Mathematics
Multiple Choice Questions (MCQ)
MCQ | Class 10 | Chapter 5
ARITHMATIC PROGRESSION
- MCQ Based on the general Arithmetic Progression.
- MCQ Based on the nth term of Arithmetic Progression.
- MCQ Based on the sum of n terms of Arithmetic Progression.
- MCQ Based on the word problems of Arithmetic Progression.
- MCQ Based from the nth term from the end of the sequence.
Features
- In this pdf given below you find the important MCQ which are strictly according to the CBSE syllabus and are very useful for the CBSE Examinations.
- Solution Hints are also given to some difficult problems.
- Each MCQ contains four options from which one option is correct.
- On the right hand side column of the pdf Answer option is given.
Action Plan
- First of all students should Learn and write all basic points and Formulas related to the Arithmetic Progression.
- Start solving the NCERT Problems with examples.
- Solve the important assignments on the Arithmetic Progression.
- Then start solving the following MCQ.
MCQ | CHAPTER 5 | CLASS 10
ARITHMETIC PROGRESSION
Q 1) In an Arithmetic Progression, if a = 28, d = – 4, n = 7, then an is:
a) 4
b) 5
c) 3
d) 7
Ans: a
Q 2) If a = 10 and d = 10, then first four terms will be:
a) 10, 30, 50, 60
b) 10, 20, 30, 40
c) 10, 15, 20, 25
d) 10, 18, 20, 30
Ans: b
a) 10, 30, 50, 60
b) 10, 20, 30, 40
c) 10, 15, 20, 25
d) 10, 18, 20, 30
Ans: b
Q 3) 30th term of the A.P: 10, 7, 4, …, is
a) 97
b) 77
c) – 77
d) – 87
Ans: c
a) 97
b) 77
c) – 77
d) – 87
Ans: c
Q 4) 11th term of the A.P. – 3, -1/2, 2 …. Is
a) 28
b) 22
c) – 38
d) – 48
a) 28
b) 22
c) – 38
d) – 48
Ans: b
Q 5) The missing terms in AP: __, 13, __, 3 are:
a) 11 and 9
b) 17 and 9
c) 18 and 8
d) 18 and 9
a) 11 and 9
b) 17 and 9
c) 18 and 8
d) 18 and 9
Ans: c
Q 6) Which term of the A.P. 3, 8, 13, 18, … is 78?
a) 12th
b) 13th
c) 15th
d) 16th
a) 12th
b) 13th
c) 15th
d) 16th
Ans: d
Q 7) The 21st term of AP whose first two terms are -3 and 4 is:
a) 17
b) 137
c) 143
d) -143
a) 17
b) 137
c) 143
d) -143
Ans: b
Q 8) The number of multiples of 4 between 10 and 250 is:
a) 50
b) 40
c) 60
d) 30
a) 50
b) 40
c) 60
d) 30
Ans: c
Q 9) 20th term from the last term of the A.P. 3, 8, 13, …, 253 is:
a) 147
b) 151
c) 154
d) 158
a) 147
b) 151
c) 154
d) 158
Ans: d
Q 10) The sum of the first five multiples of 3 is:
a) 45
b) 55
c) 65
d) 75
a) 45
b) 55
c) 65
d) 75
Ans: a
Q 11) In an AP, if d = – 4, n = 7, an = 4, then a is
a) 6
b) 7
c) 20
d) 28
a) 6
b) 7
c) 20
d) 28
Ans: d
Q 12) 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
a) an AP with d = –16
b) an AP with d = 4
c) an AP with d = –4
d) not an AP
Ans: b
Q 13) If the 2nd term of an AP is 13 and the 5th term is 25, then its 7th term is
a) 30
b) 33
c) 37
d) 38
a) 30
b) 33
c) 37
d) 38
Ans: b
Q 14) Which term of the AP: 21, 42, 63, 84,… is 210?
a) 9th
b) 10th
c) 11th
d) 12th
a) 9th
b) 10th
c) 11th
d) 12th
Ans: b
Q 15) What is the common difference of an AP in which a18 – a14 = 32?
a) 8
b) – 8
c) – 4
d) 4
a) 8
b) – 8
c) – 4
d) 4
Ans: a
Q 16) The famous mathematician associated with finding the sum of the first 100 natural numbers is
a) Pythagoras
b) Newton
c) Gauss
d) Euclid
a) Pythagoras
b) Newton
c) Gauss
d) Euclid
Ans: c
Q 17) The sum of first 16 terms of the AP: 10, 6, 2,… is
a) –320
b) 320
c) –352
d) –400
a) –320
b) 320
c) –352
d) –400
Ans: a
Q 18) The nth term of an A.P. is given by an = 3 + 4n. The common difference is
a) 7
b) 3
c) 4
d) 1
a) 7
b) 3
c) 4
d) 1
Ans: c
Q 19) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
a) 2, 4, 6
b) 1, 5, 3
c) 2, 8, 4
d) 2, 3, 4
a) 2, 4, 6
b) 1, 5, 3
c) 2, 8, 4
d) 2, 3, 4
Ans: d
Explanation: Reason: Let three numbers be a – d, a, a + d
∴ a – d + a + a + d = 9
⇒ 3a = 9 ⇒ a = 3
Also (a – d) . a . (a + d) = 24
⇒ (3 -d) .3(3 + d) = 24
⇒ 9 – d² = 8
⇒ d² = 9 – 8 = 1
∴ d = ± 1
Hence numbers are 2, 3, 4 or 4, 3, 2
Explanation: Reason: Let three numbers be a – d, a, a + d
∴ a – d + a + a + d = 9
⇒ 3a = 9 ⇒ a = 3
Also (a – d) . a . (a + d) = 24
⇒ (3 -d) .3(3 + d) = 24
⇒ 9 – d² = 8
⇒ d² = 9 – 8 = 1
∴ d = ± 1
Hence numbers are 2, 3, 4 or 4, 3, 2
Q 20) The 10th term from the end of the A.P. -5, -10, -15,…, -1000 is
a) – 955
b) – 945
c) – 950
d) – 965
a) – 955
b) – 945
c) – 950
d) – 965
Ans: a
Q 21) The sum of all two digit odd numbers is
a) 2575
b) 2475
c) 2524
d) 2425
Ans: b
Q 22) Find the sum of 12 terms of an A.P. whose nth term is given by an = 3n + 4
(a) 262
(b) 272
(c) 282
(d) 292
(a) 262
(b) 272
(c) 282
(d) 292
Ans: a
Q 23) The sum of first n odd natural numbers is
(a) 2n²
(b) 2n + 1
(c) 2n – 1
(d) n²
(a) 2n²
(b) 2n + 1
(c) 2n – 1
(d) n²
Ans: d
Q 24) The sum of first n terms of the series a, 3a, 5a, …….. is
(a) na
(b) (2n – 1) a
(c) n²a
(d) n²a²
(a) na
(b) (2n – 1) a
(c) n²a
(d) n²a²
Ans: c
Q 25) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6
(a) 0
(b) 2
(c) 4
(d) 6
Ans: d
Q 26) Which term of the AP: 27, 24, 21, ……… is zero?
(a) 8th
(b) 10th
(c) 9th
(d) 11th
(a) 8th
(b) 10th
(c) 9th
(d) 11th
Ans: b
Q 27) If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, then 18th term is
(a) 18
(b) 9
(c) 77
(d) 0
(a) 18
(b) 9
(c) 77
(d) 0
Ans: d
Q 28) 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
Ans: b
Q 29) Next term of the AP √2, 3√2, 5√2, ……. is
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2
(a) 2√7
(6) 6√2
(c) 9√2
(d) 7√2
Ans: d
Q 30) If p, q, r and s are in A.P. then r – q is
(a) s – p
(b) s – q
(c) s – r
(d) none of these
(a) s – p
(b) s – q
(c) s – r
(d) none of these
Ans: c
Q 31) If the sum of three numbers in an A.P. is 9 and their product is 24, then numbers are
(a) 2, 4, 6
(b) 1, 5, 3
(c) 2, 8, 4
(d) 2, 3, 4
Ans: d
Q 32) If the sum of the first m terms of an AP is n and the sum of its n terms is m, then the sum of its (m + n) terms will be
(a) m + n
(b) -(m + n)
(c) m – n
(d) 0
Ans: b
Q 33) The (n – 1)th term of an A.P. is given by 7,12,17, 22,… is
(a) 5n + 2
(b) 5n + 3
(c) 5n – 5
(d) 5n – 3
(a) 5n + 2
(b) 5n + 3
(c) 5n – 5
(d) 5n – 3
Ans: d
Q 34) If a, b, c, d, e are in A.P., then the value of a – 4b + 6c – 4d + e is
(a) 0
(b) 1
(c) -1.
(d) 2
Ans: a
(a) 0
(b) 1
(c) -1.
(d) 2
Ans: a
Explanation : Let common difference of A.P. be d
∴ b = a + d, c = a + 2d, d = a + 3d and e = a + 4d
Given equation a-4b + 6c-4d + c
= a – 4(a + d) + 6(a + 2d) – 4(a + 3d) + (a + 4d)
= a – 4a – 4d + 6a + 12d – 4a – 12d + a + 4d = 8a – 8a + 16d – 16d = 0
∴ b = a + d, c = a + 2d, d = a + 3d and e = a + 4d
Given equation a-4b + 6c-4d + c
= a – 4(a + d) + 6(a + 2d) – 4(a + 3d) + (a + 4d)
= a – 4a – 4d + 6a + 12d – 4a – 12d + a + 4d = 8a – 8a + 16d – 16d = 0
Q 35) nth 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
(a) a + nd
(b) a – (n – 1)d
(c) a + (n – 1)d
(d) n + nd
Ans: a
Q 36) If 2x, x + 10, 3x + 2 are in A.P., then x is equal to
(a) 0
(b) 2
(c) 4
(d) 6
(a) 0
(b) 2
(c) 4
(d) 6
Ans: d
Q 37) The 10th term from the end of the A.P. 4, 9,14, …, 254 is
(a) 209
(b) 205
(c) 214
(d) 213
(a) 209
(b) 205
(c) 214
(d) 213
Ans: a
Q 38) If the sum of first n terms of an AP is An + Bn² where A and B are constants. The common difference of AP will be
(a) A + B
(b) A – B
(c) 2A
(d) 2B
(a) A + B
(b) A – B
(c) 2A
(d) 2B
Ans: d
Q 39) The sum of all odd integers between 2 and 100 divisible by 3 is
(a) 17
(b) 867
(c) 876
(d) 786
(a) 17
(b) 867
(c) 876
(d) 786
Ans: b
Q 40) The sum of the first 15 multiples of 8 is
(a) 920
(b) 860
(c) 900
(d) 960
(a) 920
(b) 860
(c) 900
(d) 960
Ans: d
Q 41) The 21st term of the AP whose first two terms are –3 and 4 is
(a) 17
(b) 137
(c) 143
(d) –143
(a) 17
(b) 137
(c) 143
(d) –143
Ans: b
Q 42) 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
Ans: b
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