CUET UG Mathematics — Statistics & Applications previous year questions with solutions.
On 1st April 2024, person 'X' purchased a machinery costing ₹ 65000 and spent ₹ 10000 on its installation. The estimated effective life of the machinery is 5 years with a scrap value of ₹ 10000. The annual depreciation using the straight-line method with the accounting year ending on 31st March 2025 is:
Match List-I with List-II | List-I | List-II | |---|---| | (A) An observed set of population selected for analysis | (I) Parameter | | (B) A specific characteristic of the population | (II) Hypothesis | | (C) A specific characteristic of the sample | (III) Statistic | | (D) A statement made about a population parameter for testing | (IV) Sample | Choose the correct answer from the options given below:
If $y = a + b(x - 2022)$ is a straight line trend using the least square method for the following data | Year ($x$) | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---| | Profit (Rs. '000) ($y$) | 2 | 3 | 4 | 5 | 2 | Then the value of $\frac{a}{b}$ is:
A sofa set costing ₹ 36000 has a useful life of 10 years. If the annual depreciation is ₹ 3000, then the scrap value by linear method is:
Which of the following are correct? (A) Time series analysis does not help to understand the behavior of a variable in the past. (B) Time series predict the future behavior of variable. (C) Time series helps to plan future operations. (D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner. Choose the correct answer from the options given below:
A person invested ₹ 10000 in a stock of a company for 6 years. The value of his investment at the end of each year is given in the following table: | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---| | ₹ 11000 | ₹ 11500 | ₹ 13000 | ₹ 11800 | ₹ 12200 | ₹ 14000 | The compound annual growth rate (CAGR) of his investment is: [Given $(1.4)^{1/6} = 1.058$]
Which of the following are the assumptions underlying the use of t-distribution? (A) The variance of population is known. (B) The samples are drawn from a normally distributed population. (C) Sample standard deviation is an unbiased estimate of the population variance. (D) It depends on a parameter known as degree of freedom. Choose the correct answer from the options given below:
Ms. Sheela creates a fund of ₹ $1,00,000$ for providing scholarships to needy children. The scholarship is provided in the beginning of the year. This fund earns an interest of $r \%$ per annum. If the scholarship amount is taken as ₹ $8,000$, then $r=$
Match List-I with List-II: | List-I Property Type | List-II EMI amount (in ₹) | | --- | --- | | (A) P | (I) 25,600 | | (B) Q | (II) 38,400 | | (C) R | (III) 32,000 | | (D) S | (IV) 35,200 |
A Multinational company creates a sinking fund by setting a sum of ₹ $12,000$ annually for $10$ years to pay off a bond issue of ₹ $72,000$. If the fund accumulates at $5 \%$ per annum compound interest, then the surplus after paying for bond is : (Use $\left.(1.05)^{10} \approx 1.6\right)$
Which of the following are components of a time series ? (A) Irregular component (B) Cyclical component (C) Chronological Component (D) Trend Component Choose the **correct** answer from the options given below :
The following data is from a simple random sample : $15,23, x, 37,19,32$ If the point estimate of the population mean is $23$, then the value of $x$ is :
For an investment, if the nominal rate of interest is $10 \%$ compounded half yearly, then the effective rate of interest is :
If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$, then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )