NCERT Exemplar Problems – Class 10 Mathematics
Chapter 5: Arithmetic Progressions
Multiple Choice Questions (Exercise 5.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. In an AP, if \( d = -4 \), \( n = 7 \), \( a_n = 4 \), then \( a \) is
(A) 6 (B) 7 (C) 20 (D) 28
Correct Answer: (D)
2. In an AP, if \( a = 3.5 \), \( d = 0 \), \( n = 101 \), then \( a_n \) will be
(A) 0 (B) 3.5 (C) 103.5 (D) 104.5
Correct Answer: (B)
3. The list of numbers \( -10, -6, -2, 2, \ldots \) is
(A) an AP with \( d = -16 \)
(B) an AP with \( d = 4 \)
(C) an AP with \( d = -4 \)
(D) not an AP
Correct Answer: (B)
4. The 11th term of the AP: \( -5, -\dfrac{5}{2}, 0, \dfrac{5}{2}, \ldots \) is
(A) –20 (B) 20 (C) –30 (D) 30
Correct Answer: (B)
5. The first four terms of an AP, whose first term is –2 and the common difference is –2, are
(A) –2, 0, 2, 4
(B) –2, 4, –8, 16
(C) –2, –4, –6, –8
(D) –2, –4, –8, –16
Correct Answer: (C)
6. The 21st term of the AP whose first two terms are –3 and 4 is
(A) 17 (B) 137 (C) 143 (D) –143
Correct Answer: (B)
7. If the 2nd term of an AP is 13 and the 5th term is 25, what is its 7th term?
(A) 30 (B) 33 (C) 37 (D) 38
Correct Answer: (B)
8. Which term of the AP: 21, 42, 63, 84, … is 210?
(A) 9th (B) 10th (C) 11th (D) 12th
Correct Answer: (B)
9. If the common difference of an AP is 5, then what is \( a_{18} - a_{13} \)?
(A) 5 (B) 20 (C) 25 (D) 30
Correct Answer: (C)
10. What is the common difference of an AP in which \( a_{18} - a_{14} = 32 \)?
(A) 8 (B) –8 (C) –4 (D) 4
Correct Answer: (A)
11. 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
Correct Answer: (C)
12. If 7 times the 7th term of an AP is equal to 11 times its 11th term, then its 18th term will be
(A) 7 (B) 11 (C) 18 (D) 0
Correct Answer: (D)
13. The 4th term from the end of the AP: –11, –8, –5, …, 49 is
(A) 37 (B) 40 (C) 43 (D) 58
Correct Answer: (B)
14. The famous mathematician associated with finding the sum of the first 100 natural numbers is
(A) Pythagoras (B) Newton (C) Gauss (D) Euclid
Correct Answer: (C)
15. If the first term of an AP is –5 and the common difference is 2, then the sum of the first 6 terms is
(A) 0 (B) 5 (C) 6 (D) 15
Correct Answer: (A)
16. The sum of first 16 terms of the AP: 10, 6, 2, … is
(A) –320 (B) 320 (C) –352 (D) –400
Correct Answer: (A)
17. In an AP if \( a = 1 \), \( a_n = 20 \) and \( S_n = 399 \), then \( n \) is
(A) 19 (B) 21 (C) 38 (D) 42
Correct Answer: (C)
18. The sum of first five multiples of 3 is
(A) 45 (B) 55 (C) 65 (D) 75
Correct Answer: (A)
Answers taken from the official NCERT Exemplar answer key.