CBSE Class 10 Mathematics Arithmetic Progression MCQs Set 10

Question. The common difference of the A.P. \( \frac{1}{3q}, \frac{1 - 6q}{3q}, \frac{1 - 12q}{3q}, \dots \) 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. The next term of the A.P. \( \sqrt{18}, \sqrt{50}, \sqrt{98}, \dots \) is
(a) \( \sqrt{146} \)
(b) \( \sqrt{128} \)
(c) \( \sqrt{162} \)
(d) \( \sqrt{200} \)
Answer: C

Question. The value of \( a_{30} - a_{20} \) 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 \( a_n = 10 \), 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 \( 2m^2 + 3m \), then what is its second term?
(a) 9
(b) 10
(c) 11
(d) 12
Answer: A

Question. If the sum of \( n \) terms of two A.P.s are in the ratio \( (3n + 5) : (5n + 7) \), then their \( n^{\text{th}} \) 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 \( 10^{\text{th}} \) term of an A.P. is 52 and \( 17^{\text{th}} \) term is 20 more than the \( 13^{\text{th}} \) 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) \( 28^{\text{th}} \)
(b) \( 29^{\text{th}} \)
(c) \( 30^{\text{th}} \)
(d) \( 27^{\text{th}} \)
Answer: C

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

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 \( 30^{\text{th}} \) 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) \( \frac{15}{2} \)
(b) \( \frac{2}{15} \)
(c) \( -\frac{15}{2} \)
(d) \( -\frac{2}{15} \)
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 \( 44^{\text{th}} \) term?
(a) \( 66^{\text{th}} \)
(b) \( 64^{\text{th}} \)
(c) \( 65^{\text{th}} \)
(d) \( 67^{\text{th}} \)
Answer: C

Question. If \( p^{\text{th}} \) term of an A.P. is \( \frac{3p - 1}{6} \), then sum of first \( n \) terms of the A.P. is
(a) \( \frac{n}{12} [3n + 1] \)
(b) \( \frac{n}{12} [3n - 1] \)
(c) \( \frac{n}{6} [3n + 1] \)
(d) \( \frac{n}{6} [3n - 1] \)
Answer: A

Question. The common difference of the A.P. \( \frac{1}{p}, \frac{1 - p}{p}, \frac{1 - 2p}{p}, \dots \) is
(a) \( p \)
(b) \( -p \)
(c) –1
(d) 1
Answer: C

Question. For what value of \( n \), are the \( n^{\text{th}} \) 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

Case Based MCQs

Case I : Arithmetic Progression Properties
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 the optons 
Answer: C

Question. If \( a_1, a_2, a_3, \dots, a_n \) are in A.P., then which of the following is true?
(a) \( a_1 + k, a_2 + k, a_3 + k, \dots, a_n + k \) are in A.P., where \( k \) is a constant.
(b) \( k - a_1, k - a_2, k - a_3, \dots, k - a_n \) are in A.P., where \( k \) is a constant.
(c) \( ka_1, ka_2, ka_3, \dots, ka_n \) are in A.P., where \( k \) is a constant.
(d) All of these
Answer: D

Question. If the \( n^{\text{th}} \) 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 optons 
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 \( \frac{1}{bc}, \frac{1}{ca}, \frac{1}{ab} \) 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.
(a)
(b)
(c)
(d)
Answer: B

Question. Assertion : The \( n^{\text{th}} \) term of a sequence is \( 3n – 2 \). It is an A.P.
Reason : A sequence is not an A.P. if its \( n^{\text{th}} \) term is not a linear expression in \( n \).
(a)
(b)
(c)
(d)
Answer: A

Question. Assertion : The \( 10^{\text{th}} \) 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 \( n^{\text{th}} \) term from the end is \( l – (n – 1)d \).
(a)
(b)
(c)
(d)
Answer: D