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A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?

Correct answer: C. 1023

  • A. 63
  • B. 511
  • C. 1023
  • D. 15

Explanation

Each of the five problems has four possibilities: not attempted or one of three internal choices. Thus there are 4^5 = 1024 possible patterns, and excluding the pattern in which no problem is attempted gives 1024 - 1 = 1023 ways. The likely trap is option b, 511, from using 2^9 or another incorrect binary count.

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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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