1 Marks Question

Question 11 Mark

If $f(x)=\log x$, then find the value of $f(e)$.

Answer

$\begin{array}{l}f(x)=\log _{ e } x \\ \therefore f(e)=\log _{ e } e=1\end{array}$

Question 21 Mark

A relation $R$ is defined on a set $A=\{1,2,3,4,5,6\}$ such that $x R y \Leftrightarrow x+2 y=8$, then write the domain of R.

Answer

$\begin{array}{l}\text { Given, } \quad x+2 y=8 \\\therefore \quad 2 y=8-x \\\Rightarrow \quad y=\frac{8-x}{2} \\2 \text { R 3, } 4 \text { R 2, } 6 \text { R } 1 \\\therefore \text { Domain of } R=\{2,4,6\}\end{array}$

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Question 31 Mark

A relation R is defined on set N such that $R =\{(x, y)$ / $y=x+2,1 < x < 5\}$ then write the domain of relation R.

Answer

Domain $=\{2,3,4\}$.

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Question 41 Mark

If $f(x)=\frac{x}{x+1}$, then write the value of $f\left(\frac{p}{q}\right)$.

Answer

$f\left(\frac{p}{q}\right)=\frac{p / q}{\frac{p}{q}+1}=\frac{p / q}{\frac{p+q}{q}}=\frac{p}{p+q}$

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Question 51 Mark

$A$ and $B$ are two different sets, each of which has two elements. Find the number of non-empty relation from set A to set B .

Answer

Let $A =\{a, b\}$ and $B =\{x, y\}$
$n(A)=2, n(B)=2$
then, $n(A \times B )=2 \times 2=4$
So, the required number of non empty relations from A to $B=2^4-1=15$

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Question 61 Mark

If A is a set of first five natural numbers and a relation R is defined on A such that $x R y \Leftrightarrow x < y$, then write the domain of R .

Answer

$\{1,2,3,4\}$

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Question 71 Mark

If $f(x)=\tan x$ then write the value of $f(x)+f(\pi-x)$.

Answer

$\begin{array}{l}f(x)=\tan x, f(\pi-x)=\tan (\pi-x)=-\tan x \\ \therefore f(x)+f(\pi-x)=\tan x-\tan x=0\end{array}$

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Question 81 Mark

If $A =\{2,3,5,7\}$ and $f: A \rightarrow N , f(x)=x^3+2$, then find the range of function.

Answer

$\begin{array}{l}f(2)=2^3+2=8+2=10 \\f(3)=3^3+2=27+2=29 \\f(5)=5^3+2=125+2=127 \\f(7)=7^3+2=343+2=345\end{array}$
Hence, range of function $=\{10,29,127,345\}$

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