Correct Answer: −, +, ×, ÷, ×, ×, =

Solution : Given:
[{(14 @ 6) @ (2 @ 3)} @ (1 @ 7)] @ 2 @ 4

Replacing the @ signs in the given equation,

First option: ×, ÷, ×, ×, −, +, =
[{(14 @ 6) @ (2 @ 3)} @ (1 @ 7)] @ 2 @ 4
[{(14 × 6) ÷ (2 × 3)} × (1 − 7)] + 2 = 4
Solving the L.H.S, we get −
= [{(14 × 6) ÷ (2 × 3)} × (1 − 7)] + 2
= [(84 ÷ 6) × (− 6)] + 2
= [ 14 × (− 6)] + 2
= − 84 + 2
= − 82 ≠ R.H.S
Second option: −, +, ×, ×, ×, ×, =
[{(14 @ 6) @ (2 @ 3)} @ (1 @ 7)] @ 2 @ 4
[{(14 − 6) + (2 × 3)} × (1 × 7)] × 2 = 4
Solving the L.H.S, we get −
= [{(14 − 6) + (2 × 3)} × (1 × 7)] × 2
= [(8 + 6) × 7 ] × 2
= (14 × 7) × 2
= 98 × 2
= 196 ≠ R.H.S
Third option: ×, −, +, ×, ÷, ×, =
[{(14 @ 6) @ (2 @ 3)} @ (1 @ 7)] @ 2 @ 4
[{(14 × 6) − (2 + 3)} × (1 ÷ 7)] × 2 = 4
Solving the L.H.S, we get −
= [{(14 × 6) − (2 + 3)} × (1 ÷ 7)] × 2
= [(84 − 5) × 0.14] × 2
= (79 × 0.14) × 2
= 11.06 × 2
= 22.12 ≠ R.H.S
Fourth option: −, +, ×, ÷, ×, ×, =
[{(14 @ 6) @ (2 @ 3)} @ (1 @ 7)] @ 2 @ 4
[{(14 − 6) + (2 × 3)} ÷ (1 × 7)] × 2 = 4
Solving the L.H.S, we get −
= [{(14 − 6) + (2 × 3)} ÷ (1 × 7)] × 2
= [(8 + 6) ÷ 7] × 2
= (14 ÷ 7) × 2
= 2 × 2
= 4 = R.H.S

So, only the fourth option satisfies the R.H.S. of the given equation. Hence, the fourth option is correct.