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Class 11 ch 8

Sequences and series: JEE Main-style questions

Original JEE Main-style questions on sequences and series, with a worked solution and the usual trap for each. Tap an option, or type a numerical answer, to check it.

  • 6 questions
  • 3 free
  • 4 multiple choice, 2 numerical value
  • No calculator

Learn the chapters first: Class 11, Sequences and Series.

Questions

Q1

·JEE Main style·Multiple choiceGeometric progression

If \(2, x, y, 54\) are in geometric progression, then \(x + y\) equals

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Answer: (a) \(24\)

\(54 = 2r^3\), so \(r^3 = 27\) and \(r = 3\). Then \(x = 6\), \(y = 18\) and \(x + y = 24\).

Q2

·JEE Main style·Multiple choiceTelescoping sums

\(\displaystyle\sum_{k=1}^{99} \frac{1}{k(k + 1)}\) equals

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Answer: (b) \(\frac{99}{100}\)

\(\dfrac{1}{k(k + 1)} = \dfrac{1}{k} - \dfrac{1}{k + 1}\). The sum telescopes to \(1 - \dfrac{1}{100} = \dfrac{99}{100}\).

Q3

·JEE Main style·Numerical valueAM and GM

Two positive numbers have arithmetic mean 13 and geometric mean 12. Find the larger number.

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Answer: 18

\(a + b = 26\) and \(ab = 144\), so \(a, b\) are the roots of \(t^2 - 26t + 144 = 0\): \(t = 18\) or \(8\). The larger is 18.

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Next steps

All questions are original, written by CBSE Math Revision in the style of each exam; none are taken from NTA, IIT, CBSE or NCERT papers. Every answer was checked twice: by a computer re-solve and by hand. No calculator needed. Spotted a mistake? Tell us.