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.


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Exercise 1.1 Exercise 1.3 Exercise 1.4 Exercise 1.5 Exercise 1.6 Exercise 1.7 Exercise 1.8 Case Study

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)

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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)

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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)

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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)

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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)

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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)

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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)

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Q8. Show that the sum of values of totient functions of all divisors of 48 is 48.

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Q9. If μ (n) represents Mobius function, then find

(i) μ (60)
(ii) μ (110)
(iii) μ (2310)
(iv) μ (3465)

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