Properties of Functions and Graphs
Sets, Relation and Function

116950 If \(x=7+4 \sqrt{3}\) and \(x y=1\), then \(\frac{1}{x^2}+\frac{1}{y^2}\) is equal to

1 64
2 134
3 194
4 \(\frac{1}{49}\)
Sets, Relation and Function

116954 If \(\log 2+\frac{1}{2} \log a+\frac{1}{2} \log b=\log (a+b)\), then

1 \(\mathrm{a}=\mathrm{b}\)
2 \(\mathrm{a}=-\mathrm{b}\)
3 \(a=2, b=0\)
4 \(\mathrm{a}=10, \mathrm{~b}=1\)
Sets, Relation and Function

116955 If \(\log _2 x+\log _x 2=\frac{10}{3}=\log _2 y+\log _y 2\) and \(x \neq y\), then \(x+y\) is equal to

1 \(2^{1 / 3}+3^2\)
2 \(2^3+2^{1 / 3}\)
3 \(3^{1 / 3}+2^3\)
4 None of these
Sets, Relation and Function

116956 If \(x=\sqrt{7+4 \sqrt{3}}\), then \(x+\frac{1}{x}\) is equal to

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

116950 If \(x=7+4 \sqrt{3}\) and \(x y=1\), then \(\frac{1}{x^2}+\frac{1}{y^2}\) is equal to

1 64
2 134
3 194
4 \(\frac{1}{49}\)
Sets, Relation and Function

116954 If \(\log 2+\frac{1}{2} \log a+\frac{1}{2} \log b=\log (a+b)\), then

1 \(\mathrm{a}=\mathrm{b}\)
2 \(\mathrm{a}=-\mathrm{b}\)
3 \(a=2, b=0\)
4 \(\mathrm{a}=10, \mathrm{~b}=1\)
Sets, Relation and Function

116955 If \(\log _2 x+\log _x 2=\frac{10}{3}=\log _2 y+\log _y 2\) and \(x \neq y\), then \(x+y\) is equal to

1 \(2^{1 / 3}+3^2\)
2 \(2^3+2^{1 / 3}\)
3 \(3^{1 / 3}+2^3\)
4 None of these
Sets, Relation and Function

116956 If \(x=\sqrt{7+4 \sqrt{3}}\), then \(x+\frac{1}{x}\) is equal to

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

116950 If \(x=7+4 \sqrt{3}\) and \(x y=1\), then \(\frac{1}{x^2}+\frac{1}{y^2}\) is equal to

1 64
2 134
3 194
4 \(\frac{1}{49}\)
Sets, Relation and Function

116954 If \(\log 2+\frac{1}{2} \log a+\frac{1}{2} \log b=\log (a+b)\), then

1 \(\mathrm{a}=\mathrm{b}\)
2 \(\mathrm{a}=-\mathrm{b}\)
3 \(a=2, b=0\)
4 \(\mathrm{a}=10, \mathrm{~b}=1\)
Sets, Relation and Function

116955 If \(\log _2 x+\log _x 2=\frac{10}{3}=\log _2 y+\log _y 2\) and \(x \neq y\), then \(x+y\) is equal to

1 \(2^{1 / 3}+3^2\)
2 \(2^3+2^{1 / 3}\)
3 \(3^{1 / 3}+2^3\)
4 None of these
Sets, Relation and Function

116956 If \(x=\sqrt{7+4 \sqrt{3}}\), then \(x+\frac{1}{x}\) is equal to

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

116950 If \(x=7+4 \sqrt{3}\) and \(x y=1\), then \(\frac{1}{x^2}+\frac{1}{y^2}\) is equal to

1 64
2 134
3 194
4 \(\frac{1}{49}\)
Sets, Relation and Function

116954 If \(\log 2+\frac{1}{2} \log a+\frac{1}{2} \log b=\log (a+b)\), then

1 \(\mathrm{a}=\mathrm{b}\)
2 \(\mathrm{a}=-\mathrm{b}\)
3 \(a=2, b=0\)
4 \(\mathrm{a}=10, \mathrm{~b}=1\)
Sets, Relation and Function

116955 If \(\log _2 x+\log _x 2=\frac{10}{3}=\log _2 y+\log _y 2\) and \(x \neq y\), then \(x+y\) is equal to

1 \(2^{1 / 3}+3^2\)
2 \(2^3+2^{1 / 3}\)
3 \(3^{1 / 3}+2^3\)
4 None of these
Sets, Relation and Function

116956 If \(x=\sqrt{7+4 \sqrt{3}}\), then \(x+\frac{1}{x}\) is equal to

1 4
2 6
3 2
4 3