Class 12 CBSE Applied Maths Number Quantification & Numerical Applications Exercise 1.2
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.
Please Select
Q1.
If t(n) =Number of positive divisors of n, n ∈ N, then find
(i) t(16)
(ii) t(28)
(iii) t(36)
(iv) t(45)
Solution :
Q2. If σ(n)=Sum of all positive divisors of n, n ∈ N, then find (1) σ (18) (ii) σ (30) (iii) σ (36) (iv) σ (49)
Solution :
Q3.
If σk(n) = Sum of kth powers of all the positive divisors of n, n ∈ N, then find
(i) σ2(12)
(ii) σ3(4)
(iii) σ3(9)
(iv) σ4(3)
Solution :
Q4.
If π(n)= Number of primes less than or equal to n, n ∈ N, then find
(i) π(24)
(ii) π(40)
(iii) π(52)
(iv) π(63)
Solution :
Q5.
If ω (n) = Number of distinct prime factors of n, n ∈ N, then find
(i) ω(22)
(ii) ω(68)
(iii) ω(105)
(iv) ω(780)
Solution :
Q6.
If Ω(n) = Total number of prime factors of n, n ∈ N, then find
(i) Ω(36)
(ii) Ω(156)
(iii) Ω(221)
(iv) Ω(420)
Solution :
Q7.
If ϕ(n) represents Euler totient function, then find
(i) ϕ(39)
(ii) ϕ(56)
(iii) ϕ(77)
(iv) ϕ(420)
(v) ϕ(950)
(vi) ϕ(2000)
(vii) ϕ(9650)
(viii) ϕ(80850)
Solution :
Q8. Show that the sum of values of totient functions of all divisors of 48 is 48.
Solution :
Q9.
If μ (n) represents Mobius function, then find
(i) μ (60)
(ii) μ (110)
(iii) μ (2310)
(iv) μ (3465)
Solution :
