NCERT Solutions
Class 12 Applied Mathematics
8 chapters · 16 important questions
Numbers, Quantification and Numerical Applications
Covers modular arithmetic, successive discounts, partnership, time and work, time and distance, and Boats and Streams — all in the context of applied numericals.
Key Topics
Important Questions
Two partners invest in ratio 3:5 for 4 months and 6 months respectively. Find their profit sharing ratio.
A boat travels 36 km upstream and returns in 8 hours. Speed of stream is 3 km/h. Find speed of boat.
Algebra
Covers matrices (addition, scalar multiplication, multiplication, transpose) and determinants (calculation, properties, inverse of 2×2 and 3×3 matrices, solving linear equations using Cramer's rule).
Key Topics
Important Questions
Find the inverse of the matrix [[2,3],[1,4]] and use it to solve the system of equations.
Using Cramer's rule, solve: 2x + y = 5 and 3x − 2y = 4.
Calculus
Covers limits (standard results), continuity, differentiation of log and exponential functions, and applications of derivatives in business — marginal cost, marginal revenue, maxima and minima of cost and profit functions.
Key Topics
Important Questions
A company's cost function is C(x) = x³ − 6x² + 15x + 5. Find the marginal cost at x = 4 and determine whether cost is minimum or maximum.
Find dy/dx for y = x² · eˣ · log x.
Probability Distributions
Covers random variables, expected value and variance, Bernoulli trials, Binomial distribution (mean = np, variance = npq), and introduction to normal distribution.
Key Topics
Important Questions
A coin is tossed 8 times. Find P(exactly 3 heads) using Binomial distribution.
For a binomial distribution with n = 10 and p = 0.4, find mean and variance.
Index Numbers and Time-Based Data
Covers construction of index numbers (Laspeyre's, Paasche's, Fisher's), Consumer Price Index, time series analysis, and trend by moving averages.
Key Topics
Important Questions
Calculate Laspeyre's, Paasche's and Fisher's index numbers from the given price and quantity data.
Calculate 3-year moving averages for the given time series data and identify the trend.
Financial Mathematics
Covers compound interest, effective rate of interest, EMI calculation, annuities (present value and future value), sinking funds, linear depreciation, and reducing balance method.
Key Topics
Important Questions
Find the EMI for a loan of ₹5,00,000 at 12% per annum for 5 years.
A machine costing ₹2,00,000 depreciates at 20% per annum on reducing balance. Find its value after 3 years.
Linear Programming
Covers formulation of linear programming problems, graphical method (feasible region, corner points), and application to maximisation (profit) and minimisation (cost) problems in business.
Key Topics
Important Questions
A manufacturer makes two products. Formulate and solve the given LPP graphically to maximise profit.
Identify the feasible region and find the maximum value of Z = 5x + 4y subject to given constraints.
Inferential Statistics
Covers population vs sample, types of sampling (random, stratified, systematic), sampling distributions, Central Limit Theorem, confidence intervals, and basic hypothesis testing (z-test, t-test).
Key Topics
Important Questions
A sample of 100 students has mean score 72 with SD 10. Construct a 95% confidence interval for the population mean.
Distinguish between census and sample survey. What are the advantages of sampling?