Question : If 18 mechanics can repair 90 cars in 10 days, how many mechanics will be required to repair 150 cars in 12 days?

Option 1: 25

Option 2: 30

Option 3: 20

Option 4: 27

Question : If $a+b=3$ and $a b=2$, then what is the value of $2 a^3+2 b^3$?

Option 1: 25

Option 2: 27

Option 3: 18

Option 4: 20

Question : Prabodh has done $\frac{1}{2}$ of a job in 30 days. Sapan completes the rest of the job in 45 days. In how many days can they together do the job?

Option 1: 18 days

Option 2: 48 days

Option 3: 27 days

Option 4: 36 days

Question : A is twice as a good worker as B and together they finish the work in 20 days. In how many days can A alone do it?

Option 1: 25 days

Option 2: 36 days

Option 3: 20 days

Option 4: 30 days

Question : If 50 boys can finish a work in 30 days by working 6 hours per day, then how many hours per day should 25 boys work to finish that work within 24 days?

Option 1: 18 hours

Option 2: 10 hours

Option 3: 12 hours

Option 4: 15 hours

Question : If $\operatorname{cos} \theta=\frac{4}{5}$, find the value of $\operatorname{cot} \theta+\tan \theta$.

Option 1: $\frac{12}{25}$

Option 2: $\frac{25}{12}$

Option 3: $\frac{27}{12}$

Option 4: $\frac{12}{27}$