CAT Surds and Indices previous year questions

13 Surds and Indices questions from CAT 2021–2025 (Quant), each with its answer and a step-by-step solution.

• Q19For any natural number k , let a_k=3^(k) . The smallest natural number m for which \ (a_1 )¹× (a_2 )²× cdots × (a_20…CAT 2025 Slot 1 · Quant · Surds and Indices
• Q5If 9^(x²+2x-3)-4 (3^(x²+2x-2) )+27=0 , then the product of all possible values of x isCAT 2025 Slot 2 · Quant · Surds and Indices
• Q9If 12^(12x)×4^(24x+12)×5^(2y)=8^(4z)×20^(12x)×243^(3x-6) , where x , y and z are natural numbers, then x+y+z equalsCAT 2025 Slot 3 · Quant · Surds and Indices
• Q2If ( a+b√n ) is the positive square root of ( 29-12√5 ) , where a and b are integers, and n is a natural number, then…CAT 2024 Slot 1 · Quant · Surds and Indices
• Q3The sum of all real values of k for which ( (1)/(8) )^(k)× ( (1)/(32768) )^((1)/(3))=(1)/(8)× ( (1)/(32768)…CAT 2024 Slot 1 · Quant · Surds and Indices
• Q13If ( x+6√2 )^((1)/(2))- ( x-6√2 )^((1)/(2))=2√2 , then x equalsCAT 2024 Slot 2 · Quant · Surds and Indices
• Q3If ( a+b√3 )²=52+30√3 , where a and b are natural numbers, then a+b equalsCAT 2024 Slot 3 · Quant · Surds and Indices
• Q3If √(5x+9)+√(5x-9)=3 ( 2+√2 ) , then √(10x+9) is equal toCAT 2023 Slot 1 · Quant · Surds and Indices
• Q2The sum of all possible values of x satisfying the equation 2^(4x²)-2^(2x²+x+16)+2^(2x+30)=0 , isCAT 2023 Slot 2 · Quant · Surds and Indices
• Q17The number of integer solutions of the equation (x²-10 )^( (x²-3x-10 ))=1 isCAT 2022 Slot 2 · Quant · Surds and Indices
• Q11If ( √((7)/(5)) )^(3x-y)=(875)/(2401) and ( (4a)/(b) )^(6x-y)= ( (2a)/(b) )^(y-6x) , for all non-zero real values of a…CAT 2022 Slot 3 · Quant · Surds and Indices
• Q15For all possible integers n satisfying 2.25≤ 2+2^(n+2)≤ 202 , the number of integer values of 3+3^(n+1) isCAT 2021 Slot 2 · Quant · Surds and Indices
• Q20If n is a positive integer such that ( 7√(10) ) ( 7√(10) )²cdots ( 7√(10) )ⁿ>999 , then the smallest value of n isCAT 2021 Slot 3 · Quant · Surds and Indices