MCQ Questions | Class 10 Maths Chapter 5 | Arithmetic Progressions with Answers

MCQ | Arithmetic Progressions Class 10 | Sat B

Check the below NCERT MCQ Questions for Class 10 Maths Chapter 5 Arithmetic Progressions with Answers Pdf free download. MCQ Questions for Class 10 Maths with Answers were prepared based on the latest exam pattern. We have Provided Arithmetic Progressions Class 10 Maths MCQs Questions with Answers to help students understand the concept very well.

Objective Question | NCERT Maths Class 10

NCERT Solutions Class 10 Maths
Book:	National Council of Educational Research and Training (NCERT)
Board:	Central Board of Secondary Education (CBSE)
Class:	10th
Subject:	Maths
Chapter:	5
Chapters Name:	Arithmetic Progressions
Medium:	English

Ncert Solutions for Class 10 Maths | Objective Type Questions

You can refer to NCERT Solutions for Class 10 Maths Chapter 5 Arithmetic Progressions to revise the concepts in the syllabus effectively and improve your chances of securing high marks in your board exams.

Arithmetic Progressions | Class 10 Maths | NCERT Solutions

Q1.	The sum of all odd integers between 2 and 100 divisible by 3 is
	A. 17
	B. 867
	C. 876
	D. 786

Ans: 867
Explaination:Reason: The numbers are 3, 9,15, 21, …, 99
Here a = 3, d = 6 and a_n = 99
∴ a_n = a + (n – 1 )d
⇒ 99 = 3 + (n – 1) x 6
⇒ 99 = 3 + 6n – 6
⇒ 6n = 102
⇒ n = 17
Required Sum = \(\frac{n}{2}\)[a + a_n] = \(\frac{17}{2}\)[3 + 99] = \(\frac{17}{2}\) × 102 = 867

Q2.	If the numbers a, b, c, d, e form an A.P., then the value of a – 4b + 6c – 4d + e is
	A. 0
	B. 1
	C. -1
	D. 2

Ans: 0
Explaination:Reason: Let x be the common difference of the given AP
∴ b = a + x, c = a + 2x, d = a + 3x and e = a + 4x
∴ a – 4b + 6c – 4d + e = a – 4 (a + x) + 6(a + 2x) – 4(a + 3x) + (a + 4x)
= a – 4a – 4x + 6a + 12x – 4a – 12x + a + 4x = 8a – 8a + 16x – 16x = 0

Q3.	If 7 times the 7^th term of an A.P. is equal to 11 times its 11^th term, then 18^th term is
	A. 18
	B. 9
	C. 77
	D. 0

Ans:
Explaination:Reason: We have 7a₇ = 11a₁₁
⇒ 7[a + (7 – 1)d] = 11[a + (11 – 1 )d]
⇒ 7(a + 6d) = 11(a + 10d)
⇒ 7a + 42d = 11a + 110d
⇒ 4a = -68d
⇒ a = -17d
∴ a₁₈ = a + (18 – 1)d = a + 17d = -17d + 17d = 0

Q4.	If p, q, r are in AP, then p³ + r³ – 8q³ is equal to
	A. 4pqr
	B. -6pqr
	C. 2pqr
	D. 8pqr

Ans: -6pqr

Explaination:

∵ p, q, r are in AP.
∴ 2q = p + r
⇒ p + r – 2q = 0
∴ p³ + r³ + (-2p)³ = 3 × p × r × -2q
[Using ifa + 6 + c = 0 ⇒ a³ + b³ + c³ = 3 abc]
⇒ p³ + r³ – 8q³ = -6pqr.

Q5.	The number of multiples lie between n and n² which are divisible by n is
	A. n + 1
	B. n
	C. n – 1
	D. n – 2

Ans: n – 2

Q6.	If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
	A. 0
	B. 2
	C. 4
	D. 6

Ans: 6

Q7.	If p, q, r are in AP, then p³ + r³ – 8q³ is equal to
	A. 4pqr
	B. -6pqr
	C. 2pqr
	D. 8pqr

Ans: -6pqr

Q8.	n^th term of the sequence a, a + d, a + 2d,… is
	A. a + nd
	B. a – (n – 1)d
	C. a + (n – 1)d
	D. n + nd

Ans: a + nd

Q9.	An athlete wants to improve his stamina, so he decides to increase the distance he runs by half a kilometer every day. If he starts with 5 km on first day, find how much he runs on the 10 th day
	A. 6 Km
	B. 7.5 Km
	C. 9.5 Km
	D. 10 Km

Ans: 9.5 Km

Q10.	If the sum of n terms of an AP is 3n2+5n then which of its terms is 164?
	A. 27th
	B. 29th
	C. 28th
	D. 26th

Ans: 27th

Q11.	The sum of all two digit odd numbers is
	A. 2575
	B. 2475
	C. 2524
	D. 2425

Ans: 2475

Q12.	If p, q, r, s, t are the terms of an A.P. with common difference -1 the relation between p and t is:
	A. t = p – 5
	B. t = p – 4
	C. t = p – 6
	D. t = p + 4

Ans: t = p – 4

Q13.	The fourth term of an A.P. is 4. Then the sum of the first 7 terms is :
	A. 4
	B. 28
	C. 16
	D. 40

Ans: 28

Q14.	The n^th term of an A.P. 5, 2, -1, -4, -7 … is
	A. 2n + 5
	B. 2n – 5
	C. 8 – 3n
	D. 3n – 8

Ans: 8 – 3n

Q15.	In an AP, if a = 3.5, d = 0, n = 101, then a will be
	A. 0
	B. 3.5
	C. 103.5
	D. 104.5

Ans: 3.5
Explaination: (2) a₁₀₁ = 3.5 + 0(100) = 3.5

Q16.	The list of numbers -10, -6, -2, 2, … is
	A.an AP with d = -16
	B. an AP with d = 4
	C. an AP with d = -4
	D. not an AP

Ans: an AP with d = 4
Explaination: (2) An AP with d = 4.

Q17.	Two APs have the same common difference. . The first term of one of these is -1 and that of the other is -8. Then the difference between their 4th terms is
	A. -1
	B. -8
	C. 7
	D. -9

Ans: 7

Explaination:

a₄ – b₄ = (a₁ + 3d) – (b₁ + 3d)
= a₁ – b₁= – 1 – (-8) = 7

Q18.	In an AP, if d = -2, n = 5 and an = 0, the value of a is
	A. 10
	B. 5
	C. -8
	D. 8

Ans: 8

Explaination:

d = – 2, n = 5, a_n = 0
∵ a_n = 0
⇒ a + (n – 1)d=0
⇒ a + (5 – 1)(- 2) = 0
⇒ a = 8
Correct option is (d).

Q19.	If the common difference of an AP is 3, then a₂₀ – a₁₅ is
	A. 5
	B. 3
	C. 15
	D. 20

Ans: 15

Explaination:

Common difference, d = 3
a₂₀ – a₁₅ = (a + 19d) – (a+ 14d)
= 5d=5 × 3 = 15

Q20.	The next term of the AP √18, √50, √98, …….. is
	A. √146
	B. √128
	C. √162
	D. √200

Ans: √162

Explaination:

√18, √50, √98, ….. = 3√2, 5√2, 7√2, ……
∴ Next term is 9√2 = √162

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

MCQ Questions | Class 10 Maths Chapter 5

MCQ Questions | Class 10 Maths Chapter 5 | Arithmetic Progressions with Answers

MCQ | Arithmetic Progressions Class 10 | Sat B

Objective Question | NCERT Maths Class 10

Ncert Solutions for Class 10 Maths | Objective Type Questions

Arithmetic Progressions | Class 10 Maths | NCERT Solutions

CBSE Solutions | Ncert Solutions Maths Class 10

NCERT Solutions | 10th Maths Guide

NCERT | Class 10 Maths Solution

Ncert Solutions for Class 10 Maths

Ncert Solutions for Class 10 Maths Chapter 1

Ncert Solutions for Class 10 Maths Chapter 2

Ncert Solutions for Class 10 Maths Chapter 3

Ncert Solutions for Class 10 Maths Chapter 4

Ncert Solutions for Class 10 Maths Chapter 5

Ncert Solutions for Class 10 Maths Chapter 6

Ncert Solutions for Class 10 Maths Chapter 7

Ncert Solutions for Class 10 Maths Chapter 8

Ncert Solutions for Class 10 Maths Chapter 9

Ncert Solutions for Class 10 Maths Chapter 10

Ncert Solutions for Class 10 Maths Chapter 11

Ncert Solutions for Class 10 Maths Chapter 12

Ncert Solutions for Class 10 Maths Chapter 13

Ncert Solutions for Class 10 Maths Chapter 14

Ncert Solutions for Class 10 Maths Chapter 15

NCERT SOLUTIONS

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