CAT Algebraic Identities previous year questions

7 Algebraic Identities questions from CAT 2022–2025 (Quant), each with its answer and a step-by-step solution.

• Q4If (x²+(1)/(x²) )=25 and x>0 , then the value of (x⁷+(1)/(x⁷) ) isCAT 2025 Slot 3 · Quant · Algebraic Identities
• Q3If m and n are natural numbers such that n>1 , and mⁿ=2²⁵×3⁴⁰ , then m-n equalsCAT 2024 Slot 2 · Quant · Algebraic Identities
• Q21If x and y are real numbers such that 4x²+4y²-4xy-6y+3=0 , then the value of ( 4x+5y ) isCAT 2024 Slot 2 · Quant · Algebraic Identities
• Q2If x and y are real numbers such that x²+ ( x-2y-1 )²=-4y ( x+y ) , then the value x-2y isCAT 2023 Slot 1 · Quant · Algebraic Identities
• Q21If p²+q²-29=2pq-20=52-2pq , then the difference between the maximum and minimum possible value of (p³-q³ ) isCAT 2023 Slot 2 · Quant · Algebraic Identities
• Q4If x is a positive real number such that x⁸+ ( (1)/(x) )⁸=47 , then the value of x⁹+ ( (1)/(x) )⁹ isCAT 2023 Slot 3 · Quant · Algebraic Identities
• Q15Let a and b be natural numbers. If a²+ab+a=14 and b²+ab+b=28 , then ( 2a+b ) equalsCAT 2022 Slot 1 · Quant · Algebraic Identities