Given information:
- The charges Q, q, and q are placed at the vertices of a right-angled isosceles triangle.
- The net electrostatic energy of the configuration is zero.
- The value of √2 is given as 1.4.

To find:
The value of 10×∣Q/q∣.

Solution:

Step 1: Understanding the configuration:
- Let's assume that the length of each side of the isosceles triangle is 'a'.
- The angle between the two equal sides of the triangle is 90 degrees.
- The right angle is formed at the vertex where the charge Q is placed.
- The other two vertices of the triangle have charges q and q.

Step 2: Analyzing the electrostatic potential energy:
- The electrostatic potential energy between two charges can be calculated using the formula:
Potential energy = (k * Q * q) / r,
where k is the electrostatic constant (9 × 10^9 Nm^2/C^2), Q and q are the magnitudes of the charges, and r is the distance between the charges.
- In the given configuration, the net electrostatic energy is zero. This implies that the potential energy between every pair of charges is zero.

Step 3: Calculating the distances:
- Let's consider the distance between Q and q as d1, and the distance between q and q as d2.
- Since the triangle is isosceles, the length of the perpendicular from the vertex with charge Q to the base of the triangle is (a/2).
- Using Pythagoras theorem, we can calculate the distances d1 and d2 as:
d1 = √[(a/2)^2 + (a/2)^2] = √(2 * (a/2)^2) = √(a^2/2) = a/√2
d2 = a

Step 4: Analyzing the potential energy equations:
- We know that the potential energy between two charges is given by the equation:
Potential energy = (k * Q * q) / r

- Since the potential energy between every pair of charges is zero, we can write the following equations:
(k * Q * q) / d1 = 0 (between Q and q)
(k * q * q) / d2 = 0 (between q and q)

- From these equations, we can conclude that either Q or q must be zero.
- Since the value of Q is given, we can conclude that q must be zero.

Step 5: Calculating the value of 10×∣Q/q∣:
- Since q is zero, the value of Q/q is undefined.
- Therefore, the value of 10×∣Q/q∣ is also undefined in this case.

Conclusion:
- Based on the given information and calculations, the value of 10×∣Q/q∣ is undefined, not '6' as mentioned in the question.