General Aptitude

Equal sized circular regions are shaded in a square sheet of paper of 1 cm side length. Two cases, case M and case N, are considered as shown in the figures below. In the case M, four circles are shaded in the square sheet and in the case N, nine circles are shaded in the square sheet as shown.


What is the ratio of the areas of unshaded regions of case M to that of case N?

Four cities P, Q, R and S are connected through oneway routes as shown in the figure. The travel time between any two connected cities is one hour. The boxes beside each city name describe the starting time of first train of the day and their frequency of operation. For example, from city P, the first trains of the day start at 8 AM with a frequency of 90 minutes to each of R and S. A person does not spend additional time at any city other than the waiting time for the next connecting train. If the person starts from R at 7 AM and is required to visit S and return to R, what is the minimum time required?

Consider the following functions for non-zero positive integers, p and q

f(p,q)=\underbrace{p \times p \times p \times ...p}_{q \;\;times} =p^q;\;\; f(p,1)=p
g(p,q)=p^{p^{p^{\vdots ^{q \;\;times}}}};\;\; g(p,1)=p

Which one of the following options is correct based on the above?

For the past m days, the average daily production at a company was 100 units per day.
If today's production of 180 units changes the average to 110 units per day, what is the value of m?

Fish belonging to species S in the deep sea have skins that are extremely black (ultra-black skin). This helps them not only to avoid predators but also sneakily attack their prey. However, having this extra layer of black pigment results in lower collagen on their skin, making their skin more fragile.
Which one of the following is the CORRECT logical inference based on the information in the above passage?

Which one of the groups given below can be assembled to get the shape that is shown above using each piece only once without overlapping with each other?
(rotation and translation operations may be used).

A person was born on the fifth Monday of February in a particular year.
Which one of the following statements is correct based on the above information?

If f(x)=2 \ln\sqrt{e^x} what is the area bounded by f(x) for the interval [0,2] on the x- axis?

Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality 2-5x\leq -\frac{6x-5}{3} on the real number line?

Writing too many things on the ________ while teaching could make the students get _________.