Quantitative Aptitude - Arithmetic Ability Questions

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

If 5 sin2θ+ 4 cos2θ= 9/2 and 0 <θ<Π/2 then tanθ is equal to?

In each of the following questions two equations I and II are given. Solve both the equations and give answer:
$$\begin{gathered} I. x2+2x-195=0 \\ II. y2+30y+225=0 \end{gathered}$$

The alcohol and water in a mixture are in the ratio of 7 : 8 respectively. If 11 litre water is added to it, then the ratio of alcohol and water in the new mixture becomes 3 : 5. What is the total quantity (in litres) of the alcohol in the new mixture?

In a class of 55 students there are 34 girls. The average weight of these girls is 51 Kg and average weight of the full class is 55.2 kgs. What is the average weight of the boys of the class?

If a + a2 + a3 – 1 = 0, then what is the value ofa3 + (1/a)?

A man travelled a distance of 50 km in 8 hours. He travelled partly on foot at 5 km/hr and partly on bicycle at 7 km/hr. What is the distance (in kms) travelled on foot?

A can do a work in 12 days and B in 24 days. If they work on it together for 4 days, then what fraction of work is left?