Mathematical Operations Questions for UP POLICE CONSTABLE

Understanding Symbol Substitution

In these questions, you are given that a new symbol (like @, #, $, %) represents a specific mathematical operation. For example, 'A @ B means A + B' or 'A # B means A × B - 2'. Your job is to decode what the symbol means, then apply it to solve the given problem. The key is to read the definition carefully — sometimes the operation is simple (just +, -, ×, ÷), and sometimes it's a compound operation (like multiply then subtract, or divide then add). Always substitute step-by-step and follow order of operations (BODMAS).

• Read the symbol definition word-by-word — don't assume, don't skip
• Identify if the operation is simple (one step) or compound (multiple steps)
• Apply the definition exactly as stated; watch for 'first', 'then', 'and' keywords
• If multiple symbols appear, decode each one separately before solving
• Use BODMAS/PEMDAS even when symbols are involved — brackets, then operations left-to-right

Common Symbol Patterns in UP Police Papers

Examiners typically use 3-4 symbol types in one question. Pattern 1: Simple replacement (@ means +, # means ×). Pattern 2: Conditional operation (if A > B, then A @ B = A + B, else A @ B = A - B). Pattern 3: Compound formula (A @ B = 2A + B or A # B = A² - B). Pattern 4: Reverse/inverse operations (A @ B means divide A by B, not multiply). The most common trap is forgetting that the symbol definition overrides normal math — so 5 @ 3 does NOT mean 5 + 3 unless explicitly told so.

• Simple replacement: straightforward substitution, apply BODMAS
• Conditional: check the condition first (>, <, =), then apply the correct operation
• Compound formula: expand fully before calculating; don't skip steps
• Reverse/inverse: watch for 'reciprocal', 'opposite', 'inverse' language
• Multiple symbols in one expression: solve innermost/highest priority first, then work outward

Step-by-Step Solving Method

Always follow this 4-step process: (1) Identify all symbols used and write down their definitions clearly on your rough sheet. (2) Substitute the symbols in the given expression with their definitions. (3) Simplify using BODMAS — brackets first, then exponents, then ×/÷ left-to-right, then +/- left-to-right. (4) Double-check your answer by re-reading the symbol definition and verifying each step. This methodical approach prevents careless errors and saves time because you won't second-guess yourself.

• Step 1: Write definitions — this takes 5 seconds but prevents 90% of mistakes
• Step 2: Substitute carefully — use brackets if needed to avoid confusion
• Step 3: Apply BODMAS strictly — this is non-negotiable
• Step 4: Verify by working backward — plug your answer back into the definition
• If stuck, try each answer option and see which one matches the definition

Conditional & Multi-Symbol Scenarios

Some questions define operations that depend on a condition. For example, 'A @ B = A + B if A > B, else A - B'. Here you must check the condition FIRST. If A = 7 and B = 3, then 7 > 3 is true, so 7 @ 3 = 7 + 3 = 10. If A = 2 and B = 5, then 2 > 5 is false, so 2 @ 5 = 2 - 5 = -3. When multiple symbols appear in one expression like 'A @ B # C', decode left-to-right unless brackets suggest otherwise. Always respect brackets — they override left-to-right order.

• Check conditions before applying the operation — don't skip this
• Use a truth table if multiple conditions exist — write down which condition applies
• In multi-symbol expressions, solve left-to-right unless brackets say otherwise
• Brackets always take priority — solve inside brackets first, then substitute the result
• If the expression has nested operations, work from innermost to outermost

• Forgetting the symbol definition and using normal math — always re-read the definition before solving
• Ignoring BODMAS when multiple operations exist — even with symbols, order matters
• Misreading conditional statements — 'if A > B' is different from 'if A ≥ B'; check the exact symbol
• Solving right-to-left instead of left-to-right — unless brackets explicitly change the order, always go left-to-right
• Substituting wrong values — double-check which variable gets which value before plugging in numbers
• Skipping the verification step — re-reading the definition takes 3 seconds and catches 80% of errors

• Mnemonic 'DEFINE-SUBSTITUTE-SIMPLIFY-VERIFY' — this 4-step process is your safety net
• Acronym 'BODMAS' — Brackets, Orders, Division/Multiplication, Addition/Subtraction — never forget this order
• Visual hook: Treat the symbol definition as a 'recipe' — follow it exactly, don't improvise
• Phrase 'Condition first, operation second' — always check if-then-else BEFORE doing math

• UP Police papers typically give 2-3 symbol definitions upfront, then ask 2-4 questions using them — write all definitions on your rough sheet immediately
• Time pressure is real: if you decode correctly, each question takes 30-45 seconds; if you're stuck, move on and come back — don't waste 3 minutes on one symbol question
• Recent papers show a trend toward conditional operations (if-then-else) rather than simple substitution — practice these more
• Watch for trick questions where the symbol looks like a normal operation but isn't — e.g., @ might mean 'divide', not 'add'
• Answer options are often designed to catch common mistakes (e.g., forgetting BODMAS, using wrong operation) — if your answer matches an option, verify it once more before moving on