MCQ_SINGLE

Let \(R_{+}\) denote the set of all non-negative real numbers. Then the function \(f:R_{+}\rightarrow R_{+}\) defined as \(f(x)=x^{2}+1\) is :

VSA

Let $A = \{1, 2, 3, 4\}$ and let $R = \{(2, 2), (3, 3), (4, 4), (1, 2)\}$ be a relation on $A$. Then check whether $R$ is reflexive, symmetric or transitive.

SA

A relation R on set $A=\{1,2,3,4,5\}$ is defined as $R=\{(x,y):|x^{2}-y^{2}|

LA

Show that a function $f : R \to R$ defined by $f(x) = \frac{2x}{1 + x^2}$ is neither one-one nor onto. Further, find set $A$ so that the given function $f : R \to A$ becomes an onto function. [All India 2023, Delhi 2024]

VSA

Let $R = \{(a, a^3) : a \text{ is a prime number less than } 5\}$ be a relation. Find the range of $R$. [All India 2014]

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