If ‘P’ denotes ’addition’, ‘D’ denotes ’subtraction’, ’S’ denotes ‘multiplication’, and ‘V’ denotes ’division’, then what will be the value of the following expression? 5 (7 S 3) D 3 (8 P 6) V 7 D 11 (3 S 13 S 2) P 2 (41 S 9)

Correct — C.
Rule: swap the letters for signs, then apply BODMAS.
A number written against a bracket multiplies it.

Swap: 5(7 × 3) − 3(8 + 6) ÷ 7 − 11(3 × 13 × 2) + 2(41 × 9)
Brackets: 21, 14, 78 and 369
Multiply and divide: 5 × 21 = 105, 3 × 14 ÷ 7 = 6, 11 × 78 = 858, 2 × 369 = 738

Now left to right: 105 − 6 = 99
99 − 858 = −759
−759 + 738 = −21 → option (c).

Why the others are wrong

• (a)
  96 — 96 is positive, but the total cannot be. The two large terms give −858 + 738 = −120, which outweighs 105 − 6 = 99.
• (b)
  42 — 42 is 3 × 14, the second term before its division by 7. It is a step inside the working, not the value of the whole expression.
• (d)
  21 — 21 has the right size and the wrong sign. The terms total 99 − 120 = −21, so a positive result means a sign was flipped on the way.

Once the letters become signs, this is plain order of operations: brackets first, then × and ÷, then + and −, each left to right.

The trap in this layout is the number sitting against each bracket. 5 (7 S 3) means 5 × 21, not 21 alone, and the same holds for 3 (8 P 6), 11 (3 S 13 S 2) and 2 (41 S 9).

Key facts

• Here P = +, D = −, S = × and V = ÷.
• A number written before a bracket multiplies it: 11(78) = 858.
• The four terms are +105, −6, −858 and +738.

Common traps

• Using a bracket's value alone and dropping the number in front of it
• Losing the minus sign when the negative terms outweigh the positive ones

No directly related past PYQ was found.