List of top Data Science A.I Cyber Security and Computer Sci. Questions on Set Theory & Algebra asked in CUET (PG)

Consider a binary operation $*$ on set $\mathbb{Z}$ (set of integers) defined as $a * b = a + b + 1$ then :
A. $*$ is commutative

B. $*$ is associative

C. Identity element under $*$ exists

D. Every element has an inverse under $*$

E. The structure $(\mathbb{Z}, *)$ is not a group

Choose the correct answer from the options given below :

Let G be finite set, which is a group under some operation and H be a subgroup and $a \in H$. Considering their order cardinality in increasing order :
A. $O(G)$

B. $O(a)$

C. $O(H)$

D. $Card(2^G)$

Choose the correct answer from the options given below :

Given below are two statements :
one is labelled as
Assertion (A) and the other is labelled as
Reason (R).
Assertion (A) :
Every function is a relation.
Reason (R) :
A function can be one to many.
In the light of the above statements, choose the most appropriate answer from the options given below :

Which of the following operation is not a partial order relation?

If $f(x) = x^2 + 1$ and $g(x) = 2x - 3$, then $(f \circ g)(x)$ is equal to:

Consider the group $G = \{+1, -1, +i, -i\}$ under multiplication operation. Which of the following is not correct?

Let Σ be a finite non-empty alphabet and let 2Σ* be the power set of Σ*. Which one of the following is true?

Let A be a 2 × 2 matrix with elements \(a_{11} = a_{12} = a_{21} = +1\) and \(a_{22} = −1\). Then the eigenvalues of matrix A² are

If x ∈ [0, 1], and f(x) and g(x) are defined as: f(x) = sin(cos(πx/4)) and g(x) = cos(sin(πx/4)) then: