VSA

Let $A = \{1, 2, 3\}$. We define $R_1 = \{(1, 2), (3, 2), (1, 3)\}, R_2 = \{(1, 3), (3, 6), (2, 1), (1, 2)\}$. Then check which is/are the relation on $A$

LA

Let $f, g : N - \{1\} \to N$ be functions defined by $f(a) = \alpha$, where $\alpha$ is the maximum of the powers of those primes $p$ such that $p^\alpha$ divides $a$, and $g(a) = a + 1$, for all $a \in N - \{1\}$. Then, check whether the function $f + g$ is one-one or onto. [Competency]

LA

A relation $R$ is defined on $N \times N$ (where $N$ is the set of natural numbers) as $(a, b) R (c, d) \Leftrightarrow a - c = b - d$. Show that $R$ is an equivalence relation. [Delhi 2024]

VSA

A relation R on $A=\{1,2,3\}$ is defined as $R=\{(1,1),(3,3),(1,2)\}$. Is R a symmetric relation? Justify. Write the smallest relation set $R_{1}$ such that $R\cup R_{1}$ becomes an equivalence relation on the set {1, 2, 3}.

SA

$f(x) = \frac{2 \tan x}{1 - \tan^2 x}$. Find the range of $f(x)$ for $x \in R$. Show your steps. [Competency]

View All Questions