Properties of Functions and Graphs
Sets, Relation and Function

116911 If \(\log _{27}\left(\log _3 x\right)=\frac{1}{3}\), then the value of \(x\) is

1 3
2 6
3 9
4 27
Sets, Relation and Function

116914 The number of reflexive relations of a set with four elements is equal to:

1 \(2^{16}\)
2 \(2^{12}\)
3 \(2^8\)
4 \(2^4\)
Sets, Relation and Function

116923 \(\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}\) is equal to

1 2
2 7
3 \(\sqrt{7}\)
4 \(\sqrt{2}\)
Sets, Relation and Function

116930 If a and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

1 4
2 \(\frac{6}{5}\)
3 \(\frac{10}{3}\)
4 \(\frac{68}{15}\)
Sets, Relation and Function

116935 If \(x=\frac{2}{3+\sqrt{7}}\) then \((x-3)^2\) is equal to

1 1
2 3
3 6
4 7
Sets, Relation and Function

116911 If \(\log _{27}\left(\log _3 x\right)=\frac{1}{3}\), then the value of \(x\) is

1 3
2 6
3 9
4 27
Sets, Relation and Function

116914 The number of reflexive relations of a set with four elements is equal to:

1 \(2^{16}\)
2 \(2^{12}\)
3 \(2^8\)
4 \(2^4\)
Sets, Relation and Function

116923 \(\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}\) is equal to

1 2
2 7
3 \(\sqrt{7}\)
4 \(\sqrt{2}\)
Sets, Relation and Function

116930 If a and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

1 4
2 \(\frac{6}{5}\)
3 \(\frac{10}{3}\)
4 \(\frac{68}{15}\)
Sets, Relation and Function

116935 If \(x=\frac{2}{3+\sqrt{7}}\) then \((x-3)^2\) is equal to

1 1
2 3
3 6
4 7
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Sets, Relation and Function

116911 If \(\log _{27}\left(\log _3 x\right)=\frac{1}{3}\), then the value of \(x\) is

1 3
2 6
3 9
4 27
Sets, Relation and Function

116914 The number of reflexive relations of a set with four elements is equal to:

1 \(2^{16}\)
2 \(2^{12}\)
3 \(2^8\)
4 \(2^4\)
Sets, Relation and Function

116923 \(\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}\) is equal to

1 2
2 7
3 \(\sqrt{7}\)
4 \(\sqrt{2}\)
Sets, Relation and Function

116930 If a and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

1 4
2 \(\frac{6}{5}\)
3 \(\frac{10}{3}\)
4 \(\frac{68}{15}\)
Sets, Relation and Function

116935 If \(x=\frac{2}{3+\sqrt{7}}\) then \((x-3)^2\) is equal to

1 1
2 3
3 6
4 7
Sets, Relation and Function

116911 If \(\log _{27}\left(\log _3 x\right)=\frac{1}{3}\), then the value of \(x\) is

1 3
2 6
3 9
4 27
Sets, Relation and Function

116914 The number of reflexive relations of a set with four elements is equal to:

1 \(2^{16}\)
2 \(2^{12}\)
3 \(2^8\)
4 \(2^4\)
Sets, Relation and Function

116923 \(\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}\) is equal to

1 2
2 7
3 \(\sqrt{7}\)
4 \(\sqrt{2}\)
Sets, Relation and Function

116930 If a and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

1 4
2 \(\frac{6}{5}\)
3 \(\frac{10}{3}\)
4 \(\frac{68}{15}\)
Sets, Relation and Function

116935 If \(x=\frac{2}{3+\sqrt{7}}\) then \((x-3)^2\) is equal to

1 1
2 3
3 6
4 7
Sets, Relation and Function

116911 If \(\log _{27}\left(\log _3 x\right)=\frac{1}{3}\), then the value of \(x\) is

1 3
2 6
3 9
4 27
Sets, Relation and Function

116914 The number of reflexive relations of a set with four elements is equal to:

1 \(2^{16}\)
2 \(2^{12}\)
3 \(2^8\)
4 \(2^4\)
Sets, Relation and Function

116923 \(\frac{\sqrt{8+\sqrt{28}}+\sqrt{8-\sqrt{28}}}{\sqrt{8+\sqrt{28}}-\sqrt{8-\sqrt{28}}}\) is equal to

1 2
2 7
3 \(\sqrt{7}\)
4 \(\sqrt{2}\)
Sets, Relation and Function

116930 If a and \(b\) are arbitrary positive real numbers, then the least possible value of \(\frac{6 a}{5 b}+\frac{10 b}{3 a}\) is

1 4
2 \(\frac{6}{5}\)
3 \(\frac{10}{3}\)
4 \(\frac{68}{15}\)
Sets, Relation and Function

116935 If \(x=\frac{2}{3+\sqrt{7}}\) then \((x-3)^2\) is equal to

1 1
2 3
3 6
4 7