Jamia Millia Islamia Mathematical Induction Previous Year Questions (PYQs)
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Showing 4 questions
Which of the following indicates the first step of mathematical induction
for the mathematical statement $n + 1 > n$?
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Solution
R includes $(1,1), (2,2), (3,3)$ → Reflexive.
Check symmetry: $(1,2)$ exists but $(2,1)$ does not → Not symmetric.
Check transitivity: $(1,2)$ and $(2,2)$ imply $(1,2)$ already → transitive holds.
Hence, relation is reflexive and transitive but not symmetric.
What is the base case for the inequality $7^n > n^3$, where $n = 3$?
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Solution
Substitute $n = 3$:
$7^3 = 343$, and $3^3 = 27$.
Clearly $343 > 27.$
The sum of the first n natural numbers given by:
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Solution
Sum of first n natural numbers:
$S = \frac{n(n+1)}{2}$
$S = \frac{n(n+1)}{2}$
(1) + (1 + 1) + (1 + 1 + 1) + … + (1 + 1 + 1 + ... n−1 times) = ?
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Solution
n(n + 1)/2
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