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]

VSA

Find the number of all onto functions from the set $\{1, 2, 3, \dots, n\}$ to itself. [NCERT]

VSA

Consider the relation $\phi$ on a non-empty set $A$. Then, check whether $R$ is symmetric, reflexive or transitive.

LA

Show that the function $f : R_* \to R_*$ defined by $f(x) = \frac{1}{x}$ is one-one onto, where $R_*$ is the set of all non-zero real numbers. Is the result true, if the domain $R_*$ is replaced by $N$ with co-domain being same as $R_*$?

ASSERTION_REASON

Assertion (A): Let $f(x) = e^{x}$ and $g(x) = \log x$. Then $(f + g)x = e^{x} + \log x$ where domain of $(f + g)$ is $\mathbb{R}$.

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