers. If b > 0 and |x| > b, then
(a) x ∈ (–b, ∞)
(b) x ∈ (–∞, b)
(c) x ∈ (–b, b)
(d) x ∈ (–∞, –b) ∪ (b, ∞)
Answer: d

Question: The values 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 are given by
(a) 1>a >0
(b) - 1 < a<0
(c) a ≥0
(d) a > 0 or a < - 1
Answer: d

Question: If a+b= 8, then ab is greatest when
(a) a=4,b=4 
(b) a =3, b=5 
(c) a= 6,b=2
(d) None of these 
Answer: a

Question: The solution set of 1≤|x-2|≤3 is 
(a) ( -1,1)∪(3,5]
(b) [-1,1 ]∪ [3,5] 
(c) [- 1,1] ∪ [3 ,5 )
(d) None of these 
Answer: b

Question: (x-1)x²-5x+7)<(x-1), then x belongs to
(a) (1, 2) ∪ (3,∞)
(b) (2,3)
(c) (- ∞,1)∪ (2, 3)
(d) None of these 
Answer: c

Question: If x2+2ax+b≥c,∀x∈ R, then
(a) b -a ≥ a²
(b) c -a b ≥ b²
(c) a- b≥ c²
(d) None of these 
Answer: a

Question: If |x + 3| ≥ 10, then
(a) x ∈(−13,7]
(b) x ∈(−13,7)
(c) x ∈(−∞,13]∪[−7,∞)
(d) x ∈(−∞, −13]∪[7,∞)
Answer: d

Question: One lies between the roots of the equation -x²+ax+a=0,a∈R if and only if a lies in the interval
(a) (1/2,∞)
(b)(-1/2,∞)
(c) (-∞,1/2)
(d)(-∞,1/2) 
Answer: a

Question: x²-3|x|+ 2<0, then x belongs to
(a) (1, 2)
(b) (-2, -1,)
(c) (-2, -1,)∪(1, 2)
(d) (-3 5, )
Answer: a

Question: If x2+6x-27>0 and x2-3x-4>0, then
(a) x > 3
(b) x < 4
(c) 3 <x < 4
(d) x =7/2 
Answer: c

Question: The solution set of |x-2|-1/|x-2|-2≥0 is
(a) [0 ,1 ]∪(3,4)
(b) [ -1,1]∪ [3,4]
(c) [ 0,1] ∪ (3,4) 
(d) None of these 
Answer: b

Question: |2x -3|<|x+5|,then x belongs to
(a) (-3, 5)
(b) (5, 9)
(c) (-2/3,8)
(d) -8,2/3)
Answer: c

ASSERTION - REASON TYPE QUESTIONS

(a) Assertion is correct, reason is correct; reason is a correct explanation for assertion.
(b) Assertion is correct, reason is correct; reason is not a correct explanation for assertion
(c) Assertion is correct, reason is incorrect
(d) Assertion is incorrect, reason is correct.

Question:
Assertion : Two real numbers or two algebraic expressions related by the symbol < , >, ≤ or ≥ forms an inequality.
Reason : The inequality ax + by < 0 is strict inequality.
Answer: b

Question:
Assertion : If 3x + 8 > 2, then x ∈ {–1, 0, 1, 2, …}, when x is an integer.
Reason : The solution set of the inequality 4x + 3 < 5x + 7 ∀ x ∈ R is [4, ∞).
Answer: c

Question:
Assertion : The region containing all the solutions of an inequality is called the solution region.
Reason : The values of x, which make an inequality a true statement, are called solutions of the inequality.
Answer: b

Question:
Assertion : If a < b, c < 0, then a/c < b/c.
Reason : If both sides are divided by the same negative quantity, then the inequality is reversed.
Answer: d

Question:
Assertion : The inequality 3x + 2y ≥ 5 is the linear inequality.
Reason : The solution of 5x – 3 < 7, when x is a real number, is (–∞, 2).
Answer: b

Question:
Assertion : A non-vertical line will divide the plane into left and right half planes.
Reason : The solution region of a system of inequalities is the region which satisfies all the given inequalities in the system simultaneously.
Answer: d