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Modern Maths CAT 2025 Slot 1 Actual Questions
Concepts of Indices | HARD | CAT 2025 Slot 1
Question 1 of 5
For any natural number k, let aₖ = 3ᵏ. The smallest natural number m for which (a₁)¹ × (a₂)² × ... × (a₂₀)²⁰ < (a₂₁ × a₂₂ × ... × a₂₀₊ₘ)⁵ is:
In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is ______
The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is ____.
The number of distinct integers n for which log1/4 of (n² − 7n + 11) > 0 is _____.
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is