CUET UG Mathematics — Statistics & Applications previous year questions with solutions.
The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of m is
Which of the following statements are correct? (A) The method of least squares determines the position of the trend line of the given time series. (B) The trend line is called the line of best fit. (C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive. (D) The normal equations of the trend line $y = a + bx$ are $\sum y = na + b \sum x$ and $\sum xy = a \sum x + b \sum x^2$, where $n$ is the numbers of observations. Choose the *correct* answer from the options given below:
Which of the following is correct about the Sinking Fund?
If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data: | Year $(x)$ | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---|---|---| | Profit (Rs. '000) $(y)$ | 14 | 30 | 26 | 44 | 38 | 56 | 64 | The trend value for the year 2021 by least square method is:
Which of the following is correct about the compound annual growth rate?
In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?
If the price of a machinery costing ₹ 25000 is expected to have a useful life of 4 years and a scrap value of ₹ 5000. Then the annual depreciation by linear method is:
Mr. 'X' wishes to purchase a house for ₹ 49,65,000 with a down payment of ₹ 15,00,000 and balance amount in EMI for 25 years. If bank charges 6% per annum compounded monthly. Then the EMI is: [Given that $(1.005)^{300} = 4.4650]$
If the money is worth 8% per annum compounded semi-annually, then the present value of a sequence of payments of ₹1,000 made at the end of every 6 months and continuing forever, is:
A person invested ₹ 20000 in a mutual fund in year 2018. The value of the mutual fund increased to ₹ 32000 in year 2023. The compound annual growth rate of his investment is: [Given that $(1.6)^{1/5} = 1.098]$
Consider the following hypothesis test: $H_0: \mu \leq 12$ $H_a: \mu > 12$ A sample of 25 provided a sample mean $\bar{x} = 14$ and a sample standard deviation $s = 4.32$. If $t_{0.05} = 1.711$, then which of the following is correct? (A) The test statistic is defined as $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$. (B) The value of the test statistic is 1.31. (C) At $\alpha = 0.05$, the null hypothesis is rejected. (D) If the value of the t-statistic is less than $t_\alpha$, then null hypothesis is accepted. Choose the correct answer from the options given below:
In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table | Date | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---| | Number of cases | 2 | 0 | 5 | 12 | 20 | 27 | 46 | The 3-day moving averages are:
Ram invested Rs.20,000 in a mutual fund in the year 2012. The value of the mutual fund increased to Rs.32,000 in the year 2017, then the compound annual growth rate of his investment is (Given that $(1.6)^{\frac{1}{5}} = 1.098$)
Mr. Vishnu has an initial investment of Rs.80,000 in an investment plan. After 3 years, it has grown to Rs.1,00,000, then his rate of return is
Which of the following statements are TRUE? (A) The variable t of t-distribution ranges from $-\infty$ to $\infty$. (B) The probability curve of the t-distribution is symmetric about the line $t=0$ (C) The variance of the t-distribution is greater than one. (D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve. Choose the correct answer from the options given below:
For the following data: | | Size | Mean | Standard deviation | |---|---|---|---| | Sample 1 | 4 | 40 | 8 | | Sample 2 | 5 | 50 | 10 | The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to
The break-even point is the level of production where
If $(t_1, y_1)$, $(t_2, y_2)$,......,$(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variables $y$, then
Choose the correct statement about Sinking Fund?
Choose the correct statement about CAGR(compound annual growth rate)?
A machine costing Rs.2,00,000 has a useful life of 5 years.The estimated scrap value is Rs.20,000. By using straight line method, the annual depreciation is
The following data are from a random sample: 5,8,10,7,10,14, then the point estimate of the population standard deviation is
Assuming the same rate of change continues for the following data: | Year (x) | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---| | Profit(in Percentage) (y) | 38 | 40 | 65 | 72 | 69 | The equation of the straight line trend using the least square method is:
Which of the following statements are TRUE? (A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends. (B) The price of stocks in the share market repeats after a definite time interval. (C) The rise and fall of the share market is an example of a cyclic trend. (D) The rise in prices before festivals is an example of a irregular trend. Choose the correct answer from the options given below: