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Jamia Millia Islamia Previous Year Questions (PYQs)
Jamia Millia Islamia Mathematical Induction PYQ
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
Which of the following indicates the first step of mathematical induction
for the mathematical statement $n + 1 > n$?
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
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.
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
What is the base case for the inequality $7^n > n^3$, where $n = 3$?
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2020 PYQ
Solution
Substitute $n = 3$: $7^3 = 343$, and $3^3 = 27$. Clearly $343 > 27.$
Jamia Millia Islamia PYQ
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ
(1) + (1 + 1) + (1 + 1 + 1) + … + (1 + 1 + 1 + ... n−1 times) = ?
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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2018 PYQ
Solution
n(n + 1)/2Jamia Millia Islamia
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