Numbers, Quantification & Numerical Application Chapter Important Questions
Class 12 CBSE Applied Maths aims to develop an understanding of basic mathematical and statistical tools and their
applications in the field of commerce (business/ finance/economics) and social
sciences. Topics covered in Class 12th Applied Maths includes : Numbers, Quantification and
Numerical Applications, Algebra, Calculus, Probability Distributions , Inferential Statistics, Index Numbers and Time-based data , Financial Mathematics , Linear Programming.
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Arithmetic function f is a function where domain is a set of positive integer and range is a subset of complex number.
i.e. f : Z+ → C
Also known as number theoretic functions.
𝜏(n) : Number of positive divisors of n, n∈ N
σ(n) : Sum of all positive divisors of n, n∈ N
σK(n): Sum of K th power of all positive divisors of n, K, n ∈ N
π(n) : Number of primes ≤ n , n∈ N
ω(n) : Number of distinct prime factor of n, n ∈ N
Ω(n) :Total number of prime factors of n, n&isin N.
i.e. f : Z+ → C
Also known as number theoretic functions.
𝜏(n) : Number of positive divisors of n, n∈ N
σ(n) : Sum of all positive divisors of n, n∈ N
σK(n): Sum of K th power of all positive divisors of n, K, n ∈ N
π(n) : Number of primes ≤ n , n∈ N
ω(n) : Number of distinct prime factor of n, n ∈ N
Ω(n) :Total number of prime factors of n, n&isin N.
Some Arithmetic Functions :
1. Number of positive divisors of n (τ(n))
Q1. 𝜏(36)
Solution :
Q2. 𝜏(28)
Solution :
2. Sum of all positive divisors of n (σ(n))
Q3. σ(18)
Solution :
Q4. σ(30)
Solution :
3. Sum of K th power of all positive divisors of n (σK(n))
Q5. (σ2(10))
Solution :
Q6. (σ4(3))
Solution :
4. Number of primes ≤ n, (π(n))
Q7. π(14)
Solution :
Q8. π(24)
Solution :
5. Number of distinct prime factor of n (ω(n))
Q9. ω(8)
Solution :
Q10. ω(105)
Solution :
6. Total number of prime factors of n (Ω(n))
Q11. Ω(8)
Solution :
Q12. Ω(156)
Solution :
𝜏(n) is a multiplicative function
Q13. 𝜏(6)
Solution :
σ(n) is a multiplicative function
Q14. σ(10)
Solution :
ω(n) is a multiplicative function
Q15. ω(10)
Solution :
