Class 12 Applied MathematicsImportant Questions for Board Exams

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.

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.

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.

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.

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.

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.

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.

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?