What is the cardinality of these sets in the order of their serial number? (i) ${a}$ (ii) ${{a}}$ (iii) ${a, {a}}$ (iv) ${a, {a}, {{a}}}$

1

How many elements does the set $P\big({\varnothing, a, {a}, {{a}}}\big)$ has; where $a$ and $b$ are distinct elements a…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

1

Suppose that $A_i = {1, 2, 3, \ldots, i}$ for $i = 1, 2, 3, \ldots$ Then find $\displaystyle \bigcup_{i=1}^{\infty} A_i…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

2

$,\text{Find } \displaystyle \bigcup_{i=1}^{\infty} A_i \text{ and } \bigcap_{i=1}^{\infty} A_i,\ \text{for every posit…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

3

Which of the following relations are functions? (i) ${(1,(a,b)),\ (2,(b,c)),\ (3,(c,a)),\ (4,(a,b))}$ (ii) ${(1,(a,b)),…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

4

There is a direct flight from Trichy to New Delhi and 2 direct trains. There are 6 trains from Trichy to Chennai and 4 …

Topic: JAMIA MILLIA ISLAMIA MCA 2023

5

If $P,Q,R$ have truth values $T,T,F$, then the truth values of $\Big(P\to(Q\to R)\Big)\to\Big((P\to Q)\to(P\to R)\Big)$…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

6

$(A\cap B')\ \cup\ (A'\cap B)\ \cup\ (A'\cap B')$ is equal to

Topic: JAMIA MILLIA ISLAMIA MCA 2023

7

The floor function $[x]$ is

Topic: JAMIA MILLIA ISLAMIA MCA 2023

8

The domain of the real-valued function $f(x) = \sqrt{x - 3} + \sqrt{x - 4}$ is the set of all values of $x$ satisfy…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

9

The number of students who take both the subjects’ mathematics and chemistry are 30. This represents 10% of the enrolme…

Topic: JAMIA MILLIA ISLAMIA MCA 2023

10

Find the value of $ \dfrac{1}{\sin 10^\circ} - \dfrac{\sqrt{3}}{\cos 10^\circ} = ? $

Topic: JAMIA MILLIA ISLAMIA MCA 2023