A function f: R $\to$ R is given by $f(x) = x^3 + 3$. If $f(x) = -24$, then the value of x is:

For the functions $f(x) = x^2$ and $g(x) = x^3$, which of the following statements are TRUE?

[where N is the set of natural numbers and Z is the set of integers]

(A) $f: N \to N$ is one-one but not onto.

(B) $f: Z \to Z$ is neither one-one nor onto.

(C) $g: N \to N$ is one-one but not onto.

(D) $g: Z \to Z$ is one-one but not onto.

Choose the correct answer from the options given below:

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = [x]$, where [x] denotes the greatest integer less than or equal to x. Then which of the following statements are correct?

(A) f is one-one but not onto

(B) f is not onto

(C) f is not one-one

(D) f is one-one and onto

Choose the correct answer from the options given below:

Which of the following are correct?

(A) If a ≡ b(mod n), then -a ≡ -b (mod n)

(B) If a + b = c, then a(mod n) + b(mod n) ≡ (a + b + c)(mod n).

(C) If a ≡ b (mod n), then ka ≡ kb(mod n), ∀ k ∈ I.

(D) If a ≡ b (mod n), then (a + k) ≡ (b + k)(mod n), ∀ k ∈ I.

Choose the correct answer from the options given below:

Let $A = \{0, 1, 2, 3\}$ and R be a relation on set A defined as $R = \{(0,0), (0,1), (0,3), (1,0), (1,1), (2,2), (3,0), (3,3)\}$, then the relation R is

Assume that R is a relation on the set Z of integers and it is given by $(x, y) \in R \Leftrightarrow |x - y| \leq 1$. Then, R is

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is