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Jamia Millia Islamia Previous Year Questions (PYQs)

Jamia Millia Islamia Mathematical Reasoning PYQ

Jamia Millia Islamia PYQ
Which of the following is correct?





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2021 PYQ

Solution

Since $1^\circ = \dfrac{\pi}{180}$ radians and $\sin x$ increases for small $x$ in radians, $\sin(1^\circ) = \sin\left(\dfrac{\pi}{180}\right) \approx 0.01745 < \sin(1 \text{ rad}) \approx 0.841$. Hence, $\sin 1^\circ < \sin 1$.
Jamia Millia Islamia PYQ
If $P,Q,R$ have truth values $T,T,F$, then the truth values of $\Big(P\to(Q\to R)\Big)\to\Big((P\to Q)\to(P\to R)\Big)$ and $P\to(Q\vee R)$ are:





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2023 PYQ

Solution

$Q\to R = T\to F = F$, so $P\to(Q\to R)=T\to F=F$. $P\to Q = T\to T = T$, $P\to R = T\to F = F$, hence $(P\to Q)\to(P\to R)=T\to F=F$. Therefore $(F)\to(F)=T$. Also $Q\vee R = T\vee F = T$, so $P\to(Q\vee R)=T\to T=T$.
Jamia Millia Islamia PYQ
The contrapositive of $p \to (\neg q \to \neg r)$ is —





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2023 PYQ

Solution

Given statement: $p \to (\neg q \to \neg r)$ Contrapositive = $\neg(\neg q \to \neg r) \to \neg p$ Now, $\neg(\neg q \to \neg r) \equiv (\neg q \land r)$ Hence, contrapositive = $(\neg q \land r) \to \neg p.$
Jamia Millia Islamia PYQ
The statement $p \to (q \to p)$ is equivalent to...





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

Solution

$q \to p$ is true whenever $p$ is true. Hence, $p \to (q \to p)$ is always true.
Jamia Millia Islamia PYQ
At any time, the total number of people on the earth who have shaken hands an odd number of times is:





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

By the Handshake Lemma, in any graph, the number of vertices with odd degree is always even.
Jamia Millia Islamia PYQ
Ram secures $100$ marks in maths, then he will get a smartphone.” The converse is:





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

Converse of “$P\Rightarrow Q$” is “$Q\Rightarrow P$”. $\boxed{\text{If Ram will get a smartphone, then he secures 100 marks in maths.}}$
Jamia Millia Islamia PYQ
Negation of $,q \vee \sim (p \wedge r),$ is





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

$\neg\big(q \vee \neg(p\wedge r)\big)=\neg q \wedge \neg\neg(p\wedge r)=\neg q \wedge (p\wedge r)$. $\boxed{,\sim q \wedge (p \wedge r),}$
Jamia Millia Islamia PYQ
$(p\wedge \neg q)\wedge(\neg p\wedge q)$ is





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

Expression forces $p\wedge\neg p$ and $q\wedge\neg q$ simultaneously → impossible. $\boxed{\text{Contradiction}}$
Jamia Millia Islamia PYQ
The compound statement with ‘And’ is false if ______ of its component statements are.





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Jamia Millia Islamia Previous Year PYQ Jamia Millia Islamia JAMIA MILLIA ISLAMIA MCA 2024 PYQ

Solution

In logic, a conjunction $p \land q$ is true only if both $p$ and $q$ are true. Hence, it is false if any one is false.

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