List of top Mathematics Questions on Relations and functions asked in JEE Main

Which of the following is not correct for relation \( R \) on the set of real numbers?

Let $\mathbb{N}$ be the set of natural numbers and a relation R on $\mathbb{N}$ be defined by R = $\{(x, y) \in \mathbb{N} \times \mathbb{N} : x^3 - 3x^2y - xy^2 + 3y^3 = 0\}$. Then the relation R is :

Let $f\left(n\right) = \left[\frac{1}{3} + \frac{3n}{100}\right]{n},$ where $\left[n\right]$ denotes the greatest integer less than or equal to n. Then $\sum\limits^{56}_{n = 1} \Delta_{r} f\left(n\right)$ is equal to :

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?

Let $f,g:[-1,2]\to R$ be continuous functions which are twice differentiable on the interval (-1,2). Let the values of $f$ and $g$ at the points -1,0 and 2 be as given in the following table:$\begin{array}{|llll|}\hline e& x=-1& x=0& x=2\\ f(x)& 3& 6& 0\\ g(x)& 0& 1& -1\\ \hline\end{array}$In each of the intervals (-1,0) and (0,2) the function $(f-3g)$ never vanishes. Then the correct statement(s) is (are):

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.

Let f(x) = cosx - x + 1, x ∈ [0,π], then

A = {2,4,6,8}, B = {3,7,6,9}. R: A × B → A × B such that (a₁, b₁) R (a₂, b₂) ⇔ a₁ + a₂ = b₁ + b₂ where (a₁, b₁) ∈ A, (a₂, b₂) ∈ B. Find the number of elements in the relation.2)= 4, then find (a² + b² + c²).