Free Sequences and Series MCQs with Answers
163 Sequences and Series MCQs from Mathematics, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Sequences describe ordered terms formed by a pattern, while series represent the sum of those terms. Questions cover arithmetic and geometric sequences, their nth terms, common difference or ratio, finite sums, and applications, with the sequence itself kept distinct from the corresponding series.
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163 questions · page 3 of 9
- A. ²²C₁₀
- B. ²²C₁₀ + 1
- C. ²²C₉ + ¹⁰C₁
- D. ²²C₁₀ - 1Quiz Mode Feature
Explanation: There are 22 people altogether, so selecting any 10 gives ²²C₁₀ groups.
Correct answer: ²²C₁₀ - 1Quiz Mode Feature- A. ¹²C₅ * 10
- B. ¹²C₇ * 10
- C. ¹²C₇ * ¹⁰C₅
- D. 12 * ¹⁰C₅
Explanation: The 5 seniors can be selected in ¹²C₅ ways, and independently the 5 juniors can be selected in ¹⁰C₅ ways.
Correct answer: ¹²C₇ * ¹⁰C₅- A. 300
- B. 450
- C. 600
- D. 750
Explanation: Choose the required people independently: ⁴C₃ = 4 ways for men, ⁶C₂ = 15 ways for women, and ⁵C₃ = 10 ways for children.
Correct answer: 600- A. 300
- B. 600
- C. 750
- D. 900
Explanation: The selections are ⁴C₂ = 6 ways for men, ⁶C₃ = 20 ways for women, and ⁵C₁ = 5 ways for the child.
Correct answer: 600- A. 720
- B. 1440
- C. 1860
- D. 2160
Explanation: MATERIAL has 4 vowels, A, E, I, A, which must form one block, along with the 4 consonants. These 5 objects can be arranged in 5!
Correct answer: 1440- A. 20
- B. 54
- C. 42
- D. 60
Explanation: The two specified ladies are already included, so 3 more members must be chosen from the remaining 1 lady and 5 gentlemen, giving 6 people…
Correct answer: 20- A. 4000
- B. 2160
- C. 4320
- D. 5300
Explanation: The 7 players can throw in 7! = 5040 sequences. If the youngest is last, the other 6 can be arranged in 6!
Correct answer: 4320- A. 4800
- B. 5760
- C. 2880
- D. 15000
Explanation: Treat the 5 boys as one block, giving 4 objects to arrange: the boys' block and 3 girls. These objects can be arranged in 4!
Correct answer: 2880- A. 8000
- B. 8010
- C. 8020
- D. 8040
Explanation: Rewrite the products as 2003 × 2004 minus 2001 × 2002. Using n(n + 1), the difference is (2003^2 + 2003) - (2001^2 + 2001) = (2003^2 -…
Correct answer: 8010- A. 1600
- B. 900
- C. 3600
- D. 2500Islamic Studies Quiz
Explanation: The least common multiple of 10, 12, 15 and 18 is 180 = 2² x 3² x 5. To make this a square, the factor 5 must also occur twice, so the…
Correct answer: 900- A. 143
- B. 169
- C. 260
- D. 221
Explanation: Each remainder is one less than its divisor, so the number plus 1 must be divisible by 6, 8 and 12.
Correct answer: 143- A. 5073
- B. 5016
- C. 5054
- D. 5035
Explanation: The remainders are one less than the divisors, so n + 5 must be divisible by 6, 7, 8, 9 and 10.
Correct answer: 5035- A. 210
- B. 119
- C. 126
- D. 154
Explanation: Again, every remainder is one less than its divisor, so n + 1 is divisible by 2, 3, 4, 5 and 6.
Correct answer: 119- A. 7203
- B. 2403
- C. 3603
- D. 4803
Explanation: The heap leaves remainder 3 for division by 16, 20, 25 and 45, so n - 3 must be a multiple of their least common multiple, 3600.
Correct answer: 7203- A. 9654
- B. 9666
- C. 9664
- D. 9864
Explanation: Every stated remainder is 6 less than its divisor, so n + 6 must be divisible by 10, 15, 21 and 28.
Correct answer: 9654- A. 420
- B. 515
- C. 435
- D. 518
Explanation: The conditions can be written as n + 10 divisible by 35, 25 and 15, because the remainders are 10 less than their divisors.
Correct answer: 515- A. 78
- B. 68
- C. 58
- D. None
Explanation: The value 68 gives 68 ÷ 8 a remainder of 4, 68 ÷ 12 a remainder of 8, 68 ÷ 18 a remainder of 14, and 68 ÷ 24 a remainder of 20.
Correct answer: 68- A. 1 min
- B. 2 min
- C. 3 min
- D. None
Explanation: After t minutes, the wheels make 15t, 20t and 48t revolutions. They are all back at the original position when these three quantities are…
Correct answer: 1 min- A. 9985
- B. 9960
- C. 9957
- D. 9975
Explanation: The least common multiple of 3, 4 and 5 is 60, so the required number must be a multiple of 60.
Correct answer: 9960- A. 344
- B. 355
- C. 366
- D. 377
Explanation: The least common multiple of 6, 9, 15, 20 and 24 is 360, so the number increased by 5 must be 360. Therefore, the number is 360 - 5 = 355.
Correct answer: 355