QUESTION PAPER
2022 BOARD EXAM
CBSE CLASS 12-PCM MATHEMATICS Board Paper 2022 — Set 1
2022
MATHEMATICS
CLASS 12-PCM
CBSE EXAMINATION PAPER-2022
MATHEMATICS
(Solved)
General Instructions :
Read the following instructions carefully and follow them :
- This question paper contains 21 questions. All questions are compulsory.
- This question paper is divided into 4 sections.
- Section A – questions number 1 to 5 are case based questions
- Section B – questions number 6 to 13 are very short answer
- Section C – questions number 14 to 18 are short answer
- Section D – questions number 19 to 21 are long answer
- There is no overall choice given in the question paper. However, an internal choice has been provided in few questions.
- Use of calculator is NOT allowed.
Section A
In Mathematics, relations can be expressed in various ways. The matchstick patterns are based on linear relations. Different strategies can be used to calculate the number of matchsticks used in different figures.
One such pattern is shown below. Observe the pattern and answer the following questions using Arithmetic Progression.
(1) Write the AP for the number of triangles used in the figures. Also, write the nᵗʰ term of this AP.
(2) Which figure has 61 matchsticks?
[2 Marks]Gadisar Lake is located in the Jaisalmer district of Rajasthan. It was built by the King of Jaisalmer and rebuilt by Gadsi Singh in the 14ᵗʰ century. The lake has many Chhatris. One of them is shown below. observe the picture From a point A h m above water level, the angle of elevation of top of Chhatri (point B) is 45° and angle of depression of its reflection in water (point C) is 60°. If the height of Chhatri above water level is approximately 10 m, then
(1) Draw a well-labelled figure based on the above information.
[2 Marks](2) Find the height (h) of the point A above water level. (Use √3 = 1.73)
Section B
Find the sum of first 30 terms of AP: -30, -24, -18, ..... .
In an AP if Sₙ= n (4n + 1), then find the AP.
Solve the following quadratic equation for x : √3x² + 10x + 7 √3= 0
Find the mode of the following frequency distribution:
The product of Rehan’s age (in years) 5 years ago and his age 7 years from now, is one more than twice his present age. Find his present age.
Section C
For what value of x is the median of the following frequency distribution 34.5?
Following is the daily expenditure on lunch by 30 employees of a company:
Find the mean daily expenditure of the employees.
Section D
Water in a canal, 8 m wide and 6 m deep, is flowing with a speed of 12 km/hour. How much area will it irrigate in one hour, if 0.05 m of standing water is required ?
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