## Linear Inequalities Quiz-1

Mathematics is an important subject in JEE ADVANCED and other engineering exams. In any engineering enterance exam, Mathematics carries weightage of 33% of questions. In mathematics a linear inequality is an inequality which involves a linear function. A linear inequality contains one of the symbols of inequality. With focused practice good marks can be fetched from this section. These questions are very important in achieving your success in JEE and Other Engineering Exams.

Q1. If a,b,c,d are positive real numbers such that a+b+c+d=2, then M=(a+b)(c+d) satisfies the relation
•  0≤M≤1
•  1≤M≤2
•  2≤M≤3
•  3≤M≤4
Solution
Q2.The product of n positive numbers is unity. Then their sum is
•  A positive integer
•  Divisible by n
•  Equals to n+1n
•  Never less than n
Solution
Q3.  If a,b,c,d∈R+-{1}, then the minimum value of logd a+logb⁡d+loga⁡c+logc⁡b is
•  4
•  2
•  1
•  None of these
Solution

Q4. For x2– (a+3)|x|+4 =0 to have real solutions, the range of a is
•  (-∞,-7]∪[1,∞)
•  (-3,∞)
•  (-∞,-7)
•  (1,∞)
Solution

Q5.If f(x)=x2+2bx+2c2 and g(x)=-x2-2cx+b2 such that min⁡ f(x)>max⁡ g(x), then the relation between b and c, is
•  No real value of b and c
•  0<c<b√2
•  |c|<|b|√2
•  |c|>|b|√2
Solution
Q6. If a,b,c,∈R2, then (a+b+c)(1a+1b+1c) is always
•  ≥12
•  ≥9
• ≤12
•  None of these
Solution

Q7.If a,b,c,∈R+ such that a+b+c=18, then the maximum value of a2b3c4 is equal to
•  218×32
•  218×33
•  219×32
•  219×33
Solution

Q8.The minimum value of (x4+y4+z2)xyz for positive real numbers x,y,z is
•  √2
•  2√(2)
•  4√(2)
•  8√(2)
Solution
Q9.If y=3(x-1)+3(-x-1), then the least value of y is
•  2
•  6
•  2/3
•  3/2
Solution
Q10. The least value of the expression 2 log10⁡x-log10⁡⁡(0⋅01), for x>1, is
•  10
•  2
•  -0.01
• None of these
Solution

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