Question : The ratio of the amount of work done by $(x-1)$ labourers in $(x+1)$ days to that done by $(x+1)$ labourers in $(x+2)$ days is 5 : 6. Then the value of $x$ is:

Option 1: 16

Option 2: 15

Option 3: 17

Option 4: 14

Question : If $x+\frac{1}{x}=5$, then the value of $\frac{x}{1+x+x^2}$ is:

Option 1: $\frac{1}{5}$

Option 2: $\frac{1}{6}$

Option 3: $5$

Option 4: $6$

Question : To do a certain work, the ratio of the efficiencies of A and B is 7 : 5. Working together, they can complete the same work in $17 \frac{1}{2}$ days. A alone will complete 60% of the same work in:

Option 1: 18 days

Option 2: 15 days

Option 3: 16 days

Option 4: 21 days

Question : If $2=x+\frac{1}{1+\frac{1}{5+\frac{1}{2}}}$, then the value of $x$ is equal to:

Option 1: $\frac{14}{13}$

Option 2: 1

Option 3: $\frac{13}{15}$

Option 4: $\frac{15}{13}$

Question : A, B, and C can do a job in 6 days, 12 days and 15 days respectively. After $\frac{1}{8}$th of the work is completed, C leaves the job. The rest of the work is done by A and B together. The time taken to finish the work is:

Option 1: $5\frac{5}{6}$ days

Option 2: $5\frac{1}{4}$ days

Option 3: $3\frac{1}{2}$ days

Option 4: $3\frac{3}{4}$ days

Question : If $x^2-15 x+1=0$, what is the value of $x^4-223 x^2+6 ?$

Option 1: 9

Option 2: 5

Option 3: 6

Option 4: 0