Question : If $(a+b-6)^{2}+a^{2}+b^{2}+1+2b=2ab+2a$, the value of $a$ is:

Option 1: 7

Option 2: 6

Option 3: 3.5

Option 4: 2.5

Question : If $\frac{1}{6}$ of $x$ – $\frac{7}{2}$ of $\frac{3}{7}$ equals to $(-\frac{7}{4})$, then the value of $x$ is:

Option 1: –1.5

Option 2: –3

Option 3: –2.5

Option 4: 6

Question : If $\frac{a}{1-2a}+\frac{b}{1-2b}+\frac{c}{1-2c}=\frac{1}{2}$, then the value of $\frac{1}{1-2a}+\frac{1}{1-2b}+\frac{1}{1-2c}$ is:

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : The value of $\frac{7+3 \sqrt{5}}{3+\sqrt{5}}-\frac{7-3 \sqrt{5}}{3-\sqrt{5}}$ lies between:

Option 1: 3 and 3.5

Option 2: 2 and 2.5

Option 3: 1.5 and 2

Option 4: 2.5 and 3

Question : The arithmetic mean of the following numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:

Option 1: 4

Option 2: 5

Option 3: 14

Option 4: 20

Question : If $(a+b)=5$, then the value of $(a-3)^7+(b-2)^7$ is:

Option 1: $2^7$

Option 2: $3^7$

Option 3: $1$

Option 4: $0$