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Jamia Millia Islamia MCA Previous Year Questions (PYQs)

Jamia Millia Islamia MCA Mathematical Induction PYQ


Jamia Millia Islamia MCA 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 MCA Previous Year PYQ Jamia Millia Islamia MCA 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 MCA PYQ
What is the base case for the inequality $7^n > n^3$, where $n = 3$?





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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2020 PYQ

Solution

Substitute $n = 3$: $7^3 = 343$, and $3^3 = 27$. Clearly $343 > 27.$

Jamia Millia Islamia MCA PYQ
The sum of the first n natural numbers given by:





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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2025 PYQ

Solution

Sum of first n natural numbers:
$S = \frac{n(n+1)}{2}$

Jamia Millia Islamia MCA PYQ
(1) + (1 + 1) + (1 + 1 + 1) + … + (1 + 1 + 1 + ... n−1 times) = ?





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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2018 PYQ

Solution

n(n + 1)/2


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