Minimum Value of A + B, If AB = Constant

Q. If p, q, r and s are four positive real numbers such that pqrs = 1, what is the minimum value of (1+p)(1+q)(1+r)(1+s)?___

Q. If abcd = 81, what is the minimum value of a + b + c + d ?

1. 9
2. 12
3. 36
4. 18

Q. If a, b, c are positive, then the minimum value of the expression $\frac{(a^2+a+1)(b^2+b+1)(c^2+c+1)}{abc}$ is:

1. 27
2. 1
3. 3
4. 9

Q. If a > 0, b > 0 and ab = 1, then the least value of the expression (1 + a) (1 + b) is :

1. $2$
2. $4$
3. $1$
4. $\frac{1}{4}$

Q.

If three positive real numbers x, y, z satisfy y - x = z - y and xyz = 4, then what is the minimum possible value of y ?

1. 2^1/3

2. 2^2/3

3. 2^1/4

4. 2^3/4

Q.

If $a^2{b}^{3}c=\frac{256}{27}$ find min value of a + b + c, given a, b, c are positive real nos.

1. 10
2. 11
3. 12
4. 4

Q.

Find the number of integers from $0$ to $999999$ that have no two equal neighboring digits in their decimal representation.

Q. P and Q are two integers such that PQ = 64. Which of the following cannot be the value of P+Q? (CAT 1997)

1. 20
2. 65
3. 16
4. 35

Q. The minimum value of the expression; $a+\frac{1}{a};a>0$is:

1. -2
2. 2
3. 1
4. can’t be determined
5. 0

Q.

Find the minimum value of a+b+c+d in the equation $x^5-a{x}^4+b{x}^3-c{x}^2+dx-243=0,$ if it is given that the roots are positive real numbers ?

1. 660

2. 720

3. 30

4. 780

Q. Given $A\times B=2$. Find the minimum value of (A + B), where A and B are positive.

1. $4\sqrt{2}$
2. $2\sqrt{2}$
3. $3\sqrt{2}$
4. $\sqrt{2}$

Q. Given that $a^7{b}^2{c}^3{d}^5=512$. Find the minimum value of $a^7+2b^2+2c^3+2d^5$.

1. 24
2. 32
3. 56
4. 48

Q. A lies between -4 and 10. B lies between 20 and 50. $\frac{B}{A}$ lies between?

1. none of these
2. 2, 25
3. 0, 50
4. 5, 12.5