CBSE Class 10 Mathematics Arithmetic Progression MCQs Set F

Question. The common difference of the A.P. 1/3q, 1 - 6q/3q, 1 - 12q/3q ...... is
(a) q
(b) −q
(c) −2
(d) 2

Answer: C

Question. If k, 2k – 1 and 2k + 1 are three consecutive terms of an A.P., then the value of k is
(a) 2
(b) 3
(c) –3
(d) 5

Answer: B

Question. If the sum of n terms of two A.P.s are in the ratio (3n + 5) : (5n + 7), then their n^th terms are in the ratio
(a) (3n – 1) : (5n – 1)
(b) (3n + 1) : (5n – 1)
(c) (3n + 1) : (5n + 1)
(d) (5n + 1) : (3n + 1)

Answer: C

Question. If the 10th term of an A.P. is 52 and 17^th term is 20 more than the 13^th term, then find the A.P.
(a) 40, 45, 50,.....
(b) 45, 50, 55,.....
(c) 17, 22, 27,.....
(d) 7, 12, 17,.....

Answer: D

Question. Two persons Anil and Happy joined D.W. Associates. Anil and Happy started with an initial salary of ₹ 50000 and ₹ 64000 respectively with annual increment of ₹ 2500 and ₹ 2000 each respectively. In which year will Anil start earning more salary than Happy?
(a) 28^th
(b) 29^th
(c) 30^th
(d) 27^th

Answer: C

Question. The production of TV in a factory increases uniformly by a fixed number every year. It produced 8000 TV’s in 6th year & 11300 in 9th year, find the production in 8th year.
(a) 10500
(b) 9800
(c) 9700
(d) 10200

Answer: D

Question. The next term of the A.P. 18, 50, 95,... is
(a) √146
(b) √128
(c) √162
(d) √200

Answer: C

Question. The value of a₃₀ – a₂₀ for the A.P. 2, 7, 12, 17, ... is
(a) 100
(b) 10
(c) 50
(d) 20

Answer: C

Question. In an A.P., if a = −10, n = 6 and an = 10, then the value of d is
(a) 0
(b) 4
(c) −4
(d) 10/3

Answer: B

Question. If the sum of first m terms of an A.P. is 2m² + 3m, then what is its second term?
(a) 9
(b) 10
(c) 11
(d) 12

Answer: A

Question. The number of terms in the A.P. 3, 6, 9, 12,...., 111 is
(a) 25
(b) 40
(c) 37
(d) 30

Answer: C

Question. A man starts repaying a loan with first monthly installment of ₹ 1000. If he increases the installment by ₹ 50 every month, what amount will he pay in the 30th installment?
(a) ₹ 1450
(b) ₹ 2450
(c) ₹ 2050
(d) ₹ 2040

Answer: B

Question. The value of x for which (8x + 4), (6x – 2) and (2x + 7) are in A.P., is
(a) 15/2
(b) 2/15
(c) −15/2
(d) − 2/15

Answer: A

Question. The numbers –11, – 7, – 3, 1, 5, ...... are
(a) in A.P. with d = –18
(b) in A.P. with d = –4
(c) in A.P. with d = 4
(d) not in A.P.

Answer: C

Question. Which term of the A.P. 3, 15, 27, 39, ...... will be 252 more than its 44^th term?
(a) 66^th
(b) 64^th
(c) 65^th
(d) 67^th

Answer: C

Question. If a, (a – 2) and 3a are in A.P., then the value of a is
(a) – 3
(b) – 2
(c) 3
(d) 2

Answer: B

Question. If m^th term of an A.P. is 1/n and nth term is 1/m, then the sum of first mn terms is
(a) mn + 1
(b) mn +1/2
(c) mn −1/2
(d) mn −1/3

Answer: B

Question. For what value of n, are the n^th terms of two A.P.’s 52, 54, 56, ..... and 4, 12, 20, ..... equal ?
(a) 11
(b) 12
(c) 10
(d) 9

Answer: D

Question. Find the sum of all two digit natural numbers which when divided by 3 yield 1 as remainder.
(a) 1605
(b) 1780
(c) 1080
(d) 1960

Answer: A

Question. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(a) Pythagoras
(b) Newton
(c) Gauss
(d) Euclid

Answer: C

Question. If the common difference of an A.P. is 5, then what is a₁₈ –a₁₃ ?
(a) 5
(b) 20
(c) 25
(d) 30

Answer: C

Question. What is the common difference of four terms in an A.P. such that the ratio of the product of the first and fourth terms to that of the second and third is 2 : 3 and the sum of all four terms is 20?
(a) 3
(b) 1
(c) 4
(d) 2

Answer: D

Question. If 9 times the 9th term in an arithmetic progression is equal to 15 times of its 15^th term, then what is the 24^th term?
(a) 0
(b) 9
(c) 15
(d) 23

Answer: A

Question. If x ≠ y and the sequences x, a₁, a₂, y and x, b₁, b₂, y each are in A.P., then a a (a₂ - a₁ / b₂ - a₁) is
(a) 2/3
(b) 3/2
(c) 1
(d) 3/4

Answer: C

Question. Find the sum of first 10 terms of the A.P. x – 8, x – 2, x + 4, …
(a) 10x + 210
(b) 10x + 190
(c) 5x + 190
(d) 5x + 210

Answer: B

Question. In an A.P., the sum of first n terms is 3n²/2 + (13/2)n. Find its 15^th term.
(a) 45
(b) 50
(c) 60
(d) 75

Answer: B

Question. Three numbers in an A.P. have sum 18. Its middle term is
(a) 6
(b) 8
(c) 3
(d) 2

Answer: A

Question. If p^th term of an A.P. is 3p -1/6, then sum of first n terms of the A.P. is
(a) n/12 [3n + 1]
(b) n/12 [3n – 1]
(c) n6/[3n + 1]
(d) n6/[3n – 1]

Answer: A

Question. The common difference of the A.P. 1/p, 1-p/p, 1-2p/p,  ..... is
(a) p
(b) –p
(c) –1
(d) 1

Answer: C

Question. If the seventh term of an A.P. is 1/9 and its ninth term is 1/7, find common difference.
(a) 1
(b) 2/63
(c) 3/64
(d) 1/63

Answer: D

Question. The sum (– 6) + (0) + (6) + ..... upto 13^th term =
(a) 390
(b) 1380
(c) 378
(d) 1830

Answer: A

Question. Find the sixteenth term of the A.P. –10, –6, –2, 2,...
(a) 10
(b) 20
(c) 40
(d) 50

Answer: D

Question. If the sum of 7 terms of an A.P. is 49 and that of 17 terms is 289, then, its first term is
(a) 1
(b) – 1
(c) 2
(d) –2

Answer: A

Question. Find how many terms are there in the A.P. 16, 24, 32, ......, 96.
(a) 10
(b) 11
(c) 12
(d) 14

Answer: B

Question. If the first, second and last terms of an A.P. are a, b and 2a respectively, its sum is
(a) ab/2(b − a)
(b) ab/b − a
(c) 3ab/2(b − a)
(d) None of these

Answer: C

Question. Find the sum of first 15 multiples of 8.
(a) 840
(b) 1020
(c) 960
(d) 920

Answer: C

Question. 3/√5 + √5 + 7/√5 ... to 15 terms is equal to
(a) 51√5
(b) 17√5
(c) 81√5
(d) 9√5

Answer: A

Question. Which of the following is not an A.P. ?
(a) −3 − 5/2, −2, − 3/2 ......
(b) 0.3, 0.33, 0.333, ......
(c) √3, √12, √27, √48, .....
(d) p, 2p + 1, 3p + 2, 4p + 3, ....

Answer: B.

Case Based MCQs

Case I : Read the following passage and answer the questions.

Discussion on A.P.

In a class the teacher asks every student to write an example of A.P. Two friends Geeta and Madhuri writes their progressions as –5, –2, 1, 4, … and 187, 184, 181, …. respectively. Now, the teacher asks various students of the class the following questions on these two progressions. Help students to find the answers of the questions.

Question. Find the 34^th term of the progression written by Madhuri.
(a) 286
(b) 88
(c) –99
(d) 190

Answer: B

Question. Find the sum of common difference of the two progressions.
(a) 6
(b) –6
(c) 1
(d) 0

Answer: D

Question. Find the 19^th term of the progression written by Geeta.
(a) 49
(b) 59
(c) 52
(d) 62

Answer: A

Question. Find the sum of first 10 terms of the progression written by Geeta.
(a) 85
(b) 95
(c) 110
(d) 200

Answer: A

Question. Which term of the two progressions will have the same value?
(a) 31
(b) 33
(c) 32
(d) 30

Answer: B

Case II : Read the following passage and answer the questions.

Number Cards Game

Amit was playing a number card game. In the game, some number cards (having both +ve or –ve numbers) are arranged in a row such that they are following an arithmetic progression. On his first turn, Amit picks up 6^th and 14th card and finds their sum to be –76. On the second turn he picks up 8^th and 16^th card and finds their sum to be –96.

Question. What is the difference between the numbers on any two consecutive cards?
(a) 7
(b) –5
(c) 11
(d) –3

Answer: B

Question. The number on first card is,
(a) 12
(b) 3
(c) 5
(d) 7

Answer: D

Question. What is the number on the 19th card?
(a) –88
(b) –83
(c) –92
(d) –102

Answer: B

Question. What is the number on the 23rd card?
(a) –103
(b) –122
(c) –108
(d) –117

Answer: A

Question. The sum of numbers on the first 15 cards is
(a) –840
(b) –945
(c) –427
(b) –420

Answer: D

Case III : Read the following passage and answer the questions.

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.).

Question. Which of the following sequence is an A.P.?
(a) 10, 24, 39, 52, ….
(b) 11, 24, 39, 52, …
(c) 10, 24, 38, 52, …
(d) 10, 38, 52, 66, ….

Answer: C

Question. If x, y and z are in A.P., then
(a) x + z = y
(b) x – z = y
(c) x + z = 2y
(d) None of these

Answer: C

Question. If a₁, a₂, a₃, ….., an are in A.P., then which of the following is true?
(a) a₁ + k, a₂ + k, a₃ + k, ….., an + k are in A.P., where k is a constant.
(b) k – a₁, k – a₂, k – a₃, ….., k – a_n are in A.P., where k is a constant.
(c) ka₁, ka₂, ka₃, ….., kan are in A.P., where k is a constant.
(d) All of the options

Answer: D

Question. 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
(a) d > 0
(b) d < 0
(c) d = 0
(d) Can’t be determined

Answer: B

Question. Which of the following is incorrect about A.P.?
(a) All the terms of constant A.P. are same.
(b) Some terms of an A.P. can be negative.
(c) All the terms of an A.P. can never be negative.
(d) None of the options

Answer: C

Assertion & Reasoning Based MCQs

Directions : In these questions, a statement of Assertion is followed by a statement of Reason is given. Choose
the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : If a, b, c are in A.P., then 1/bc, 1/ca, 1/ab are also in A.P.
Reason : If a constant is added to each term of an A.P., then the resulting pattern of numbers is also an A.P.

Answer: B

Question. Assertion : The n^th term of a sequence is 3n – 2. It is an A.P.
Reason : A sequence is not an A.P. if its n^th term is not a linear expression in n.

Answer: B

Question. Assertion : The 10^th term from the end of the A.P.7, 10, 13, ...., 184 is 163.
Reason : In an A.P. with first term a, common difference d and last term l, the n^th term from the end is l – (n – 1)d.

Answer: D

Question. Assertion : The common difference of the A.P. 19, 18, 17, .... is 1.
Reason : Let a₁, a₂, a₃, a₄, ... is an A.P. Then, common difference of this A.P. will be the difference between any two consecutive terms, i.e., common difference (d) = a₂ – a₁ or a₃ – a₂ or a₄ – a₃ and so on.

Answer: D

Question. Assertion : The ninth term of an A.P. is equal to seven times the second term and twelfth term exceeds five times the third term by 2. Then the first term is 1.
Reason : If Sn and S_n–1 are the sum of first n terms and (n – 1) terms of an A.P., then nth term, a_n = S_n–1 – S_n

Answer: C

Question. Assertion : Sum of first 20 multiples of 4 is 480.
Reason : In an A.P., sum of n terms, S_n = n/2 {a + l } where, n, a and l are number of terms, first term and last term respectively.

Answer: D

Question. Assertion : If the first term of an A.P. is 4, last term is 81 and the sum of the given terms is 510. Then, there are 12 terms in the given A.P.
Reason : If a is the first term, l is the last term and n is the number of terms of an A.P., then S_n = n/2(a + l).

Answer: A