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?

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

2:3 | |

1:1 | |

3:2 | |

2:1 |

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?

6 hours 30 minutes | |

3 hours 45 minutes | |

4 hours 30 minutes | |

5 hours 15 minutes |

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

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?

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?

f(2,2)=g(2,2) | |

f(g(2,2),2) \lt f(2,g(2,2)) | |

g(2,1) \neq f(2,1) | |

f(3,2) \gt g(3,2) |

Question 3 Explanation:

f(2,2) = 2 x 2 = 4

g(2,2) = 4

f(2,2) = g(2,2)

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?

If today's production of 180 units changes the average to 110 units per day, what is the value of m?

18 | |

10 | |

7 | |

5 |

Question 4 Explanation:

Total production = Average x No. of days

P= 100 m

and

P + 180 = 110 (m+1)

Solving, m = 7

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?

Which one of the following is the CORRECT logical inference based on the information in the above passage?

Having ultra-black skin is only advantageous to species S | |

Species S with lower collagen in their skin are at an advantage because it helps them avoid predators | |

Having ultra-black skin has both advantages and disadvantages to species S | |

Having ultra-black skin is only disadvantageous to species S but advantageous only to their predators |

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.

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 | |

B | |

C | |

D |

Question 6 Explanation:

Priority: Shape, position and size.

As per size point of view parallelogram is not suitable.

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?

Which one of the following statements is correct based on the above information?

The 2nd February of that year is a Tuesday | |

There will be five Sundays in the month of February in that year | |

The 1st February of that year is a Sunday | |

All Mondays of February in that year have even dates |

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.

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?

\frac{1}{2} | |

1 | |

2 | |

4 |

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

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 | |

B | |

C | |

D |

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 _________.

bored / board | |

board / bored | |

board / board | |

bored / bored |

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.