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Jamia Millia Islamia MCA Previous Year Questions (PYQs)
Jamia Millia Islamia MCA Probability Critical Thinking PYQ
Jamia Millia Islamia MCA PYQ
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2018 PYQ
Find the remainder when $67^{99}$ is divided by 7.
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2018 PYQ
Solution
$67 \equiv 4 \pmod7$, so $4^3 \equiv 1$. $99$ is multiple of 3 → remainder $=1$.
Jamia Millia Islamia MCA PYQ
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ
Three letters are dictated to three persons and an envelope is addressed to each of them.
The letters are inserted into the envelopes at random so that each envelope contains exactly one letter.
What is the probability that at least one letter is in its proper envelope?
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ
Solution
Total permutations of 3 letters = $3! = 6$. Derangements (no letter in correct envelope) = $!3 = 2$. Hence, number of favorable cases (at least one correct) = $6 - 2 = 4$. Probability $= \dfrac{4}{6} = \dfrac{2}{3}$.
Jamia Millia Islamia MCA PYQ
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ
A tourist visits four cities A, B, C and D in a random order.
What is the probability that he visits A before B?
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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2019 PYQ
Solution
Out of all $4! = 24$ permutations, in half of them A comes before B, and in the other half B comes before A. Therefore probability = $\dfrac{1}{2}$.Jamia Millia Islamia MCA
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