# General Aptitude

 Question 1
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?
 A $2:3$ B $1:1$ C $3:2$ D $2:1$
GATE ME 2022 SET-2      Numerical Ability
Question 1 Explanation:

$2d=1\Rightarrow d=\frac{1}{2}$
Area of circle $=\frac{\pi d^2}{4}=\frac{\pi}{16}$
Total circle area $= 4 \times \frac{\pi}{16}=\frac{\pi}{4}$

$3d=1\Rightarrow d=\frac{1}{3}$
Area of circle $=\frac{\pi d^2}{4}=\frac{\pi}{36}$
Total circle area $= 9 \times \frac{\pi}{36}=\frac{\pi}{4}$
$\frac{\text{Unshaded area M}}{\text{Unshaded area N}}=\frac{1^2-\frac{\pi}{4}}{1-\frac{\pi}{4}}=\frac{1}{1}=1:1$
 Question 2
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?

 A 6 hours 30 minutes B 3 hours 45 minutes C 4 hours 30 minutes D 5 hours 15 minutes
GATE ME 2022 SET-2      Numerical Ability
Question 2 Explanation:
R at 7 am
1 hour journey
Reached Q at 8 am
At Q buses available timings are 5 am, 7am, 9 am ..
Person started at Q at 9 am
1 hour journey reached P at 10 am.
Buses timings at P are 8 am, 9:30am, 11 am, 12:30 pm...
Person started at P at 11 am
1 hour journey
Reached S at 12 noon.
Buses timings at S are
8am, 8:45 am, 9:30 am, 10:15 am, 11am, 11:45 am, 12:30pm ....
Person started at S at 12:30 pm
1 hour journey
Reached R at 1:30 pm
Minimum Total time = 1:30 pm - 7 am
= 6 hrs 30 min
 Question 3
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?
 A $f(2,2)=g(2,2)$ B $f(g(2,2),2) \lt f(2,g(2,2))$ C $g(2,1) \neq f(2,1)$ D $f(3,2) \gt g(3,2)$
GATE ME 2022 SET-2      Numerical Ability
Question 3 Explanation:
f(2,2) = 2 x 2 = 4
g(2,2) = 4
f(2,2) = g(2,2)
 Question 4
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?
 A 18 B 10 C 7 D 5
GATE ME 2022 SET-2      Numerical Ability
Question 4 Explanation:
Total production = Average x No. of days
P= 100 m
and
P + 180 = 110 (m+1)
Solving, m = 7
 Question 5
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?
 A Having ultra-black skin is only advantageous to species S B Species S with lower collagen in their skin are at an advantage because it helps them avoid predators C Having ultra-black skin has both advantages and disadvantages to species S D Having ultra-black skin is only disadvantageous to species S but advantageous only to their predators
GATE ME 2022 SET-2      Verbal Ability
Question 5 Explanation:
Ultra-black skin advantages that avoids predators and attacks their prey.
Ultra-black skin disadvantage is that the skin is more fragile means easily broken or destroyed.
 Question 6

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 A B B C C D D
GATE ME 2022 SET-2      Numerical Ability
Question 6 Explanation:
Priority: Shape, position and size.
As per size point of view parallelogram is not suitable.
 Question 7
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?
 A The 2nd February of that year is a Tuesday B There will be five Sundays in the month of February in that year C The 1st February of that year is a Sunday D All Mondays of February in that year have even dates
GATE ME 2022 SET-2      Verbal Ability
Question 7 Explanation:
February month have 5 Mondays.
February - 29 days = 4 weeks 1 day -> Monday
29th Feb is Monday
1st | 8th | 15th | 22nd | 29th Feb is Mondays.
So, 2nd Feb is Tuesday.
 Question 8
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?
 A $\frac{1}{2}$ B $1$ C $2$ D $4$
GATE ME 2022 SET-2      Numerical Ability
Question 8 Explanation:
\begin{aligned} f(x)&=2 \ln ( \sqrt{e^x})\\ &=2 \ln (e^{x/2})=2 \log _e e^{x/2}\\ f(x)&=2\left ( \frac{x}{2} \right )=x \end{aligned}

Area =(1/2) x 2 x 2=2
 Question 9
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?

 A A B B C C D D
GATE ME 2022 SET-2      Numerical Ability
Question 9 Explanation:
\begin{aligned} 2-5x \leq -\frac{6x-5}{3}\\ 1-9x\leq 0\\ \Rightarrow 1\leq 9x\Rightarrow x\geq \frac{1}{9} \end{aligned}
 Question 10
Writing too many things on the ________ while teaching could make the students get _________.
 A bored / board B board / bored C board / board D bored / bored
GATE ME 2022 SET-2      Verbal Ability
Question 10 Explanation:
Board means a surface, frame, or device for posing notices or writing on the blackboard. Bored means filled with or characterized by boredom.

There are 10 questions to complete.