## Linear Inequalities Quiz-3

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. f(x)=((x-2)(x-1))((├ x-3) ),∀ x>3. The minimum value of f(x) is equal to
•  3+2√2
•  3+2√3
•  3+2√3
•  3√2-2
Solution
Q2.A rod fixed length k slides along the coordinate axes. If it meets the axes at A(a,0) and B(0,b), then the minimum value of (a+1/a)2+(b+1/b)2 is
•  0
•  8
•  k2-4+4⁄k2
•  k2+4+4⁄k2
Solution
Q3.  If positive numbers a,b,c be in H.P., then equation x2–kx+2b101-a101-c101 = 0 (k∈R) has
•  Both roots positive
•  Both roots negative
•  One positive and one negative root
•  Both roots imaginary
Solution

Q4. If a,b,c are the sides of a triangle, then the minimum value of ab+c-a+bc+a-b+ca+b-c is equal to
•  3
•  6
•  9
•  12
Solution
Q5.The least value of 6 tan^2⁡Ï•+54 cot^2⁡Ï•+18 is (I) 54 when A.M.≥G.M. is applicable for 6 tan2Ï•, 54 cot2Ï•, 18 (II) 54 whenA M.≥G.M. is applicable for 6 tan2Ï•, 54 cot2Ï• and 18 is added future (III) 78 when tan2Ï•=cot2Ï•
•  (I) is correct, II is false
•  (I) and (II) are correct
•  (III) is correct
•  None of the above are correct
Solution
Q6.If roots of the equation f(x)= x6-12x^5+bx4+cx3+dx2+ex+64=0 are positive, then Which has the greatest absolute value?
•  b
•  c
• d
•  e
Solution
Q7.Equation x4+ax3+bx2+cx+1=0 has real roots (a,b,c are non-negative). Minimum non-negative real value of a is
•  10
•  9
•  6
•  4
Solution

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