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Class 11 · Algebra

Maths 1A: Mathematical Induction, Course Quiz

Ten questions across the whole chapter, from the steps of an induction proof to standard sums, series and divisibility. Pick one answer for each.

10 questions, one mark each. 6 to pass. Suggested time: 20 minutes. Your answers are not recorded.

  1. If P(n)P(n): 5+14+23+⋯+(9n−4)=n(9n+1)2\displaystyle 5 + 14 + 23 + \dots + (9 n - 4) = \frac{n (9 n + 1)}{2}, then the value of each side of P(4)P(4) is
  2. If P(k)P(k) true implies P(k+1)P(k+1) true for every kk, but P(1)P(1) is false, then
  3. 14+24+⋯+104=1^4 + 2^4 + \dots + 10^4 =
  4. 13+33+53+…1^3 + 3^3 + 5^3 + \dots to 44 terms ==
  5. 12−22+32−⋯−262=1^2 - 2^2 + 3^2 - \dots - 26^2 =
  6. The 88th term of the A.P. 15,21,27,…15, 21, 27, \dots is
  7. The sum of the first 77 terms of 6+12+24+…6 + 12 + 24 + \dots is
  8. The sum to infinity of 6+7⋅12+8⋅14+9⋅18+…\displaystyle 6 + 7 \cdot \frac{1}{2} + 8 \cdot \frac{1}{4} + 9 \cdot \frac{1}{8} + \dots is
  9. The largest number that divides 12n−112^{n} - 1 for every n∈Nn \in \mathbb{N} is
  10. If 76≡r(mod7)76 \equiv r \pmod{7} with 0≤r<70 \le r < 7, then r=r =
Unanswered questions are marked wrong.

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