Let R be a relation defined on the set of natural number N as \[\mathbf{R}=\left\{ \left( \mathbf{x},\mathbf{y} \right):\mathbf{x}\in \mathbf{N},\mathbf{y}\in \mathbf{N},\mathbf{2x}+\mathbf{y}=\mathbf{41} \right\}\], Then
A)
Domain of \[R=\left\{ 1,1,3,4,5.....19,20 \right\}\]
A, B, C be three exhaustive and mutually exclusive events associated with a random experiment. If \[\mathbf{P}\left( B \right)=-\mathbf{P}\left( A \right)\]and\[\mathbf{P}\left( C \right)=-\mathbf{P}\left( B \right)\],the \[\mathbf{P}\left( A \right)\]is equal to:
If\[\mathbf{3}{{.}^{\mathbf{x}+1}}{{\mathbf{C}}_{\mathbf{2}}}{{+}^{\mathbf{2}}}{{\mathbf{P}}_{\mathbf{2}}}.\mathbf{x}=\mathbf{4}{{.}^{\mathbf{X}}}{{\mathbf{P}}_{\mathbf{2}}},\mathbf{x}\in \mathbf{N}\]. Then the value of x is:
If \[\frac{{{\left( \mathbf{a}+\mathbf{ib} \right)}^{\mathbf{2}}}}{\mathbf{a}-\mathbf{ib}~~}-\frac{{{\left( \mathbf{a}-\mathbf{ib} \right)}^{\mathbf{2}}}}{\mathbf{a}+\mathbf{ib}}=x+iy\] then x =.....
If \[\mathbf{a},\mathbf{b},\mathbf{c}\] are in G.P. then the equation \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{2bx}+\mathbf{c}=\mathbf{0}\]and \[\mathbf{d}{{\mathbf{x}}^{\mathbf{2}}}+2\mathbf{ex}+\mathbf{f}=\mathbf{0}\]have a common root if \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\] are in:
If the sum of the roots of the equation \[\mathbf{a}{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{bx}+\mathbf{c}=\mathbf{0}\]is equal to the sum of the reciprocals of their square then \[\mathbf{b}{{\mathbf{e}}^{\mathbf{2}}},\mathbf{c}{{\mathbf{a}}^{\mathbf{2}}}\]and \[\mathbf{a}{{\mathbf{b}}^{\mathbf{2}}}\]are in
If \[\frac{\mathbf{b}+\mathbf{c}-\mathbf{2a}}{a}\text{,}\frac{\mathbf{c}+\mathbf{a}-\mathbf{2b}}{b}\text{,}\frac{\mathbf{a}+\mathbf{b}-\mathbf{2c}}{c}\]are in A.P. Then a, bare in