AfterBoards Logo
Skip to main contentSkip to solution

CUET Mathematics 2025 PYQs16 May Shift 1. Free, no login required.

Statistics & Applications

past year questions, CUET Mathematics 2025 16 May Shift 1

Trends & Data

past year questions, Statistics & Applications, CUET Mathematics 2025 16 May Shift 1

Hard

applied

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year (x)Rural Household (y%)Urban Household (y%)
202026
202137
202239
2023415
2024520

Based on the above data, which of the following statements are correct?

(A) A straight line trend by the method of the least squares for rural Indians is yty^t = 3.4 + 0.7 (x - 2022)

(B) A straight line trend by the method of the least squares for urban Indians is yty^t = 11.4 + 4.3 (x - 2022)

(C) The forecast for the year 2025 for urban group using the trend equation is 22.2 %.

(D) The forecast for the year 2025 for rural group using the trend equation is 5.5 %.

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 2

In the Method of Least Squares, the trend line equation is:

yt=a+b(X)y^t = a + b(X)

where X=x−xˉX = x - \bar{x},   a=∑yn\;a = \dfrac{\sum y}{n},   b=∑Xy∑X2\;b = \dfrac{\sum Xy}{\sum X^2}

Since there are 5 years (odd), the middle year 2022 is the origin, so X=x−2022X = x - 2022.

This makes ∑X=0\sum X = 0, which simplifies the calculations.

YearXXRural (y1y_1)Urban (y2y_2)X2X^2X⋅y1X \cdot y_1X⋅y2X \cdot y_2
2020−2264−4−12
2021−1371−3−7
2022039000
202314151415
2024252041040
Total0175710736

Statement (A) — Rural Trend Line:

a=175=3.4a = \dfrac{17}{5} = 3.4

b=710=0.7b = \dfrac{7}{10} = 0.7

yt=3.4+0.7(x−2022)y^t = 3.4 + 0.7(x - 2022)

Statement (A) is correct. ✅

Statement (B) — Urban Trend Line:

a=575=11.4a = \dfrac{57}{5} = 11.4

b=3610=3.6b = \dfrac{36}{10} = 3.6

yt=11.4+3.6(x−2022)y^t = 11.4 + 3.6(x - 2022)

Statement (B) claims b=4.3b = 4.3, but the correct value is 3.63.6.

Statement (B) is incorrect. ❌

Statement (C) — Urban Forecast for 2025:

yt=11.4+3.6(2025−2022)y^t = 11.4 + 3.6(2025 - 2022)

=11.4+3.6(3)= 11.4 + 3.6(3)

=11.4+10.8= 11.4 + 10.8

=22.2%= 22.2\%

Statement (C) is correct. ✅

Statement (D) — Rural Forecast for 2025:

yt=3.4+0.7(2025−2022)y^t = 3.4 + 0.7(2025 - 2022)

=3.4+0.7(3)= 3.4 + 0.7(3)

=3.4+2.1= 3.4 + 2.1

=5.5%= 5.5\%

Statement (D) is correct. ✅

Statements (A), (C) and (D) are correct.

The correct answer is Option 2.

Related questions:

2025: 15 May Shift 1

The rise in prices before festivals is an example of

2025: 13 May Shift 1

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table

Date1234567
Number of cases20512202746

The 3-day moving averages are:

2025: 21 May Shift 1

If (t1,y1),(t2,y2),(t3,y3),...,(tn,yn)(t_1, y_1), (t_2, y_2), (t_3, y_3), ..., (t_n, y_n) denote the time series and yty_t are the trend values of the variable y, then ∑(y−yt)\sum(y - y_t), the sum of the deviations of y from their corresponding trend value is equal to:

2026: 15 May Shift 1

Which of the following statements are correct?

A. If x1,x2,x3,…,xnx_1,x_2,x_3,\dots,x_n is the given annual time series, then 3-yearly moving averages are x1+x2+x33,x2+x3+x43,……\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots

B. In the method of the least squares, if (t1,y1),(t2,y2),…(tn,yn)(t_1,y_1),(t_2,y_2),\dots(t_n,y_n) denote the time series and yty_t are trend values of yy, then ∑(y−yt)=0\sum(y-y_t)=0

C. In the method of the least squares, the sum of squares of the deviations of the values of yy from their corresponding trend values is least.

D. The rise in prices before Diwali is an example of a cyclical trend.

Choose the correct answer from the options given below:

2026: 22 May Shift 1

For the given 9 values, 4,5,5,6,7,8,9,8,10, the three years moving averages are

2026: 30 May Shift 1

In reference to the Time Series Analysis, which of the following statements are correct?

A. Variations which generally occur due to the general tendency of the data to increase or decrease, are known as secular variations.

B. Variations which occur due to change in climate, wheather conditions, festivals etc. are known as seasonal variations.

C. Variations which occur due to some unpredictable forces are known as cyclic variations.

D. Variations which occur due to booms and depressions are known as irregular variations.

Choose the correct answer from the options given below:

Keyboard Shortcuts

  • Left arrow: Previous question
  • Right arrow: Next question
  • S key: Jump to solution
  • Q key: Jump to question

CUET Mathematics Past Year Questions (Topic-Wise)