case study questions for ap class 10

Case Study Questions Class 10 Maths Arithmetic Progressions

Case study questions class 10 maths chapter 5 arithmetic progressions.

CBSE Class 10 Case Study Questions Maths Arithmetic Progressions. Term 2 Important Case Study Questions for Class 10 Board Exam Students. Here we have arranged some Important Case Base Questions for students who are searching for Paragraph Based Questions Arithmetic Progressions.

At Case Study Questions there will given a Paragraph. In where some Important Questions will made on that respective Case Based Study. There will various types of marks will given 1 marks, 2 marks, 3 marks, 4 marks.

CBSE Case Study Questions Class 10 Maths Arithmetic Progressions

Case Study – 1

Q.1) Aditya is celebrating his birthday. He invited his friends. He bought a packet of toffees/candies which contains 120 candies. He arranges the candies such that in the first row there are 3 candies, in second there are 5 candies, in third there are 7 candies and so on.

[ KVS Raipur 2021 – 22 ]

On the basis of the above information, answer any four of the following questions:

(i) Find the total number of rows of candies.

(ii) Find the difference in number of candies placed in 7th and 3rd rows.

(i) There is an AP: 3,5,7,

a = 3 & d = 2 so apply let there are n rows sum of n terms = n/2 {2 + ( − 1)}

120 = n/2 {2 × 3 + (n − 1) 2}

we get n 2 + 2n − 120 = 0 then n = 10 & − 12 So there are 10 rows

(ii) 7th row=3+(7-1)X2 = 3 + 12 = 15 and 3rd row = 3+(3-1) X 2 = 7 their diff.= 8

CASE STUDY 2:

Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, answer the following:

[ CBSE Academic Question Bank ]

(1) The amount paid by him in 30th installment is

Answer: (a) 3900

(2) The amount paid by him in the 30 installments is

Answer: (b) 73500

(3) What amount does he still have to pay offer 30th installment?

Answer: (c) 44500

(4) If total installments are 40 then amount paid in the last installment?

Answer: (a) 4900

(5) The ratio of the 1st installment to the last installment is

Answer: (b) 10:49

Case Study – 3

India is competitive manufacturing location due to the low cost of manpower and strong technical and engineering capabilities contributing to higher quality production runs. The production of TV sets in a factory increases uniformly by a fixed number every year. It produced 16000 sets in 6th year and 22600 in 9th year.

1.) In which year, the production is Rs 29,200.

2.) Find the production during first year.

Ans: Rs – 5000

3.) Find the difference of the production during 7th year and 4th year.

Ans: Difference= 18200-11600=6600

4.) Find the production during first 3 years.

Ans: Production during first 3 year= 5000 + 7200 + 9400 = 21600

5.) Find the production during 8th year.

Ans: Production during 8th year is (a+7d) = 5000 + 2 (2200) = 20400

We hope that above case study questions will help you for your upcoming exams. To see more click below – 

• CBSE Class 10 Maths (standard)
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Chapter 5 Class 10 Arithmetic Progressions

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Updated for new NCERT Book - 2023-24 Edition

Get solutions of all NCERT Questions with examples of Chapter 5 Class 10 Arithmetic Progressions (AP). Video of all questions are also available. 

In this chapter, we will learn

• What is an AP - and what is First term (a) and Common Difference (d) of an Arithmetic Progression
• Finding n th term of an AP (a n )
• Finding n using a n formula
• Finding AP when some terms are given
• Finding n th term from the last term
• Finding Sum of n terms of an AP ( S n ) - both formulas
• Finding number of terms when Sum is given
• If n th term is given, finding S
• Some statement questions using a n and S n formulas, including optional exercise

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CBSE Case Study Questions for Class 10 Maths Arithmetic Progressions Free PDF

Mere Bacchon, you must practice the CBSE Case Study Questions Class 10 Maths Arithmetic Progressions  in order to fully complete your preparation . They are very very important from exam point of view. These tricky Case Study Based Questions can act as a villain in your heroic exams!

I have made sure the questions (along with the solutions) prepare you fully for the upcoming exams. To download the latest CBSE Case Study Questions , just click ‘ Download PDF ’.

CBSE Case Study Questions for Class 10 Maths Arithmetic Progressions PDF

Checkout our case study questions for other chapters.

• Chapter 3: Pair of Linear Equations in Two Variables Case Study Questions
• Chapter 4: Quadratic Equation Case Study Questions
• Chapter 6: Triangles Case Study Questions
• Chapter 7: Coordinate Geometry Case Study Questions

How should I study for my upcoming exams?

First, learn to sit for at least 2 hours at a stretch

Solve every question of NCERT by hand, without looking at the solution.

Solve NCERT Exemplar (if available)

Sit through chapter wise FULLY INVIGILATED TESTS

Practice MCQ Questions (Very Important)

Practice Assertion Reason & Case Study Based Questions

Sit through FULLY INVIGILATED TESTS involving MCQs. Assertion reason & Case Study Based Questions

After Completing everything mentioned above, Sit for atleast 6 full syllabus TESTS.

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CBSE Class 10 Maths Case Study Questions PDF

Download Case Study Questions for Class 10 Mathematics to prepare for the upcoming CBSE Class 10 Final Exam. These Case Study and Passage Based questions are published by the experts of CBSE Experts for the students of CBSE Class 10 so that they can score 100% on Boards.

CBSE Class 10 Mathematics Exam 2024  will have a set of questions based on case studies in the form of MCQs. The CBSE Class 10 Mathematics Question Bank on Case Studies, provided in this article, can be very helpful to understand the new format of questions. Share this link with your friends.

Table of Contents

Chapterwise Case Study Questions for Class 10 Mathematics

Inboard exams, students will find the questions based on assertion and reasoning. Also, there will be a few questions based on case studies. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

The above  Case studies for Class 10 Maths will help you to boost your scores as Case Study questions have been coming in your examinations. These CBSE Class 10 Mathematics Case Studies have been developed by experienced teachers of cbseexpert.com for the benefit of Class 10 students.

• Class 10th Science Case Study Questions
• Assertion and Reason Questions of Class 10th Science
• Assertion and Reason Questions of Class 10th Social Science

Class 10 Maths Syllabus 2024

Chapter-1  real numbers.

Starting with an introduction to real numbers, properties of real numbers, Euclid’s division lemma, fundamentals of arithmetic, Euclid’s division algorithm, revisiting irrational numbers, revisiting rational numbers and their decimal expansions followed by a bunch of problems for a thorough and better understanding.

Chapter-2  Polynomials

This chapter is quite important and marks securing topics in the syllabus. As this chapter is repeated almost every year, students find this a very easy and simple subject to understand. Topics like the geometrical meaning of the zeroes of a polynomial, the relationship between zeroes and coefficients of a polynomial, division algorithm for polynomials followed with exercises and solved examples for thorough understanding.

Chapter-3  Pair of Linear Equations in Two Variables

This chapter is very intriguing and the topics covered here are explained very clearly and perfectly using examples and exercises for each topic. Starting with the introduction, pair of linear equations in two variables, graphical method of solution of a pair of linear equations, algebraic methods of solving a pair of linear equations, substitution method, elimination method, cross-multiplication method, equations reducible to a pair of linear equations in two variables, etc are a few topics that are discussed in this chapter.

Chapter-4  Quadratic Equations

The Quadratic Equations chapter is a very important and high priority subject in terms of examination, and securing as well as the problems are very simple and easy. Problems like finding the value of X from a given equation, comparing and solving two equations to find X, Y values, proving the given equation is quadratic or not by knowing the highest power, from the given statement deriving the required quadratic equation, etc are few topics covered in this chapter and also an ample set of problems are provided for better practice purposes.

Chapter-5  Arithmetic Progressions

This chapter is another interesting and simpler topic where the problems here are mostly based on a single formula and the rest are derivations of the original one. Beginning with a basic brief introduction, definitions of arithmetic progressions, nth term of an AP, the sum of first n terms of an AP are a few important and priority topics covered under this chapter. Apart from that, there are many problems and exercises followed with each topic for good understanding.

Chapter-6  Triangles

This chapter Triangle is an interesting and easy chapter and students often like this very much and a securing unit as well. Here beginning with the introduction to triangles followed by other topics like similar figures, the similarity of triangles, criteria for similarity of triangles, areas of similar triangles, Pythagoras theorem, along with a page summary for revision purposes are discussed in this chapter with examples and exercises for practice purposes.

Chapter-7  Coordinate Geometry

Here starting with a general introduction, distance formula, section formula, area of the triangle are a few topics covered in this chapter followed with examples and exercises for better and thorough practice purposes.

Chapter-8  Introduction to Trigonometry

As trigonometry is a very important and vast subject, this topic is divided into two parts where one chapter is Introduction to Trigonometry and another part is Applications of Trigonometry. This Introduction to Trigonometry chapter is started with a general introduction, trigonometric ratios, trigonometric ratios of some specific angles, trigonometric ratios of complementary angles, trigonometric identities, etc are a few important topics covered in this chapter.

Chapter-9  Applications of Trigonometry

This chapter is the continuation of the previous chapter, where the various modeled applications are discussed here with examples and exercises for better understanding. Topics like heights and distances are covered here and at the end, a summary is provided with all the important and frequently used formulas used in this chapter for solving the problems.

Chapter-10  Circle

Beginning with the introduction to circles, tangent to a circle, several tangents from a point on a circle are some of the important topics covered in this chapter. This chapter being practical, there are an ample number of problems and solved examples for better understanding and practice purposes.

Chapter-11  Constructions

This chapter has more practical problems than theory-based definitions. Beginning with a general introduction to constructions, tools used, etc, the topics like division of a line segment, construction of tangents to a circle, and followed with few solved examples that help in solving the exercises provided after each topic.

Chapter-12  Areas related to Circles

This chapter problem is exclusively formula based wherein topics like perimeter and area of a circle- A Review, areas of sector and segment of a circle, areas of combinations of plane figures, and a page summary is provided just as a revision of the topics and formulas covered in the entire chapter and also there are many exercises and solved examples for practice purposes.

Chapter-13  Surface Areas and Volumes

Starting with the introduction, the surface area of a combination of solids, the volume of a combination of solids, conversion of solid from one shape to another, frustum of a cone, etc are to name a few topics explained in detail provided with a set of examples for a better comprehension of the concepts.

Chapter-14  Statistics

In this chapter starting with an introduction, topics like mean of grouped data, mode of grouped data, a median of grouped, graphical representation of cumulative frequency distribution are explained in detail with exercises for practice purposes. This chapter being a simple and easy subject, securing the marks is not difficult for students.

Chapter-15  Probability

Probability is another simple and important chapter in examination point of view and as seeking knowledge purposes as well. Beginning with an introduction to probability, an important topic called A theoretical approach is explained here. Since this chapter is one of the smallest in the syllabus and problems are also quite easy, students often like this chapter

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Class 10 Maths Chapter 5 Case Based Questions - Arithmetic Progressions

Case study - 1.

Your elder brother wants to buy a car and plans to take loan from a bank for his car. He repays his total loan of Rs 1,18,000 by paying every month starting with the first instalment of Rs 1000. If he increases the instalment by Rs 100 every month, answer the following:

Case Study - 2

Case Study - 3

Based on the above information, answer the following questions:

Q1: Find the production during first year. Ans: We are given that the production of TV sets in the factory is increasing uniformly. This means that we can apply the formula of an arithmetic progression, where the nth term (a_n) is given by a + (n-1)d. Here, 'a' is the first term, 'n' is the term number, and 'd' is the common difference. We know that the 6th year production (a_6) is 16000 and the 9th year production (a_9) is 22600. We can subtract the 6th year production from the 9th year to find the total increase over 3 years, which is 6600. This means that the common difference ('d') is 6600/3 = 2200 sets per year. Substituting the values into the nth term formula: 16000 = a + (6-1)*2200 16000 = a + 11000 => a = 16000 - 11000 => a = 5000 So, the production during the first year was 5000 sets.   Q2: Find the production during 8th year. Ans: We can use the nth term formula again to find the production in the 8th year. a_8 = a + (8-1)*d = 5000 + 7*2200 = 5000 + 15400 = 20400 So, the production during the 8th year was 20400 sets.   Q3: Find the production during first 3 years. Ans:  To find the total production over the first 3 years, we sum the production over each year. In an arithmetic progression, the sum of the first n terms (S_n) is given by n/2 * (2a + (n-1)d). S_3 = 3/2 * (2*5000 + (3-1)*2200) = 1.5 * (10000 + 4400) = 1.5 * 14400 = 21600 So, the total production during the first 3 years was 21600 sets.   Q4: In which year, the production is Rs 29,200. Ans: To find the year when the production was 29200, we can use the nth term formula and solve for n. 29200 = 5000 + (n-1)2200 => 24200 = (n-1)2200 => n-1 = 24200/2200 => n-1 = 11 => n = 12 So, the production was 29200 sets in the 12th year.   Q5: Find the difference of the production during 7th year and 4th year. Ans: We can find the production in the 7th and 4th years using the nth term formula, and then subtract the two. a_7 = 5000 + 6*2200 = 18200 a_4 = 5000 + 3*2200 = 11600 Difference = a_7 - a_4 = 18200 - 11600 = 6600 So, the difference in production between the 7th and 4th years was 6600 sets.  

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Case Study Class 10 Maths Questions

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Download the app to get CBSE Sample Papers 2023-24, NCERT Solutions (Revised), Most Important Questions, Previous Year Question Bank, Mock Tests, and Detailed Notes.

Now, CBSE will ask only subjective questions in class 10 Maths case studies. But if you search over the internet or even check many books, you will get only MCQs in the class 10 Maths case study in the session 2022-23. It is not the correct pattern. Just beware of such misleading websites and books.

We advise you to visit CBSE official website ( cbseacademic.nic.in ) and go through class 10 model question papers . You will find that CBSE is asking only subjective questions under case study in class 10 Maths. We at myCBSEguide helping CBSE students for the past 15 years and are committed to providing the most authentic study material to our students.

Here, myCBSEguide is the only application that has the most relevant and updated study material for CBSE students as per the official curriculum document 2022 – 2023. You can download updated sample papers for class 10 maths .

First of all, we would like to clarify that class 10 maths case study questions are subjective and CBSE will not ask multiple-choice questions in case studies. So, you must download the myCBSEguide app to get updated model question papers having new pattern subjective case study questions for class 10 the mathematics year 2022-23.

Class 10 Maths has the following chapters.

• Real Numbers Case Study Question
• Polynomials Case Study Question
• Pair of Linear Equations in Two Variables Case Study Question
• Quadratic Equations Case Study Question
• Arithmetic Progressions Case Study Question
• Triangles Case Study Question
• Coordinate Geometry Case Study Question
• Introduction to Trigonometry Case Study Question
• Some Applications of Trigonometry Case Study Question
• Circles Case Study Question
• Area Related to Circles Case Study Question
• Surface Areas and Volumes Case Study Question
• Statistics Case Study Question
• Probability Case Study Question

Format of Maths Case-Based Questions

CBSE Class 10 Maths Case Study Questions will have one passage and four questions. As you know, CBSE has introduced Case Study Questions in class 10 and class 12 this year, the annual examination will have case-based questions in almost all major subjects. This article will help you to find sample questions based on case studies and model question papers for CBSE class 10 Board Exams.

Maths Case Study Question Paper 2023

Here is the marks distribution of the CBSE class 10 maths board exam question paper. CBSE may ask case study questions from any of the following chapters. However, Mensuration, statistics, probability and Algebra are some important chapters in this regard.

Case Study Question in Mathematics

Here are some examples of case study-based questions for class 10 Mathematics. To get more questions and model question papers for the 2021 examination, download myCBSEguide Mobile App .

Case Study Question – 1

In the month of April to June 2022, the exports of passenger cars from India increased by 26% in the corresponding quarter of 2021–22, as per a report. A car manufacturing company planned to produce 1800 cars in 4th year and 2600 cars in 8th year. Assuming that the production increases uniformly by a fixed number every year.

• Find the production in the 1 st year.
• Find the production in the 12 th year.
• Find the total production in first 10 years. OR In which year the total production will reach to 15000 cars?

Case Study Question – 2

In a GPS, The lines that run east-west are known as lines of latitude, and the lines running north-south are known as lines of longitude. The latitude and the longitude of a place are its coordinates and the distance formula is used to find the distance between two places. The distance between two parallel lines is approximately 150 km. A family from Uttar Pradesh planned a round trip from Lucknow (L) to Puri (P) via Bhuj (B) and Nashik (N) as shown in the given figure below.

• Find the distance between Lucknow (L) to Bhuj(B).
• If Kota (K), internally divide the line segment joining Lucknow (L) to Bhuj (B) into 3 : 2 then find the coordinate of Kota (K).
• Name the type of triangle formed by the places Lucknow (L), Nashik (N) and Puri (P) OR Find a place (point) on the longitude (y-axis) which is equidistant from the points Lucknow (L) and Puri (P).

Case Study Question – 3

• Find the distance PA.
• Find the distance PB
• Find the width AB of the river. OR Find the height BQ if the angle of the elevation from P to Q be 30 o .

Case Study Question – 4

• What is the length of the line segment joining points B and F?
• The centre ‘Z’ of the figure will be the point of intersection of the diagonals of quadrilateral WXOP. Then what are the coordinates of Z?
• What are the coordinates of the point on y axis equidistant from A and G? OR What is the area of area of Trapezium AFGH?

Case Study Question – 5

The school auditorium was to be constructed to accommodate at least 1500 people. The chairs are to be placed in concentric circular arrangement in such a way that each succeeding circular row has 10 seats more than the previous one.

• If the first circular row has 30 seats, how many seats will be there in the 10th row?
• For 1500 seats in the auditorium, how many rows need to be there? OR If 1500 seats are to be arranged in the auditorium, how many seats are still left to be put after 10 th row?
• If there were 17 rows in the auditorium, how many seats will be there in the middle row?

Case Study Question – 6

• Draw a neat labelled figure to show the above situation diagrammatically.

• What is the speed of the plane in km/hr.

More Case Study Questions

We have class 10 maths case study questions in every chapter. You can download them as PDFs from the myCBSEguide App or from our free student dashboard .

As you know CBSE has reduced the syllabus this year, you should be careful while downloading these case study questions from the internet. You may get outdated or irrelevant questions there. It will not only be a waste of time but also lead to confusion.

Here, myCBSEguide is the most authentic learning app for CBSE students that is providing you up to date study material. You can download the myCBSEguide app and get access to 100+ case study questions for class 10 Maths.

How to Solve Case-Based Questions?

Questions based on a given case study are normally taken from real-life situations. These are certainly related to the concepts provided in the textbook but the plot of the question is always based on a day-to-day life problem. There will be all subjective-type questions in the case study. You should answer the case-based questions to the point.

What are Class 10 competency-based questions?

Competency-based questions are questions that are based on real-life situations. Case study questions are a type of competency-based questions. There may be multiple ways to assess the competencies. The case study is assumed to be one of the best methods to evaluate competencies. In class 10 maths, you will find 1-2 case study questions. We advise you to read the passage carefully before answering the questions.

Case Study Questions in Maths Question Paper

CBSE has released new model question papers for annual examinations. myCBSEguide App has also created many model papers based on the new format (reduced syllabus) for the current session and uploaded them to myCBSEguide App. We advise all the students to download the myCBSEguide app and practice case study questions for class 10 maths as much as possible.

Case Studies on CBSE’s Official Website

CBSE has uploaded many case study questions on class 10 maths. You can download them from CBSE Official Website for free. Here you will find around 40-50 case study questions in PDF format for CBSE 10th class.

10 Maths Case Studies in myCBSEguide App

You can also download chapter-wise case study questions for class 10 maths from the myCBSEguide app. These class 10 case-based questions are prepared by our team of expert teachers. We have kept the new reduced syllabus in mind while creating these case-based questions. So, you will get the updated questions only.

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• CBSE Reduced Syllabus Class 10 (2020-21)
• Class 10 Maths Basic Sample Paper 2024
• How to Revise CBSE Class 10 Maths in 3 Days
• CBSE Practice Papers 2023
• Class 10 Maths Sample Papers 2024
• Competency Based Learning in CBSE Schools

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Arithmetic Progressions (AP) - PYQ

Class 10 | chapter - 5 | arithmetic progression (ap).

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CBSE 10th Standard Maths Subject Arithmetic Progressions Case Study Questions With Solution 2021

By QB365 on 22 May, 2021

QB365 Provides the updated CASE Study Questions for Class 10 Maths, and also provide the detail solution for each and every case study questions . Case study questions are latest updated question pattern from NCERT, QB365 will helps to get  more marks in Exams

QB365 - Question Bank Software

10th Standard CBSE

Final Semester - June 2015

Case Study Questions

(ii) Find the sum of common difference of the two progressions.

(iii) Find the 19 th term of the progression written by Geeta.

(iv) Find the sum of first 10 terms of the progression written by Geeta.

(v) Which term of the two progressions will have the same value?

(ii) What is the total amount saved by Anuj in 8 days?

(iii) What is the amount saved by Anuj on 30 th day?

(iv) What is the total amount saved by him in the month of June, if he starts savings from 1 st June?

(v) On which day, he save tens times as much as he saved on day-I?

(ii) The number on first card is

(iii) What is the number on the 19 th card?

(iv) What is the number on the 23 rd card?

(v) The sum of numbers on the first 15 cards is 

A sequence is an ordered list of numbers. A sequence of numbers such that the difference between the consecutive terms is constant is said to be an arithmetic progression (A.P.). On the basis of above information, answer the following questions. (i) Which of the following sequence is an A.P.?

(ii) If x, y and z are in A.P., then

(iii) If a 1  a 2 , a 3  ..... , a n are in A.P., then which of the following is true?

(iv) If the n th term (n > 1) of an A.P. is smaller than the first term, then nature of its common difference (d) is

(v) Which of the following is incorrect about A.P.?

(ii) What is the first term?

(iii) Which term of the A.P. is -160?

(iv) Which of the following is not a term of the given A.P.?

(v) What is the 75 th term of the A.P.?

*****************************************

Cbse 10th standard maths subject arithmetic progressions case study questions with solution 2021 answer keys.

Geeta's A.P. is -5, -2, 1,4, ... Here, first term (a 1 ) = -5 and common difference (d 1 ) = -2 + 5 = 3 Similarly, Madhuri's A.P. is 187, 184, 181, ... Here first term (a 2 ) = 187 and common difference (d 2 ) = 184 - 187 = -3 (i) (b): t 34 = a 2 + 33d 2 = 187 + 33(-3) = 88 (ii) (d): Required sum = 3 + (-3) = 0 (iii) (a): t 19  = a 1  + 18d 1  = (-5) + 18(3) = 49 (iv) (a) :  \(S_{10}=\frac{n}{2}\left[2 a_{1}+(n-1) d_{1}\right]=\frac{10}{2}[2(-5)+9(3)]=85\) (v) (b): Let n th terms of the two A.P:s be equal. \(\therefore\) -5 + (n - 1)3 = 187 + (n - 1)(-3) \(\Rightarrow\) 6(n - 1) = 192 \(\Rightarrow\) n = 33

Here the savings form an A.P. i.e., Rs 2.75, Rs 3, Rs 3.25, ... So, a = 2.75, d = 3 - 2.75 = 0.25 (i) (b): Amount saved by Anuj on 14 th day = t 14 = a + 13d = 2.75 + 13(0.25) = ₹ 6 (ii) (d): Total amount saved by Anuj in 8 days \(=S_{8}=\frac{8}{2}[2(2.75)+7(0.25)]=₹ 29\) (iii) (a): Amount saved by Anuj on 30 th day = t 30 = a + 29d = 2.75 + 29(0.25) = ₹ 10 (iv) (b): Number of days in June = 30 \(\therefore S_{30}=\frac{30}{2}[2(2.75)+29(0.25)]=₹ 191.25\) (v) (d): Let on nth day, he saves 10 times as he saves on 1 st day. t n = 10(2.75) \(\Rightarrow\) a + (n - 1)d = 27.5 \(\Rightarrow\) n = 100.

Let the numbers on the cards be a, a + d, a + Zd, ... According to question, We have (a + 5d) + (a + 13d) = -76 \(\Rightarrow\) 2a+18d = -76 \(\Rightarrow\) a + 9d= -38 ... (1) And (a + 7d) + (a + 15d) = -96 \(\Rightarrow\) 2a + 22d = -96 \(\Rightarrow\) a + 11d = -48 ...(2) From (1) and (2), we get 2d= -10 \(\Rightarrow\) d= -5 From (1), a + 9(-5) = -38 \(\Rightarrow\) a = 7 (i) (b): The difference between the numbers on any two consecutive cards = common difference of the A.P.=-5 (ii) (d): Number on first card = a = 7 (iii) (b): Number on 19th card = a + 18d = 7 + 18(-5) = -83 (iv) (a): Number on 23rd card = a + 22d = 7 + 22( -5) = -103 (v) (d):  \(S_{15}=\frac{15}{2}[2(7)+14(-5)]=-420\)

(i) (c) (ii) (c) (iii) (d) (iv) (b) (v) (c)

We have, 3 rd term = 4 and 9 th term = -8 i.e., a + 2d = 4 ........(i) and a + 8d = -8 .........(ii) Solving (1) and (2), we get d = -2, a = 8 (i) (c) (ii) (d) (iii) (b): Let t n = -160 \(\Rightarrow\) a + (n - 1) d = -160 \(\Rightarrow\) 8 + (n - 1)(-2) = -160 \(\Rightarrow\) (n - 1)(-2) = -168 \(\Rightarrow\) n - 1 = 84 \(\Rightarrow\) n = 85 So, t 85  = -160 (iv) (a) (v) (a): t 75 = a + 74d = 8 + 74( -2) = -140

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Case Study Class 10 Maths

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Case Study Questions Class 10 Maths Chapter 1 Real Numbers

Case Study Questions Class 10 Maths Chapter 2 Polynomials

Case Study Questions Class 10 Maths Chapter 3 Pair of Equations in Two Variables

Case Study Questions Class 10 Maths Chapter 4 Quadratic Equations

Case Study Questions Class 10 Maths Chapter 5 Arithmetic Progressions

Case Study Questions Class 10 Maths Chapter 6 Triangles

Case Study Questions Class 10 Maths Chapter 7 Coordinate Geometry

Case Study Questions Class 10 Maths Chapter 8. Introduction to Trigonometry

Case Study Questions Class 10 Maths Chapter 9 Some Applications of Trigonometry

Case Study Questions Class 10 Maths Chapter 10 Circles

Case Study Questions Class 10 Maths Chapter 12 Areas Related to Circles

Case Study Questions Class 10 Maths Chapter 13 Surface Areas & Volumes

Case Study Questions Class 10 Maths Chapter 14 Statistics

Case Study Questions Class 10 Maths Chapter 15 Probability

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Extra Questions For Class 10 Maths Chapter 5 Arithmetic Progression

• Last modified on: 1 year ago
• Reading Time: 30 Minutes

nth Term of an ARITHMETIC PROGRESSION ( AP ) nth term an of the AP with first term a and common difference d is given by a n = a + (n – 1) d.

nth Term from the end of an ARITHMETIC PROGRESSION ( AP ) Let the last term of an AP be ‘l’ and the common difference of an AP is ‘d’ then the nth term from the end of an AP is given by ln = l – (n – 1) d.

Q.1. Find the 10th term of the AP : 2, 7, 12, . . .

Q.2. Which term of the AP : 21, 18, 15, . . . is – 81?

Q.3. Which term of the AP : 3, 8, 13, 18, . . . ,is 78?

Q.4. How many two-digit numbers are divisible by 3?

Q.5. How many three-digit numbers are divisible by 7?

Q.6. How many multiples of 4 lie between 10 and 250?

Q.7. Find the 31st term of an AP whose 11th term is 38 and the 16th term is 73.

Q.8. An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29th term.

Q.9. If the 3rd and the 9th terms of an AP are 4 and – 8 respectively, which term of this AP is zero?

Q.10. Which term of the AP : 3, 15, 27, 39, . . . will be 132 more than its 54th term?

Q.11. Determine the AP whose third term is 16 and the 7th term exceeds the 5th term by 12.

Q.12. The sum of 4th term and 8th term of an AP is 24 and the sum of 6th and 10th terms is 44. Find the AP.

Q.13. The sum of 5th term and 9th term of an AP is 72 and the sum of 7th and 12th terms is 97. Find the AP.

Q.14. If the numbers n – 2, 4n – 1 and 5n + 2 are in AP, find the value of n.

Q.15. Find the value of the middle most term (s) of the AP : –11, –7, –3,…, 49.

Q.16. The sum of the first three terms of an AP is 33. If the product of the first and the third term exceeds the second term by 29, find the AP.

Q.17. The sum of the 5th and the 7th terms of an AP is 52 and the 10th term is 46. Find the AP.

Q.18. Find the 20th term of the AP whose 7th term is 24 less than the 11th term, first term being 12.

Q.19. If the 9th term of an AP is zero, prove that its 29th term is twice its 19th term.

Q.20. The 26th, 11th and the last term of an AP are 0, 3 and –1/5 , respectively. Find the common difference and the number of terms.

Q.21. Find whether 55 is a term of the AP: 7, 10, 13,— or not. If yes, find which term it is.

Q.22. Determine k so that k2+ 4k + 8, 2k2 + 3k + 6, 3k2 + 4k + 4 are three consecutive terms of an AP.

Q.23. Split 207 into three parts such that these are in AP and the product of the two smaller parts is 4623.

Q.24. The angles of a triangle are in AP. The greatest angle is twice the least. Find all the angles of the triangle.

Q.25. If the nth terms of the two APs: 9, 7, 5, … and 24, 21, 18,… are the same, find the value of n. Also find that term.

Q.26. If sum of the 3rd and the 8th terms of an AP is 7 and the sum of the 7th and the 14th terms is –3, find the 10th term.

Q.27. Which term of the AP: 53, 48, 43,… is the first negative term?

Q.28. A sum of Rs 1000 is invested at 8% simple interest per year. Calculate the interest at the end of each year. Do these interests form an AP? If so, find the interest at the end of 30 years making use of this fact.

Q.29. In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 in the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

Q.30. Find the 20th term from the last term of the AP : 3, 8, 13, . . ., 253.

Q.31. Find the 10th term from the last term of the AP : 4, 9 , 14, . . ., 254.

Q.32. Find the 6th term from the end of the AP 17, 14, 11, …… (–40).

Q.33. Find the 8th term from the end of the AP 7, 10, 13, …… 184.

Q.34. Find the 10th term from the last term of the AP : 8, 10, 12, . . ., 126.

Q.35. Find the 12th term from the end of the AP: –2, –4, –6,…, –100.

Sum of First n Terms of an ARITHMETIC PROGRESSION ( AP )

The sum of the first n terms of an AP is given by

where a = first term, d = common difference and n = number of terms.

where l = last term

Q.36. If the sum of the first 14 terms of an AP is 1050 and its first term is 10, find the 20th term.

Q.37. How many terms of the AP : 24, 21, 18, . . . must be taken so that their sum is 78?

Q.38. How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?

Q.39. Find the sum of first 24 terms of the list of numbers whose nth term is given by an = 3 + 2n

Q.40. Find the sum of the first 40 positive integers divisible by 6.

Q.41. Find the sum of the first 15 multiples of 8.

Q.42. Find the sum of the odd numbers between 0 and 50.

Q.43. Find the sum of first 22 terms of an AP in which d = 7 and 22nd term is 149.

Q.44. Find the sum of first 51 terms of an AP whose second and third terms are 14 and 18 respectively.

Q.45. If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

Q.46. If an = 3 – 4n, show that a1,a2 ,a3 ,… form an AP. Also find S20 .

Q.47. In an AP, if Sn = n (4n + 1), find the AP.

Q.48. In an AP, if S n = 3n 2 + 5n and a k = 164, find the value of k.

Q.49. If Sn denotes the sum of first n terms of an AP, prove that S 12 = 3(S 8 –S 4 )

Q.50. Find the sum of first 17 terms of an AP whose 4th and 9th terms are –15 and –30 respectively.

Q.51. If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, find the sum of first 10 terms.

Q.52. Find the sum of all the 11 terms of an AP whose middle most term is 30.

Q.53. Find the sum of last ten terms of the AP: 8, 10, 12,—, 126.

Q.54. How many terms of the AP: –15, –13, –11,— are needed to make the sum –55? Explain the reason for double answer.

Q.55. The first term of an AP is –5 and the last term is 45. If the sum of the terms of the AP is 120, then find the number of terms and the common difference.

Q.56. Which term of the AP: –2, –7, –12,… will be –77? Find the sum of this AP upto the term –77.

Q.57. Find the sum of first seven numbers which are multiples of 2 as well as of 9.

Q.58. The sum of the first n terms of an AP whose first term is 8 and the common difference is 20 is equal to the sum of first 2n terms of another AP whose first term is – 30 and the common difference is 8. Find n.

Q.59. The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last terms to the product of the two middle terms is 7 : 15. Find the numbers.

Q.60. The sum of the first five terms of an AP and the sum of the first seven terms of the same AP is

Q.61. If the sum of the first ten terms of this AP is 235, find the sum of its first twenty terms.

Q.62. Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5.

Q.63. Find the sum of those integers from 1 to 500 which are multiples of 2 as well as of 5 .

Q.64. Find the sum of those integers from 1 to 500 which are multiples of 2 or 5.

Q.65. The eighth term of an AP is half its second term and the eleventh term exceeds one third of its fourth term by 1. Find the 15th term.

Q.66. An AP consists of 37 terms. The sum of the three middle most terms is 225 and the sum of the last three is 429. Find the AP.

Q.67. Find the sum of the integers between 100 and 200 that are (i) divisible by 9 (ii) not divisible by 9

Q.68. The ratio of the 11th term to the 18th term of an AP is 2 : 3. Find the ratio of the 5th term to the 21st term, and also the ratio of the sum of the first five terms to the sum of the first 21 terms.

Q.69. Solve the equation : 1 + 4 + 7 + 10 +…+ x =287

Q.70. Solve the equation – 4 + (–1) + 2 +…+ x = 437

Q.71. Jaspal Singh repays his total loan of Rs. 118000 by paying every month starting with the first installment of Rs 1000. If he increases the installment by Rs 100 every month, what amount will be paid by him in the 30th installment? What amount of loan does he still have to pay after the 30th installment?

Q.72. The houses of a row are numbered consecutively from 1 to 49. Show that there is a value of x such that the sum of the numbers of the houses preceding the house numbered x is equal to the sum of the numbers of the houses following it. Find this value of x.

Q.73. A manufacturer of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find : (i) the production in the 1st year (ii) the production in the 10th year (iii) the total production in first 7 years

Q.74. 200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how may rows are the 200 logs placed and how many logs are in the top row?

Q.75. A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: Rs 200 for the first day, Rs 250 for the second day, Rs 300 for the third day, etc., the penalty for each succeeding day being Rs 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

Q.76. A sum of Rs 700 is to be used to give seven cash prizes to students of a school for their overall academic performance. If each prize is Rs 20 less than its preceding prize, find the value of each of the prizes.

Q.77. In a school, students thought of planting trees in and around the school to reduce air pollution. It was decided that the number of trees, that each section of each class will plant, will be the same as the class, in which they are studying, e.g., a section of Class I will plant 1 tree, a section of Class II will plant 2 trees and so on till Class XII. There are three sections of each class. How many trees will be planted by the students?

Q.78. A spiral is made up of successive semicircles, with centres alternately at A and B, starting with centre at A, of radii 0.5 cm, 1.0 cm, 1.5 cm, 2.0 cm, . . . . What is the total length of such a spiral made up of thirteen consecutive semicircles?

Q.79. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line. A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Q.80. The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books? What is the maximum distance she travelled carrying a flag?

Q.81. Show that the sum of an AP whose first term is a, the second term b and the last term c, is equal to

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AP Class 10 Maths Important Questions for Board Exam 2024, Free PDF Download

Ap ssc maths important questions: get important questions to prepare for ap ssc class 10 maths exam 2024. check questions of 1, 2 and 4 marks to practise important questions and secure good marks in the mathematics exam..

AP Class 10 Maths Important Questions 2024

1 mark important questions.

1.Find the value of Log x √x.

2.If HCF (306, 657) = 9, find LCM.

3.If the prime factorization of natural number (n) is 2 3 x3 2 x5 2 x7. How many consecutive zeroes will it have at the end of it justify your answer?

4.If log 2  (x 2 -4x+7)=2 find the value of'x'.

5.If n(AUB)=51,n(A)=20, n(B)=44 then find n(A∩B)

6.If A={0,1,2}, B={2,4} find n(AUB)

7.Is 1/(x-1) a polynomial? Justify your answer.

8.The number of skirts is two less than twice the number of pants purchased. Also the number of skirts is four less than for times the number of pants purchased. Express this data in the form of a linear equation.

9.Check whether the pair of linear equations 2x+y-5 = 0 and 3x-2y-4 = 0 intersecting, parallel, or coincident lines?

10.The sum of the reciprocals of Rehman's ages (in years) 3 year ago and 5 years from now is 1/3. Find his present age.

11.Find the value of k for 2x 2 -kx+3=0,so that it has two equal roots ?

12.Evaluate cos36cos54 - sin36 sin54?

2 Mark Important Questions

1.Why 6 n +5 n  always end with 1? Explain

2.Prove that log a a=1

3.A number when divided by 61 gives 21 as quotient and 32 as remainder find the number.

4.Represent AUB, A∩B, A-B, B-A, A⊆B, B⊆A, A⊆B⊆C as Venn Diagrams

5.If A={1,2,3,4}, B= {1,2,3,5,6} then find A∩B and B∩A. Are they equal?

6.(i) If A={1,2,3},B={3,4,5}

(ii) A= (3,4,5,6,7}, B= {1,6,7,8,9} then verify n(AU B)=n(A)+n(B)-n(A-B)

7.Why are ¼ and - 1 zeroes of the polynomials p(x) = 4x 2  + 3х- 1?

8.Find quadratic polynomial whose zeroes are 2 and -1/3 respectively?

10.The difference of squares of two numbers is 180, the square of the smaller number is 8 times the larger number. Find the two numbers.

11.Find the roots of the equation

x + 1/x = 4(1/4), x≠0.

12.Find the 10th term of the AP 5, 1, -3, -7, ……………

13.Find x so that x, x+2, x+6 are consecutive terms of GP?

14.Subbarao started work in 1995 at annual salary of Rs.5000 received an increment of and Rs. 206 each year. In which year did his income reach Rs.7000?

15.A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved surface areas?

16.If sin(A-B)= ½ and cos(A+B) = ½ find A and B.

17.Find 'X' if the median of the observations in ascending order is

4 Mark Important Questions

1.(i) If x 2 +y 2 =25xy then show that 21og(x+y)=3log3+logx+logy

(ii)x 2 +y 2 =6xy then show that 2log(x+y)=3log2+logx+logy

2.(2.3) x =(0.23) Y  = 1000 then find the value of (1/x)-(1/y)

3.Show that a positive odd integer is of the form 4q+1 or 4q+3 where q is integer

4.Which of the following are sets? Justify

(i) the collection of all months of a year beginning with "j" (ii) The collection of ten most talented writers of India.

(iii) A team of eleven best cricket batsmen of the world.

(iv) The collection of all boys In your class

(v) the collection of all even

5.Find all the zeroes of 2x 4  - 3x 3  - 3x 2  + 6x- 2, if you know that two of its zeroes are √2 and - √2.

6.Verify that 1, -1 and - 3 are the zeroes of the cubic polynomial x 3  + 3x 2  - x - 3 and check the relationship between zeroes and the coefficients.

7.A boat goes 30km upstream and 44km downstream in 10hrs in 13hrs it can go 40km upstream and 55km downstream. Determine the speed of the stream and that of the boat in still water.

8.2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.

9.Solve 2/3 + 3/y  = 13 and 5/x - 4/y = -2.

10.Solve 3x+2y = 5 and 2x-2y = 7 graphically?

11.In a competitive exam, 3 marks are to awarded for every correct answer and for every wrong answer, 1 mark will ba deducted. Madhu scored 40 marks in this exam. Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer, Madhu would have scored 50 marks. How many questions were there in/the test? (Madhu attempted all the questions)

12.Two water taps together can fill a tank in 9(3/8) hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately find the time in which watch tap can separately fill the tank.

13.A manufacture of TV sets produced 600 sets in the third year and 700 sets in the seventh year. Assuming that the production increases uniformly by a fixed number every year, find

(i) the production in the 1 year?

(ii) the production in the 10 year?

(iii)the total production in 7 years?

15.Find the area of the segments shaded in figure, if PQ=24 cm, PR = 7 cm and QR is the diameter of the circle with centre Q. (Take  π=22/7)

16.Construct a triangle of sides 4cm, 5cm and 6 cm. Then Construct a triangle similar to it, whose sides are 2/3 of corresponding sides of first triangle.

17.If cosecθ + cotθ = k then prove that

cosθ = (k 2  − 1)/(k 2  + 1).

18.A straight high way leads to the foot of the tower. Ramaiah standing at the top of the tower observes a car at angle of depression 30 0 . The car is approaching the foot of the tower with a uniform speed. Six seconds later, the angle of depression of the cars is found to be 60 0 . Find the time taken by a car to reach the foot of the tower from this point?

19.A 1.5m tall boy is looking at the top of the temple which is 30m in height from a point at a certain distance. The angle of elevation from his eye to the top of the crown of the temple increases from 30º to 60 0  as he walks towards the temple. Find the distance he walked towards the temple.

20.A die is thrown once. Find the probability of getting:

(i) a prime number

(ii) a number lying between 2 and 6

(iii) an odd number

NCERT Solutions for Class 10 Maths (2023 - 2024) All Chapters, PDF Download

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• Class 10 Maths Important Questions

AP Board Class 10 Maths Important Questions

Class 10 is a crucial stage and are extremely important from a career point of view. The Class 10 results help the students getting into a choice of their colleges and in the desired stream. The topics that will be covered in Class 10 will help the students to improve basic concepts of the things that they are going to study in Class 11th and 12th. Important question paper for Maths should be added in the preparation strategy to score good marks in the examination. These questions usually cover the important concepts taken from the ap ssc maths study material . AP board Class 10 Maths important question should be practised on a regular basis, which will enhance skills and time management.

Important Questions for Class 10 Maths are prepared by subject experts by taking reference from the Class 10 Maths previous year question paper and the important questions given here are of utmost importance and some of them can be expected in the coming examinations also. Solving these important questions for Class 10 Maths will help students to grasp the concept of the subject and it will be a big help while preparing for the Class 10 Maths exam.

Important Questions for Class 10 Maths cover all the important topics from all the chapters as per the AP Board Class 10 Maths syllabus . It is a fruitful resource for Class 10 Maths student, so that they can clear out concepts without any doubt.

Download AP Board Class 10 Maths important Question PDF

1. Find the [HCF×LCM] for the number 100 and 190

2. If 1 is a zero of the polynomial p(x) = ax 2 – 3(a-1) x-1, then find the value of a.

3. In ΔLMN, ∠L = 50 0 and ∠N = 60 0 . If ΔLMN ~ ΔPQR, then find ∠Q

4. If sec 2 θ (1 + sin θ) (1- sin θ) = k, then find k

5. If the diameter of a semicircular protractor is 14 cm, what is its perimeter.

6. Find the number of solutions of the following pair of linear equations: x + 2y – 8 =0 and 2x + 4y =1

7. If one of the roots of the quadratic equation is 4, then the value of p is:

8. If the 17 th term of an AP exceeds the 10 th term by 7, then the common difference is:

9. Find all the zeroes of the polynomial x 3 + 3x 2 – 2x – 6.

10. In the A.P. 3, 15, 27, 39, … which term will be 120 more than the twenty first term?

11. In the figure below, Δ ABD is a right triangle, 90 degree at A and AC ^ BD. Prove that AB 2 = BC .

12. Calculate tan 60 practically.

13. The sum of two numbers is 8. if the sum of their reciprocals is What are the nos.

14. Draw a right triangle in which sides (other than hypotenuse) are of lengths 8 cm and 6 cm. Thereafter draw another triangle where sides are times the corresponding sides of the first triangle.

15. In the figure below, M is mid-point of CD. The line BM intersects AC at L and AD produced at E. Prove that EL = 2 BL.

16. Find the area of the quadrilateral ABCD whose vertices are A(-4, -2), B(-3, -5), C(3, -2) and D(2,3)

17. If -5 is a root of the quadratic equation 2x 2 + px – 15 = 0 and the equation p(x 2 +x) + k = 0 has discriminant zero, find p and k.

18. Prove that the lengths of the tangents drawn from an external point to a circle are equal. Using the above theorem, prove than If quadrilateral ABCD is circumscribing a circle, then AB + CD = AD + BC

19. A plane when flying at a height of 3125 m from the ground passes vertically below another plane at an instant when the angles of elevation of the two planes from the same point on the ground are 30° and 60° respectively. Find the length of ground between the two planes at that instant.

20.  Find the length of the tangent from a point 13cm away from the centre of the circle of radius 5cm.

21 . Find the total surface area of a hemisphere of radius 7cm.

22.  Half of the perimeter of a rectangular garden, whose length is 4m more than its width, is 36m. Find the dimensions of the garden.

Students who wish to get more practice in ap SSC maths can go through these important questions after solving the previous year and class 10 sample papers of mathematics.

Students can also access the ap ssc textbooks pdf from BYJU’S. Know more about AP Class 10 Question Papers , as well. 

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