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In "The Complete IPU CET Number System & Arithmetic Course 2026," the concept of prime factorization is crucial for understanding divisibility rules and LCM/HCF calculations. If a number N is expressed as $N = 2^a \times 3^b \times 5^c$, what is the condition on 'a', 'b', and 'c' for N to be a perfect cube?
The course emphasizes the efficient calculation of arithmetic series. Consider an arithmetic progression where the sum of the first 'n' terms is given by $S_n = 3n^2 + 2n$. What is the 5th term of this series?
"The Complete IPU CET Number System & Arithmetic Course 2026" covers the nuances of percentage changes. If the price of an item is first increased by 20% and then decreased by 25%, what is the net percentage change in its original price?
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