IBA ফ্যাকাল্টি ভিত্তিক প্রস্তুতি

Question: Today is Wednesday. After 45 days, it will be:

Solution:
We know that each day of the week is repeated after 7 days.

45 ÷ 7 = 6 (remainder 3)

So, after (7 × 6) = 42 days it will be Wednesday.
∴ after 45 days it will be (Wednesday + 3 days) = Saturday

Question: Which of the following is not a leap year?

Solution:
A leap year is divisible by 4.

Here, 
2008 ÷ 4 = 502, divisible by 4 , so leap year.
2012 ÷ 4 = 503, divisible by 4 , so leap year.
2020 ÷ 4 = 505, divisible by 4 , so leap year.
2022 ÷ 4 = 505, remainder 2, so not leap year.

Question: If cotθ = 5/12, then secθ = ?

Solution:
এখানে,
cotθ = 5/12 = ভূমি/লম্ব

∴ ভূমি = 5, লম্ব= 12
∴ অতিভুজ = √(5²+ 12²)
= √169 = 13

∴ secθ = অতিভুজ/ভূমি
= 13/5

Question: If the day before yesterday was Thursday, when will Sunday be?

Solution:
Day before yesterday was Thursday
⇒ Yesterday was a Friday
⇒ Today is a Saturday
⇒ Tomorrow is a Sunday

Question: What will come at the place of question mark?
4, 7, 12, 19, 28, ?

Solution:
7 - 4 = 3
12 - 7 =5
19 - 12 = 7
28 - 19 = 9

Difference increases by 2 each time.

So, next difference is = 9 + 2 = 11

∴ Next term = 28 + 11 = 39

Question: If tan(θ + 30°) = √3, then what is the value of cosθ?

Solution:
Given that,
tan(θ + 30°) = √3
⇒ tan(θ + 30°) = tan60°
⇒ (θ + 30°) = 60°
∴  θ = 30°

Now,
cosθ
= cos30°
= √3/2

Question: A clock is started at noon. By 20 minutes past 4, through how many degrees has the hour hand turned?

From noon (12.00 pm) to 4 pm = 4 hours
and 20 minutes = 20/60 hours = 1/3 hours

Total time = (4 + 1/3) = 13/3 hours

We know,
Angle traced by hour hand in 12 hours =  360°

∴ Angle in 13/3 hours,
= (360/12) × (13/3)
= 130°

Question: What will come at the place of question mark ?
9, 17, 33, 65, ?

Solution:
Here,
First term = 9
Second term = (9 × 2 -1) = 17
Third term = (17 × 2 -1) = 33
Fourth term = (33 × 2 -1) = 65
∴ Fifth term = (65 × 2 -1) = 129

Question: If tanθ = 1, then the the value of

Solution:
Given, 
tanθ = 1
⇒ tanθ = tan45°
∴ θ = 45°

Now,

Question: In a code, "STONE" is written as 12345 and "FLAME" is written as 67895. How is "FLOAT" written in the same code?

Solution:
STONE is written as 12345
S = 1
T = 2
O = 3
N = 4
E = 5

FLAME is written as 67895
F = 6
L = 7
A = 8
M = 9
E = 5

So, FLOAT will be 
F = 6
L = 7
O = 3
A = 8
T = 2

∴ FLOAT = 67382

Question: If tanθ = 4/3, then what is the value of (3sinθ + 2cosθ)/(3sinθ - 2cosθ)?

Solution: 
Given,
tanθ = 4/3

Now,

Question: Anika is taller than Bristi but shorter than Kabir. Rafi is shorter than Bristi. Shawon is taller than Anika but shorter than Kabir. Who is the tallest among them?

Solution: 
From the first statement:
Kabir > Anika > Bristi

From the second statement:
Bristi > Rafi

From the third statement:
Kabir > Shawon > Anika

Putting everything together:
Kabir > Shawon > Anika > Bristi > Rafi

∴ Kabir is the tallest.

Question: If tanθ =√3 and sinθ = √3/2. Find the value of cosθ.

Solution:
Given,
tanθ =√3 and sinθ = √3/2

We know,
tanθ = sinθ/cosθ
⇒√3 = (√3/2)/cosθ
⇒ cosθ = (√3/2)/√3
∴ cosθ = 1/2   

Question: A 50-meter cable is attached from the top of a vertical pole down to the ground. If the cable makes an angle of 30 degrees with the ground, find the height of the pole.

Solution: 

ধরি,
উচ্চতা(Height), AB = h

দেয়া আছে,
AC = 50m                    
∠ACB = 30°

∴ sin30°= AB/AC
⇒ 1/2 = h/50
⇒ h = 50 × 1/2
∴ h = 25 m

Question: At what angle the hands of a clock are inclined at 10 minutes past 4?

Solution:
Hours hand moves in 10 past 4 from 12 pm = (4 + 10/60) hour
= 4 + 1/6 
= 25/6 hour

We know,
Angle traced by hours hand in 12 hours =  360°

∴ Angle of hours hand in 25/6 hour,
= (360 × 25)/(12 ×6)
= 125°

Again,
Angle traced by Minutes hand in 60 min =  360°

∴ Angle of minutes hand in 10 min,
= (360 × 10)/60
= 60°

∴ Angle between hours and minutes hand  = (125° - 60°)
= 65°

Question: Four boys are sitting on a bench to be photographed. Amin is to the left of Bilal. Rafi is to the right of Bilal. Tariq is between Bilal and Rafi. Who would be third from the left in the photograph?

solution:
Amin is to the left of Bilal
→ Amin — Bilal

Rafi is to the right of Bilal
→ Bilal — Rafi

Tariq is between Bilal and Rafi
→ Bilal — Tariq — Rafi

Now place all four:
Amin — Bilal — Tariq — Rafi

∴ Tariq would be third from the left in the photograph.

Question: An observer 1.5 m tall stands 10√3 meters away from a flagpole. The angle of elevation from his eye to the top of the flagpole is 30°. What is the height of the flagpole?

Solution:

Here,
Flagpole Height = AB

Now,
tan∠c = AE/CE
⇒ tan30° = AE/10√3
⇒ 1/√3 = AE/10√3 
∴ AE = 10

∴ AB = AE + BE 
= 10 + 1.5
= 11.5 m