| 2024-01-23 | If \( f(x)=64 x^{3}+\frac{1}{x^{3}} \) and \( \alpha, \beta \) are the roots of \( 4 x+\frac{1}{.... |
| 2024-01-23 | Let \( f=\{(2,4),(5,6),(8,-1),(10,-3)\} \) and \( g=\{(2,5),(7 \), \( 1),(8,4),(10,13),(11,5)\} .... |
| 2024-01-23 | Let \( f=\{(2,4),(5,6),(8,-1),(10,-3)\} \) and \( g=\{(2,5),(7 \), \( 1),(8,4),(10,13),(11,5)\} .... |
| 2024-01-23 | If \( f: R \rightarrow R \) and \( g: R \rightarrow R \) are defined by \( f(x)=2 x+ \)
3 and \(.... |
| 2024-01-23 | If \( 3 f(x)+5 f\left(\frac{1}{x}\right)=\frac{1}{x}-3 \) for all non-zero \( x \), then \( f(x).... |
| 2024-01-23 | Let \( f=\{(2,4),(5,6),(8,-1),(10,-3)\} \) and \( g=\{(2,5),(7 \),
\( 1),(8,4),(10,13),(11,5)\} .... |
| 2024-01-23 | If \( f \) is a real valued function given by \( f(x)=27 x^{3}+ \)
\( \frac{1}{x^{3}} \) and \( .... |
| 2024-01-23 | The domain of the function \( f \) defined by
\( f(x)=\frac{x^{2}+2 x+1}{x^{2}-x-6} \) is equal .... |
| 2024-01-23 | If \( f:[-2,2] \rightarrow R \) is defined by \( f(x)=\left\{\begin{array}{l}-1, \text { for }-2.... |
| 2024-01-23 | Let \( A=\left\{(x, y): x \in R, y \in R, x^{3}+y^{3}=1\right\}, B=\{(x, y) \)
\( : x \in R, y \.... |
| 2024-01-23 | Let \( A=\{x \in R: x \neq 0,-4 \leq x \leq 4\} \) and \( f: A \rightarrow R \) be
defined by \(.... |
| 2024-01-23 | If \( R \) is a relation from a finite set \( A \) having \( m \) elements
to a finite set \( B .... |
| 2024-01-23 | Let \( n(A)=m \) and \( n(B)=n \). Then the total number of
non-empty relations that can be defi.... |
| 2024-01-23 | If \( R \) is a relation on a finite set having \( n \) elements, then
the number of relations o.... |
| 2024-01-23 | If \( X=\{1,2,3,4\}, Y=\{2,3,5,7\}, Z=\{3,6,8,9\} \),
\( W=\{2,4,8,10\} \), then.... |
| 2024-01-23 | Let \( R \) is a relation from \( \{11,12,13\} \) to \( \{8,10,12\} \) defined by \( y=x-3 \). T.... |
| 2024-01-23 | Let \( R \) be a relation from a set \( A \) to a set \( B \), then
(1) \( R=A \cup B \)
(2) \( .... |
| 2024-01-23 | Passage
In some question of sets, we have to make the use of graphs.
For example
\[
\begin{array.... |
| 2024-01-23 | In a class of 42 students, the number of students
studying different subjects are 23 in mathemat.... |
| 2024-01-23 | A relation \( \phi \) from \( \mathrm{C} \) to \( \mathrm{R} \) is defined by \( \mathrm{x} \phi.... |
| 2024-01-23 | A relation \( R \) is defined form \( \{2,3,4,5\} \) to \( \{3,6,7 \), \( 10\} \) by : \( x R y .... |
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