Vedic Patterns G Strategy | Quadratic Equations | Hard If m and n are integers such that (m + 2n)(2m + n) = 27,then the maximum possible value of 2m − 3n is ___ Vedic Patterns G Strategy | Moderate Suppose a, b, c are three distinct natural numbers, such that 3ac = 8(a + … Read more
Vedic Patterns G Strategy | Inequality | EASY | CAT 2025 Slot 1 The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is ____. Vedic Pattern + Concepts of Logs DPAC G Strategy The number of distinct integers n for which … Read more
Question 1: Recurrence Relation If x₀ = 1, x₁ = 2, andxₙ₊₂ = (1 + xₙ₊₁) / xₙ for n = 0, 1, 2, …,then what is the value of x₂₀₂₁? Options: Answer:We calculate the first few values using the recurrence: From x₄ onward, the values repeat in a cycle: [1, 1, 2, 3, 2]This … Read more
The number of distinct integer solutions (x, y) of the equation |x + y| + |x – y| = 2, is If 10^68 is divided by 13, the remainder is1) 8 2) 9 3) 4 4) 5 Find the number of all positive integers up to 500 with non-repeating digits. Show/Hide Solution Type of Number … Read more
Ques 1 When 3^333 is divided by 11, the remainder is Ques 2 A function f maps the set of natural numbers to whole numbers, such that f(xy) = f(x)f(y) + f(x) + f(y) for all x, y and f(p) = 1 for every prime number p. Then, the value of f(160000) is 1) 4095 2) 1023 … Read more
MathJax Question For any natural number \( n \), let \( a_n \) be the largest integer not exceeding \( \sqrt{n} \). Then the value of \( a_1 + a_2 + \cdots + a_{50} \) is When 10^100 is divided by 7, find the remainder. a. 1 b. 6 c. 3 d. 4
CAT 2023 QA Slot 3 Quiz CAT 2023 QA Slot 3 Quiz 7. Algebra – Surds & Indices Let \( n \) be any natural number such that \( 5^{n-1} < 3^{n+1} \). The least integer value of \( m \) that satisfies \( 3^{n+1} < 2^{n+m} \) for all such \( n \) is? ... Read more
CAT 2023 QA Slot 2 – Questions and Solutions CAT 2023 QA Slot 2 Questions and Solutions Question 1 The number of positive integers less than 50, having exactly two distinct factors other than 1 and itself, is: A. 13 B. 15 C. 16 D. 17 Show Solution Answer: B. 15 Detailed Solution: Positive integers … Read more
CAT 2023 QA Question 1 CAT 2023 QA Question and Solution Question 13 A lab experiment measures the number of organisms at 8 am every day. Starting with 2 organisms on the first day, the number of organisms on any day is equal to 3 more than twice the number on the previous day. If … Read more