Please refer to MCQ Questions Chapter 5 Arithmetic Progression Class 10 Mathematics with answers provided below. These multiple-choice questions have been developed based on the latest NCERT book for class 10 Mathematics issued for the current academic year. We have provided MCQ Questions for Class 10 Mathematics for all chapters on our website. Students should learn the objective based questions for Chapter 5 Arithmetic Progression in Class 10 Mathematics provided below to get more marks in exams.

**Chapter 5 Arithmetic Progression MCQ Questions**

Please refer to the following **Chapter 5 Arithmetic Progression MCQ Questions Class 10 Mathematics** with solutions for all important topics in the chapter.

**Question. Which term of the arithmetic progression 30, 27, 24,…. is O? **

(a) 8th term

(b) 10th term

(c) 13th term

(d) 11th term

**Answer**

D

**Question. The given figure shows a pattern of several squares drawn consecutively. **

**The perimeters of the squares in figure form an arithmetic progression. The length of the first square is x cm and the length of the other consecutive squares differ from each other by 1 cm. Given the sum of the perimeters of the first five squares is 160 cm, find the sum of the perimeters of the first 10 squares.**

(a) 280cm

(b) 240cm

(c) 420 cm

(d) 360 cm

**Answer**

C

**Question. A roll of thread 907i cm long is cut into 5 parts to make up 5 circles as shown in the figure. **

**The radii of the circles increase by 1 cm consecutively. Find the radius of the smallest circle.**

(a) 7 cm

(b) 5 cm

(c) 6 cm

(d) 9 cm

**Answer**

A

**Question. The numbers 28, 22, ‘x’, ‘y’, 4 are in arithmetic progression. What are the respective values of ‘x’ and ‘y’?**

(a) 10, 16

(b) 20, 18

(c) 18, 16

(d) 16, 10

**Answer**

D

**Question. Given P=3+5+7+ …. (n terms) and Q = 5 + 8 +11 +….. (10 terms).What is the value of ‘n’ if P/Q = 7 ? **

(a) 25

(b) 35

(c) 30

(d) 20

**Answer**

B

**Question. What is the value of ‘x’ if 2x, x + 10and 3x + 2 are in arithmetic progression? **

(a) 5

(b) 6

(c) 4

(d) -6

**Answer**

B

**Question. How many terms of the arithmetic progression 1, 9, 17, …. must be taken to give a sum of 1540? **

(a) 10

(b) 40

(c) 20

(d) 15

**Answer**

C

**Question. Find three numbers in arithmetic progression whose sum is 3 and product is- 35. **

(a) 1,5,7

(b) -5,7,-1

(c) -5,1,7

(d) -7,5,-1

**Answer**

C

**Question. Which is the first negative term of the arithmetic progression 35, 30, 25,…..? **

(a) 7th term

(b) 5th term

(c) 9th term

(d) 11th term

**Answer**

C

**Question. What is the sum of 36 terms of the series whose th n term is 5n + 4? **

(a) 4347

(b) 3474

(c) 4374

(d) 3447

**Answer**

B

**Question. How many numbers between 100 and 1000 are divisible by 7? **

(a) 7

(b) 128

(c) 132

(d) 127

**Answer**

B

**Question. The first, second and last terms of an arithmetic progression are 5, 9 and 101 respectively. Find the number of terms in the arithmetic progression. **

(a) 30

(b) 50

(c) 25

(d) 75

**Answer**

C

**Question. The sum of the first 10 terms of an arithmetic progression is four times the sum of its first five terms. Find the ratio of the first term to the common difference. **

(a) 1:4

(b) 4:1

(c) 2:1

(d) 1:2

**Answer**

D

**Question. Find the next term of the arithmetic progression √12, √27, √48 **

(a) √75

(b) √60

(c) √80

(d) √90

**Answer**

A

**Question. Identify the formula for then n ^{th} term of the arithmetic progression whose first term, (a) is 2 – x, and the common difference, (d) is ‘x’. **

(a) 2+ x -nx

(b) 2+ (n – 2)x

(c) 2- x – nx

(d) 2+ (n – 1)x

**Answer**

B

**Question. If th m term of an arithmetic progression is ‘n’ and n ^{th} term is ‘m’, find its (m+ n)^{th} term. **

(a) 0

(b) m+ n -p

(c) m+ n

(d) mn/m + n

**Answer**

A

**Question. In an arithmetic progression, the fourth term is 8 and the sum of 12 terms is 156. Find the value of ‘p’ if the th p term is 1000. **

(a) 200

(b) 500

(c) 300

(d) 100

**Answer**

B

**Question. The sum to ‘n’ natural numbers is S _{1} sum of the squares of ‘n’ natural numbers is S_{2} and sum of the cubes of ‘n’ natural numbers is 3 S Which of the following is equal to 9S^{2}_{2} ? **

(a) (1- 8S1)S

_{2}

(b) S

_{3}(1+ 8S

_{1})

(c) S

_{1}(1+8S

_{2})

(d) S

_{1}(1- 8S

_{3})

**Answer**

B

**Question. In an arithmetic progression if 7 times the 7 ^{th} term is equal to 11 times the 11^{th} term, find its 18^{th} term. **

(a) 1

(b) 0

(c) -1

(d) 2

**Answer**

B

**Question. Find the sum from the sixth term to the twelfth term of the arithmetic progression 6, 10, 14, …. **

(a) 176

(b) 232

(c) 266

(d) 184

**Answer**

C

**Question. What is the sum of first ‘n’ odd numbers starting from 11? **

(a) n^{2} + 10n

(b) n^{2} – 10n

(c) 10n – n^{2}

(d) n^{2}

**Answer**

A

**Question. Find the sum of 14 AM’s between 5 and 8. **

(a) 91

(b) 89

(c) 90

(d) 85

**Answer**

A

**Question. Find the general term of the series 4, 7, 10, 13…… **

(a) 3n – 7

(b) 3n + 7

(c) 3n +1

(d) 3n – 1

**Answer**

C

**QuestionIn an arithmetic progression, if t _{p} =q, t_{q} = p, find t_{pq} . **

(a) p + q – pq

(b) p + q

(c) p – q + pq

(d) pq – p – q

**Answer**

A

**Question. Which of the following is incorrect? **

(a) S_{n} of the arithmetic progression 3, 13,23,…. is 5n^{2} – 8n .

(b) S_{n} = 3n^{2} – 8n is the sum of an arithmetic progression whose common difference is 6.

(c) n^{th} term, tn = s_{n} – s_{n-1}

(d) The n^{th} term of an arithmetic progression is tn = a + (n – 1)d .

**Answer**

A

**Question. Which term of the arithmetic progression 3, 8, 13, ….. is 55 more than its 20th term? **

(a) 29th term

(b) 31st term

(c) 25th term

(d) 27th term

**Answer**

B

**Question. What is the term of an arithmetic progression whose sum to ‘n’ terms is 2n ^{2} – 3n ? **

(a) 4n – 3

(b) 4n – 5

(c) 4n + 5

(d) 5 – 4n

**Answer**

B

**Question. Find the sum of the numbers in between 1 and 1000 which are divisible by 9. **

(a) 55944

(b) 54954

(c) 99994

(d) 99894

**Answer**

A

**Question. How many two digit numbers are divisible by 4? **

(a) 20

(b) 16

(c) 25

(d) 22

**Answer**

D

**Question. The first term and the common difference of an arithmetic progression are 13 and 5 respectively. Find the sum from the 6th term to the 20th term. **

(a) 876

(b) 146

(c) 1095

(d) 1080

**Answer**

C

**Question. An arithmetic progression has 10 terms. The sum of the odd terms is 245 whereas the sum of the even terms is 305. Find the common difference. **

(a) 2

(b) 7

(c) 3

(d) 1

**Answer**

D

**Question. Find the number of terms of the arithmetic progression 1/3 , 1/2 , 2/3 , ….. 11/6 **

(a) 8

(b) 10

(c) 12

(d) 13

**Answer**

B

**Question. There are ‘n’ arithmetic means in between ‘a’ and ‘b’. Find the common difference. **

(a) b – a/n + 1

(b) b + a /n – 1

(c) b – a /n – 1

(d) b + a /n + 1

**Answer**

A

**Question. A piece of wire is used to make circles of the following pattern. **

**The radius of the first circle is ‘r’ cm and it is increased by 1 cm successively. Find the length of the wire that is required to make 5 such circles.**

(a) (10π + r)cm

(b) 2π cm

(c) 10π (r + 2)cm

(d) 2π (r + 2)cm

**Answer**

C

**Question an arithmetic progression -10,-5, 0,….. Identify three consecutive terms of the progression whose sum is 90. **

(a) 26, 31, 36

(b) 25, 30, 35

(c) 20, 30, 40

(d) 18, 23, 28

**Answer**

B

**Question. What is the sum of the first ‘n’ even numbers? **

(a) n^{2} +1

(b) n(n – 1)

(c) n^{2} – n

(d) n(n +1)

**Answer**

D

**Question. If 1 ^{3} + 2^{3} +…..+ m^{3} + 3025, find m. **

(a) 12

(b) 10

(c) 17

(d) 12

**Answer**

B

**Question. A secondary school had an enrolment of 1620 students in the year 2009 which increases by 150 students per year. What was the enrolment in the year 2013? **

(a) 2170

(b) 2070

(c) 2220

(d) 2150

**Answer**

C

**Question. A piece of wire is used to make rectangles with the same height of ‘h’ cm. The lengths of the rectangles are increased by 1 cm successively. **

**Find the total length of wire required to make 7 rectangles in this pattern.**

(a) 2[h + b + 7]

(b) 2b + h + 7

(c) 2n + h + 6

(d) 2[b + h + 6]

**Answer**

D

**Question. What is the sum of ‘n’ arithmetic means between ‘a’ and ‘b’? **

(a) 3/2 (a + 2b)

(b) n/2 [a + b]

(c) n/2 [a – b]

(d) n/4 [a + b]

**Answer**

B

**Question. The postal rates in India from town M to town N are tabulated as shown. **

**Amir posts a 230 g parcel from town M to town N, what is the postal charge?**

(a) ₹ 8.00

(b) ₹ 7.50

(c) ₹ 7.00

(d) ₹ 6.00

**Answer**

B

**Question. A cineplex has 13 rows of seats with 10 seats in the first row, 12 in the second, 14 in the third and so on. What is the total number of seats in the cineplex? **

(a) 252

(b) 256

(c) 258

(d) 286

**Answer**

D

**Question. Sulekha intends to read a 200 page book within a specific period-She starts by reading 11 pages on the first day and increases her rate of reading by reading an extra 2 pages for each subsequent day How long will she take to finish reading the book? **

(a) 20

(b) 10

(c) 15

(d) 25

**Answer**

B

**Question. Find the sum of (1- ,1/n) + (1 – 2/n) + (1- 3/n) …… **

(a) n/2

(b) n – 1/2

(c) n + 1/2

(d) n(n + 1)/2

**Answer**

B

**Question. Divide 21 into three parts that are in arithmetic progression and whose product is 168. **

(a) 3, 6, 9

(b) 14, 17, 11

(c) 2, 6, 14

(d) 2, 7, 12

**Answer**

D

**Question. Find the sum of the first 18 terms, of the arithmetic progression 12b, 8b, 4b,…… **

(a) 126b

(b) -56b

(c) 256b

(d) – 288b

**Answer**

D

**Question. Find the value of ‘n’ if the sum of the first ‘n’ terms of the A.P.I 5, 23, 31, ……. is 708. **

(a) 9

(b) 8

(c) 12

(d) 10

**Answer**

C

**Question. An arithmetic progression has a 3rd term of 13 and a last term of 148. If the common difference is 5, find the number of terms of the progression. **

(a) 30

(b) 40

(c) 50

(d) 75

**Answer**

A

**Question. The 6 ^{th} term of an arithmetic progression is 30 and the sum of the first six terms is 210. Find the sum of the next 6 consecutive terms. **

(a) 100

(b) 50

(c) 138

(d) 204

**Answer**

C

**Question. Given that the sum of the first ‘n’ terms of an arithmetic progression is 2n ^{2} + 3n, find the twelfth term. **

(a) 7

^{2}

(b) 36

(c) √625

(d) 56

**Answer**

A

**Question. Find the sum of the arithmetic progression, x – 2y,2x – y,3x……11x – 8y . **

(a) 33(2x + y)

(b) 22(2x + y)

(c) 28(x + y)

(d) 33x +11y

**Answer**

A

**Question. The first two terms of an arithmetic progression are 27 and 24 respectively. How many terms of the progression are to be added to get – 30? **

(a) 15

(b) 20

(c) 25

(d) 18

**Answer**

B

**Question. A circle is divided into 18 sectors such that the angles subtended at the centre form an arithmetic progression. Given that the angle of the smallest sector is 11.5° , find the angle of the biggest sector. **

(a) 30°

(b) 15.5°

(c) 45°

(d) 28.5°

**Answer**

D

**Question. What is the sum to ‘n’ terms of the series √5, √20, √45, √80,…..? **

(a) n(n + 1)√5/2

(b) n(n + 1)√2

(c) n/2[(n + 1)/√5]

(d) n(n +1)√5

**Answer**

A

**Question. The first three terms of a sequence are 8, ‘y’ and 18. Find the positive value of ‘y’ so that the sequence is an arithmetic progression. **

(a) 26

(b) 18

(c) 12

(d) 13

**Answer**

D

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