Jamia Millia Islamia MCA Mathematical Reasoning Previous Year Question Paper and Solution with PDF

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Jamia Millia Islamia MCA Mathematical Reasoning PYQ

Qus : 1 Jamia Millia Islamia MCA PYQ

Which of the following is correct?

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA 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, $\sin 1^\circ < \sin 1$.

Qus : 2 Jamia Millia Islamia MCA 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 MCA Previous Year PYQ Jamia Millia Islamia MCA 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 $P\to(Q\vee R)=T\to T=T$.

Qus : 3 Jamia Millia Islamia MCA PYQ

The contrapositive of $p \to (\neg q \to \neg r)$ is —

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA 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 = $(\neg q \land r) \to \neg p.$

Qus : 4 Jamia Millia Islamia MCA PYQ

Consider the following statements: S1: There exists infinite sets A, B, C such that A ∪ C = B ∪ C is finite. S2: There exist two irrational numbers x and y such that (x+y) is rational. Which of the following is true about S1 and S2?

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

Solution

Consider the statements:

S1: There exists infinite sets A,B,C such that A C = B C is finite.

If A and C are infinite, then A C must be infinite. So this is impossible.

S2: There exist two irrational numbers x and y such that (x+y) is rational.

Qus : 5 Jamia Millia Islamia MCA PYQ

The statement $p \to (q \to p)$ is equivalent to...

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Solution

$q \to p$ is true whenever $p$ is true. Hence, $p \to (q \to p)$ is always true.

Qus : 6 Jamia Millia Islamia MCA 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 MCA Previous Year PYQ Jamia Millia Islamia MCA JAMIA MILLIA ISLAMIA MCA 2022 PYQ

Solution

By the Handshake Lemma, in any graph, the number of vertices with odd degree is always even.

Qus : 7 Jamia Millia Islamia MCA PYQ

Ram secures $100$ marks in maths, then he will get a smartphone.” The converse is:

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

Solution

Converse of “$P\Rightarrow Q$” is “$Q\Rightarrow P$”. $\boxed{\text{If Ram will get a smartphone, then he secures 100 marks in maths.}}$

Qus : 8 Jamia Millia Islamia MCA PYQ

Negation of $,q \vee \sim (p \wedge r),$ is

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

Solution

$\neg\big(q \vee \neg(p\wedge r)\big)=\neg q \wedge \neg\neg(p\wedge r)=\neg q \wedge (p\wedge r)$. $\boxed{,\sim q \wedge (p \wedge r),}$

Qus : 9 Jamia Millia Islamia MCA PYQ

$(p\wedge \neg q)\wedge(\neg p\wedge q)$ is

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

Solution

Expression forces $p\wedge\neg p$ and $q\wedge\neg q$ simultaneously → impossible. $\boxed{\text{Contradiction}}$

Qus : 10 Jamia Millia Islamia MCA PYQ

The compound statement with ‘And’ is false if ______ of its component statements are.

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Jamia Millia Islamia MCA Previous Year PYQ Jamia Millia Islamia MCA 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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