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মোট প্রশ্ন১৬,১২৪এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
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উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Bank Math

PrepBank · পাতা ৪২ / ১৬১ · ৪,১০১–৪,২০০ / ১৬,১২৪

৪,১০১.
What is the probability of getting a sum of 9 when a die is thrown twice?
  1. ক
    1
  2. খ
    1/36
  3. গ
    6/7
  4. ঘ
    1/9
ব্যাখ্যা

Question: What is the probability of getting a sum of 9 when a die is thrown twice?

Solution: 
In two throws of a dice, n(S) = (6 x 6) = 36
Let E = the event of getting a sum
= {(3, 6), (4, 5), (5, 4), (6, 3)}
∴ n(E) = 4

Hence, P(E) = n(E)/n(S)
= 4/36
= 1/9

৪,১০২.
If a car travels 20 meters in a second, what is it speed (in kilometer) per hour?
  1. ক
    72 km/hr
  2. খ
    66 km/hr
  3. গ
    88 km/hr
  4. ঘ
    60 km/hr
ব্যাখ্যা
Question: If a car travels 20 meters in a second, what is it speed (in kilometer) per hour?

Solution: 
speed = 20 meters/second
= (20 /1000) km/second [1km = 1000m]
= 1/50 km/second
= (3600/50) km/hr [1 hour = 3600 second]
= 72 km/hr
৪,১০৩.
  1. ক
    ক) 12°
  2. খ
    খ) 18°
  3. গ
    গ) 30°
  4. ঘ
    ঘ) 42°
ব্যাখ্যা
Question:

Solution:
Given,
sin(A + 18°) = 1/2
⇒ sin(A + 18°) = sin30°
⇒ A + 18° = 30°
⇒ A = 30° - 18°
∴ A = 12° 
৪,১০৪.
Ashim bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit? 
  1. ক
    20%
  2. খ
    25%
  3. গ
    30%
  4. ঘ
    40%
ব্যাখ্যা
Question: Ashim bought 5 apples at taka 10 and sold 4 apples at taka 10. What will be the rate of profit? 

Solution: 
5টি আপেলের ক্রয়মূল্য 10 টাকা 
1টি আপেলের ক্রয়মূল্য 10/5 টাকা 
= 2 টাকা 

4টি আপেলের বিক্রয়মূল্য 10 টাকা 
1টি আপেলের বিক্রয়মূল্য 10/4 টাকা 
= 2.5 টাকা 
লাভ = (2.5 - 2)টাকা  = 0.5 টাকা 

শতকরা লাভ = {(0.5/2) × 100}%
= 25%
৪,১০৫.
If tanθ = 1 then sinθ - cos(- θ) = ?
  1. ক
    - 1
  2. খ
    0
  3. গ
    1
  4. ঘ
    2
ব্যাখ্যা
Question: If tanθ = 1 then sinθ - cos(- θ) = ?

Solution:
Given, 
tanθ = 1
⇒ sinθ/cosθ = 1
⇒ sinθ = cosθ

∴ sinθ - cos(- θ)
= sinθ - cosθ
= cosθ - cosθ
= 0
৪,১০৬.
There are 10 true-false questions in an examination, these questions can be answered in-
  1. ক
    898 ways
  2. খ
    2024 ways
  3. গ
    720 ways
  4. ঘ
    1028 ways
  5. ঙ
    1024 ways
ব্যাখ্যা

Question: There are 10 true-false questions in an examination, these questions can be answered in-
(পরীক্ষায় ১০টি সত্য-মিথ্যা প্রশ্ন আছে, এই প্রশ্নগুলোর উত্তর দেওয়া যেতে পারে কত উপায়ে?)

Solution: 
Total number of question = 10 
Each question has 2 answer.

∴ These question can be answered in 210 ways = 1024 ways

৪,১০৭.
30% of 80% of 5/2 is -
  1. ক
    ক) 6/11
  2. খ
    খ) 2/5
  3. গ
    গ) 5/3
  4. ঘ
    ঘ) 3/5
ব্যাখ্যা
Question: 30% of 80% of 5/2 is -

Solution:
80% of 5/2 is = 5/2 × 80% 
= 5/2 × 8/10
= 2

30% of 2 is = 2 × 30%
= 2 × 3/10
= 3/5
৪,১০৮.
Rafiul has more marbles than Roman and they have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.
  1. ক
    36, 9
  2. খ
    35, 10
  3. গ
    37, 8
  4. ঘ
    34, 11
ব্যাখ্যা
Question: Rafiul has more marbles than Roman and they have 45 marbles together. After losing 5 marbles each, the product of the number of marbles they both have now is 124. How to find out how many marbles they had to start with.

Solution:
Let
The number of marbles Rafiul had be x.
Then the number of marbles Roman had = 45 - x.

The number of marbles left with Rafiul after losing 5 marbles = x - 5
The number of marbles left with Roman after losing 5 marbles = 45 - x - 5 = 40 - x

ATQ,
(x - 5) (40 - x) = 124
⇒ 40x - x2 - 200 + 5x = 124
⇒ - x2 + 45x - 200 = 124
⇒ x2 - 45x + 324 = 0
⇒ x2 - 36x - 9x + 324 = 0
⇒ x(x - 36) - 9(x - 36) = 0
⇒ (x - 36)(x - 9) = 0
∴ x = 36 and x = 9

So, the number of marbles Rahul had is 36 and Rohan had is 9.
৪,১০৯.
The 2nd and 6th term of an arithmetic progression are 8 and 20 respectively. What is the 20th term?
  1. ক
    ক) 56
  2. খ
    খ) 59
  3. গ
    গ) 62
  4. ঘ
    ঘ) 65
ব্যাখ্যা
Question: The 2nd and 6th term of an arithmetic progression are 8 and 20 respectively. What is the 20th term?

Solution:
2nd term, T2 = a + d = 8....... (1)
6th term, T6 = a + (6 - 1)d
Or, a + 5d = 20...... (2)

Subtract (1) from (2) we get,
4d = 12
∴ d = 3

From (1)
a + 3 = 8
∴ a = 5

20th term = a + (20 - 1)d
 = a + 19d
= 5 + (19 × 3)
= 62
৪,১১০.
A rectangular plot measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of the fence are kept 5 meters apart, how many poles will be needed?
  1. ক
    ক) 55
  2. খ
    খ) 56
  3. গ
    গ) 57
  4. ঘ
    ঘ) 58
ব্যাখ্যা

perimeter of the plot = 2(90+50) = 280m
number of poles =280/5 = 56m

৪,১১১.
The speed of A and B are in the ratio 3 : 4. A takes 15 minutes more than B to reach a destination. Time in which A reach the destination?
  1. ক
    ক) 1 hour
  2. খ
    খ) 2 hours
  3. গ
    গ) 1.5 hours
  4. ঘ
    ঘ) 2.5 hours
ব্যাখ্যা
Question: The speed of A and B are in the ratio 3 : 4. A takes 15 minutes more than B to reach a destination. Time in which A reach the destination?

Solution: 
Ratio of speed = 3 : 4
Ratio of time taken = 4 : 3 

Let time taken by A and B be 4x and 3x hour respectively.

Now 
4x - 3x = 15/60
x = 1/4

Hence, time taken by A = 4x hours
= 4 × 1/4
 = 1 hour
৪,১১২.
A cake is divided into 27 pieces. If Saiful takes 1/3 of the cake and Mahin takes 1/3 of the rest that are left, how many pieces are still left?
  1. ক
    15 pieces
  2. খ
    12 pieces
  3. গ
    10 pieces
  4. ঘ
    9 pieces
ব্যাখ্যা
Question: A cake is divided into 27 pieces. If Saiful takes 1/3 of the cake and Mahin takes 1/3 of the rest that are left, how many pieces are still left?

Solution:
Saiful takes 1/3 of cake
Left after Saiful takes = (1 - 1/3) of cake
= 2/3 of cake

Mahin takes = (2/3) × (1/3)
= 2/9 of cake
Saiful and Mahin takes = (1/3 + 2/9) = (3 + 2) / 9 = 5/9 of cake

Left after both take = (1 - 5/9)
= 4/9 of cake

Full cake divided into 27 pieces
∴ 4/9 of cake divided into = (27 × 4)/9 pieces
= 12 pieces
৪,১১৩.
The angle of elevation of a ladder leaning against a wall is 60° and the foot of the ladder is 4.6 m away from the wall. The length of the ladder is -
  1. ক
    ক) 9.2 m
  2. খ
    খ) 8.7 m
  3. গ
    গ) 7.2 m
  4. ঘ
    ঘ) 6.5 m
ব্যাখ্যা


ধরি,
AB হচ্ছে দেয়াল এবং BC হচ্ছে মই।
এখানে ∠ACB = 60° এবং AC = 4.6 মিটার
তাহলে, AC/BC = cos 60° = 1/2 [ যেহেতু, cosθ = ভূমি/অতিভুজ]
⇒ BC = 2 × AC
∴ BC = 2 × 4.6
= 9.2m

৪,১১৪.
In how many years will Tk. 4000 amounts to Tk. 5324 at 10% per annum compound interest?
  1. ক
    3 years
  2. খ
    2.5 years
  3. গ
    4 years
  4. ঘ
    2 years
ব্যাখ্যা
Question: In how many years will Tk. 4000 amounts to Tk. 5324 at 10% per annum compound interest?

Solution:
Given,
P = Tk. 4000
Compound amount = Tk. 5324
Rate r = 10% = 1/10

We know,
Compound amount = P(1 + r)n
⇒ 5324 = 4000(1 + 1/10)n
⇒ 5324/4000 = (11/10)n
⇒ 1331/1000 = (11/10)n
⇒ (11/10)3 = (11/10)n
∴ n = 3
৪,১১৫.
In a party every person shakes hands with every other person. If there are 55 hands shakes, find the number of person in the party.
  1. ক
    ক) 10
  2. খ
    খ) 11
  3. গ
    গ) 12
  4. ঘ
    ঘ) 13
ব্যাখ্যা
Question: In a party every person shakes hands with every other person. If there are 55 hands shakes, find the number of person in the party.

Solution:
Let n be the number of persons in the party
Total number of hands shake is given by nC2

so,
nC2 = 55
⇒ n!/2! (n - 2)! = 55
⇒ n(n - 1)/2 = 55
⇒ n2 - n = 110
⇒ n2 - n - 110 = 0
⇒ n2 - 11n + 10n - 110 = 0
⇒ n(n - 11) + 10(n - 11) = 0
⇒ (n - 11) (n + 10) = 0

∴ n + 10 = 0
n = - 10, not possible
∴ n - 11 = 0
n = 11

so, there are 11 persons.
৪,১১৬.
m, n, o are natural numbers. If m> n> o then which of the following is not true?
  1. ক
    mno > 0
  2. খ
    mn - o > 0
  3. গ
    n - mo > 0
  4. ঘ
    None
ব্যাখ্যা
Question: m, n, o are natural numbers. If m> n> o then which of the following is not true?

Solution: let, m = 4, n = 3, o = 2
a) mno = 4 × 3 × 2 = 24>0
b) mn - o = 4 × 3 - 2 = 12 - 2 = 10 > 0
c) n - mo = 3 - 4 × 2 = 3 - 8 = -5 < 0
৪,১১৭.
A person crosses a 1200 m long street in 10 minutes. What is his speed in km per hour?
  1. ক
    3.6 km/hr
  2. খ
    7.2 km/hr
  3. গ
    8.4 km/hr
  4. ঘ
    10 km/hr
ব্যাখ্যা
Question: A person crosses a 1200 m long street in 10 minutes. What is his speed in km per hour?

Solution:
Speed = 1200 meters/10 minutes
= (1200 × 60)/(10× 1000) km/hr
= 7.2 km/hr
৪,১১৮.
A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?
  1. ক
    11236 cabbages
  2. খ
    11025 cabbages
  3. গ
    10582 cabbages
  4. ঘ
    10644 cabbages
  5. ঙ
    None
ব্যাখ্যা
Question: A lady grows cabbages in her garden that is in the shape of a square. Each cabbage takes 1 square feet of area in her garden. This year, she has increased her output by 211 cabbages as compared to last year. The shape of the area used for growing the cabbages has remained a square in both these years. How many cabbages did she produce this year?

Solution:
Let,
the side of the square area used for growing cabbages this year = X ft.
∴ the area of the ground used for cultivation this year = X2 sq. ft.

and
the side of the square area used for growing cabbages last year be Y ft.
∴ the area of the ground used for cultivation last year = Y2 sq. ft.

The cabbage field remained square-shaped in both years.
Given the increase of 211 cabbages (1 sq ft per cabbage),
∴ the area difference is: X2 - Y2 = 211
⇒ (X + Y)(X - Y) = 211

Since 211 is prime, the only factor pair is (211, 1), so:
X + Y = 211
X - Y = 1
→ Solving gives: X = 106 and Y = 105

This year's production = 1062 = 11236 cabbages
৪,১১৯.
A tank can be filled by a tap in 20 minutes and by another tap in 60minutes. Both the taps are kept open for 10 minutes and the first tap is shut off. After this, the tank will be completely filled what time? 
  1. ক
    ক) 10 minutes
  2. খ
    খ) 15 minutes
  3. গ
    গ) 30 minutes
  4. ঘ
    ঘ) 20 minutes
ব্যাখ্যা
Question: A tank can be filled by a tap in 20 minutes and by another tap in 60minutes. Both the taps are kept open for 10 minutes and the first tap is shut off. After this, the tank will be completely filled what time? 

Solution: 
Part of the tank filled by both the taps in 1 minutes = (1/20)​ + (1/60​) = (3 + 1​)/60 = 1/15
Part of the tank filled by both the taps in 10 minutes =10(1/15) = 2/3
Remaining part =1- (2/3) =1/3

1​/60  part of the tank is filled by the second pipe in 1 min.
∴1/3 of the tank will be filled by the second pipe in (60 × 1​)/3= 20 min.
৪,১২০.
6 years ago, the ratio of the ages of Kamal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?
  1. ক
    16 years
  2. খ
    18 years
  3. গ
    20 years
  4. ঘ
    Cannot be determined
ব্যাখ্যা
Question: 6 years ago, the ratio of the ages of Kamal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

Solution:
Let the ages of Kamal and Sagar 6 years ago be 6x and 5x years
Then,
(6x + 6 + 4)/(5x + 6 + 4) = 11/10
⇒ (6x + 10)/(5x + 10) = 11/10
⇒ 10(6x + 10) = 11(5x + 10)
⇒ 60x + 100 = 55x + 110
⇒ 5x = 10
∴ x = 2

Sagar's present age
= (5x + 6) years
= (5 × 2 + 6) years
= 16 years
৪,১২১.
How many integers from 1 to 1000 are divisible by 30 but not by 16?
  1. ক
    ক) 29
  2. খ
    খ) 31
  3. গ
    গ) 32
  4. ঘ
    ঘ) 38
ব্যাখ্যা

এখানে,
30 দ্বারা বিভাজ্য সংখ্যা = 1000/30
ভাগফল 33 এবং ভাগশেষ 10
সুতরাং 30 দ্বারা বিভাজ্য সংখ্যা = 33 টি
30 ও 16 এর ল, সা, গু = 240
এখন 1000/240 =
ভাগফল 4 এবং ভাগশেষ 40
∴ 30 ও 16 দ্বারা বিভাজ্য সংখ্যা = 4 টি
সুতরাং, (33 - 4) = 29 টি সংখ্যা 30 দ্বারা বিভাজ্য কিন্তু 16 দ্বারা বিভাজ্য নয়।

৪,১২২.
What is the median of the modes in the dataset {-5, 4, 3, 7, 2, 1, 3, 4, 5,-1, 7, 8, -4, 2, 6}?
  1. ক
    3.5
  2. খ
    3
  3. গ
    4
  4. ঘ
    5.5
ব্যাখ্যা
Question: What is the median of the modes in the dataset {- 5, 4, 3, 7, 2, 1, 3, 4, 5,- 1, 7, 8, - 4, 2, 6}?

Solution: 
The given dataset, when arranged in order, is:
- 5, - 4, -1, 1, 2, 2, 3, 3, 4, 4, 5, 6, 7, 7, 8

The numbers 2, 3, 4, and 7 each appear twice.
The frequencies are: 2, 3, 4, 7

Here,
n = 4
The median = {(4/2)th term and ((4/2) + 1)th term} / 2
= {2nd and 3rd terms added together}/2
= (3 + 4)/2
= 3.5
৪,১২৩.
A man can do 1 work in 8 hours. How many work he can do at 40 hours?
  1. ক
    ক) 2
  2. খ
    খ) 4
  3. গ
    গ) 5
  4. ঘ
    ঘ) 7
ব্যাখ্যা
Question: A man can do 1 work in 8 hours. How many work he can do at 40 hours?

Solution: 
In 8 hours 1 work is done
In 1 hour 1/8 work is done
∴ In 40 hours 40/8 work = 5 work can be done 
৪,১২৪.
The volume of a sphere with radius r is (4/3)πr3 and the surface area is 4πr2. If a spherical ball has a surface area of 324π square centimeters. Find its volume.
  1. ক
    792π cm2
  2. খ
    925π cm3
  3. গ
    972π cm3
  4. ঘ
    520π cm2
  5. ঙ
    None of these
ব্যাখ্যা
Question: The volume of a sphere with radius r is (4/3)πr3 and the surface area is 4πr2. If a spherical ball has a surface area of 324π square centimeters. Find its volume.

Solution:
surface area = 4πr2

ATQ,
⇒ 4πr2 = 324π
⇒ r2 = 324π/4π
⇒ r2 = 81 = 92
∴ r = 9

Now,
volume = (4/3)πr3 
= (4/3)π × (9)3
= (4/3)π × 729
= 972π

So, the surface volume would be 972π cm3
৪,১২৫.
A and B invest in a business in the ratio of 2 : 3. If 10% of the total profit goes to charity and A's share is Tk. 684, What is the total profit?
  1. ক
    ক) Tk. 1700
  2. খ
    খ) Tk. 1710
  3. গ
    গ) Tk. 1850
  4. ঘ
    ঘ) Tk. 1900
ব্যাখ্যা
Question: A and B invest in a business in the ratio of 2:3. If 10% of the total profit goes to charity and A's share is Tk. 684, What is the total profit?   

Solution: 
Let the total profit be Tk. 100
After paying 10% to charity, A's share = (90 × 2)/5 = Tk.36 
If A's share is Tk.36 then total profit = Tk. 100
If A's share is Tk. 1 then total profit = Tk. 100/36
If A's share is Tk. 684 then total profit = (100 × 684)/36 = Tk. 1900
৪,১২৬.
A team of 4 men and 3 women is to be formed from 6 men and 5 women. In how many ways can the team be formed?
  1. ক
    120 ways
  2. খ
    150 ways
  3. গ
    180 ways
  4. ঘ
    210 ways
ব্যাখ্যা

Question: A team of 4 men and 3 women is to be formed from 6 men and 5 women. In how many ways can the team be formed?

Solution:
We have 6 men and 5 women.
We need to choose 4 men from 6 and 3 women from 5.

Number of ways to choose 4 men from 6:
6C4 = 6!/(4!(6 - 4)!) 
= (6 × 5)/(2 × 1)
= 15

Number of ways to choose 3 women from 5:
5C3 = 5!/(3!(5 - 3)!)
= (5 × 4)/(2 × 1)
= 10

Total number of ways to form the team = 15 × 10 = 150

Therefore, the team can be formed in 150 different ways.

৪,১২৭.
In an examination, 32% is the pass mark. If an examinee gets 14 marks and fails by 10 marks, what is the maximum mark?
  1. ক
    60
  2. খ
    65
  3. গ
    70
  4. ঘ
    75
ব্যাখ্যা

Question: In an examination, 32% is the pass mark. If an examinee gets 14 marks and fails by 10 marks, what is the maximum mark?

Solution: 
If the candidate fails by 10 marks, it means the pass marks = 14 + 10
= 24

Let the maximum marks be x

ATQ,
32% of x = 24
⇒ x × (32/100) = 24
⇒ 32x = 2400
⇒ x = 2400/32
⇒ x = 75

৪,১২৮.
What is the ratio of the areas of two squares if one has its diagonal double than the other?
  1. ক
    ক) 4 : 1
  2. খ
    খ) 2 : 1
  3. গ
    গ) 8 : 1
  4. ঘ
    ঘ) 16 : 1
ব্যাখ্যা
Question: What is the ratio of the areas of two squares if one has its diagonal double than the other?

Solution:
Let the diagonal of two squares be 2x and x respectively

length of first square = 2x/√2 = √2x
length of second square = x/√2 = x/√2

Ratio = (√2x)2 : (x/√2)2
= 2x2 : x2/2
= 2 : 1/2
= 4 : 1
৪,১২৯.
X buys a product for Tk. 400 and sells it to Y at a profit of 30%. Y then sells it to Z at a profit of 15%. How much does Z pay to Y?
  1. ক
    Tk. 698
  2. খ
    Tk. 588
  3. গ
    Tk. 620
  4. ঘ
    Tk. 598
ব্যাখ্যা

Question: X buys a product for Tk. 400 and sells it to Y at a profit of 30%. Y then sells it to Z at a profit of 15%. How much does Z pay to Y?

সমাধান:
X এর 30% লাভে বিক্রয়মূল্য = 400 + 400 এর 30%
= 400 + (400 × 30/100)
= 400 + 120
= 520

X এর বিক্রয়মূল্য = Y এর ক্রয়মূল্য

Y এর 15% লাভে বিক্রয়মূল্য = 520 + 520 এর 15%
= 520 + (520 × 15/100)
= 520 + 78
= 598

সুতরাং, Y এর বিক্রয়মূল্য = Z এর ক্রয়মূল্য = Tk. 598

৪,১৩০.
The area of a rectangle is 40cm2 and one of its sides is 8cm long. What will be its perimeter?
  1. ক
    ক) 26 cm
  2. খ
    খ) 13 cm
  3. গ
    গ) 28 cm
  4. ঘ
    ঘ) 20 cm
ব্যাখ্যা
দেয়া আছে,
আয়তক্ষেত্রের ক্ষেত্রফল 40 বর্গ  সে.মি.
আয়তক্ষেত্রের এক পাশের দৈর্ঘ্য 8 সে.মি.
আয়তক্ষেত্রের অপর পাশের দৈর্ঘ্য 40/8 সে.মি.
                                                     =5 সে.মি.

আয়তক্ষেত্রের পরিসীমা = 2 (8 + 5) সে.মি.
                                     = 26 সে.মি.
৪,১৩১.
A Hudi is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?
  1. ক
    loss 5.25%
  2. খ
    profit 5.25%
  3. গ
    profit 6.25%
  4. ঘ
    loss 6.25%
ব্যাখ্যা
Question: A Hudi is sold for Tk. 2400 at a profit of 25%. What would have been the actual profit or loss if it had been sold at Tk. 1800?

Solution:
Firstly let us find the cost price of the same. C.P. = 2400 × (100/125) = 1920.
New selling price = 1800
Loss = 1920 - 1800 = 120

∴ Loss percentage = 100 × (120/1920)
= 6.25%.
৪,১৩২.
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is :
  1. ক
    ক) 35
  2. খ
    খ) 40
  3. গ
    গ) 50
  4. ঘ
    ঘ) None
ব্যাখ্যা
প্রশ্ন: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is :

সমাধান:
৩ বছর পূর্বে স্বামী, স্ত্রী ও সন্তানের বয়সের গড় = 27 বছর 
৩ বছর পূর্বে স্বামী, স্ত্রী ও সন্তানের বয়সের সমষ্টি = 27 × 3 বছর 
= 81 বছর 

 স্বামী, স্ত্রী ও সন্তানের বর্তমান বয়সের সমষ্টি = 81 + (3 × 3) = 81 + 9 = 90 বছর 

৫ বছর পূর্বে  স্ত্রী ও সন্তানের বয়সের গড় = 20 বছর 
৫ বছর পূর্বে  স্ত্রী ও সন্তানের বয়সের সমষ্টি = 20 × 2 বছর = 40 বছর

 স্ত্রী ও সন্তানের বর্তমান বয়সের সমষ্টি = 40 + (2 × 5) = 50 বছর

স্বামীর বর্তমান বয়স = (90 - 50)বছর = 40 বছর 
৪,১৩৩.
In a simultaneous throw of two coins, the probability of getting at least one head is-
  1. ক
    1/3
  2. খ
    4/5
  3. গ
    1/2
  4. ঘ
    3/4
ব্যাখ্যা
Question: In a simultaneous throw of two coins, the probability of getting at least one head is-

Solution:
Here,
S = {HH, HT, TH, TT}

Let,
E = event of getting at least one head = {HT, TH, HH}

∴ P(E) = n(E)/n(S)
= 3/4
৪,১৩৪.
5 mat-weavers can weave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-wevers in 10 days?
  1. ক
    18 mats
  2. খ
    20 mats
  3. গ
    22 mats
  4. ঘ
    24 mats
ব্যাখ্যা
Question: 5 mat-weavers can weave 5 mats in 5 days. At the same rate, how many mats would be woven by 10 mat-wevers in 10 days?

Solution:
5 mat-weavers in 5 days weave = 5 mats
∴ 1 mat-weavers in 1 days weave = 5/(5 × 5) mats
∴ 10 mat-weavers in 10 days weave = (5 × 10 × 10)/(5 × 5) mats
= 20 mats
৪,১৩৫.
If two men or four women or six boys can finish a job in 72 days, then find out the number of days in which that work can be done by one man, two women, and three boys?
  1. ক
    48 days
  2. খ
    38 days
  3. গ
    58 days
  4. ঘ
    28 days
ব্যাখ্যা

Question: If two men or four women or six boys can finish a job in 72 days, then find out the number of days in which that work can be done by one man, two women, and three boys?

Solution:
Given,
2 men = 4 women = 6 boys
1 man = 2 women = 3 boys
∴ 1 man + 2 women + 3 boys = (1 + 1 + 1) men
= 3 men

Here,
2 men can do in = 72 days
∴ 1 men can do in = (72 × 2) days
= 144 days
∴ 3 men can do in = (144 ÷ 3) days
= 48 days

৪,১৩৬.
A train running at a certain speed crosses a 496-meter-long platform in 56 seconds. If the length of the train is 560 meters, how long will it take to cross a bridge that is 100 meters in length?
  1. ক
    21 seconds
  2. খ
    27 seconds
  3. গ
    28 seconds
  4. ঘ
    35 seconds
ব্যাখ্যা
Question: A train running at a certain speed crosses a 496-meter-long platform in 56 seconds. If the length of the train is 560 meters, how long will it take to cross a bridge that is 100 meters in length?

Solution:
We know,
When a train crosses any object, it covers a distance equal to the sum of the object's length and its own length.

So, when crossing a platform, the distance covered by the train = (496 + 560) meters = 1056 meters
And
when crossing a bridge, the distance covered by the train = (100 + 560) meters = 660 meters

Now,
The train covers 1056 meters in = 56 seconds
∴ It covers 1 meter in = (56/1056) seconds
∴ It covers 660 meters in = (56 × 660)/1056 seconds = 35 seconds
৪,১৩৭.
  1. ক
    47
  2. খ
    49
  3. গ
    51
  4. ঘ
    45
ব্যাখ্যা
Question:

Solution:
Given that,
x - 1/x = - √5
⇒ (x - 1/x)2 = (- √5)2
⇒ x2 + 1/x2 - 2 . x . (1/x) = 5
⇒ x2 + 1/x2 = 5 + 2
⇒ (x2 + 1/x2)2 = 7
⇒ (x2)2 + (1/x2)2 + 2 . x2 . (1/x2) = 49
⇒ x4 + 1/x4 = 49 - 2
∴ x4 + 1/x4 = 47
৪,১৩৮.
Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km?
  1. ক
    2 hours
  2. খ
    3 hours
  3. গ
    3.5 hours
  4. ঘ
    4 hours
ব্যাখ্যা
Question: Speed of a boat along and against the current are 14 kms/hr and 8 kms/hr respectively. If there is no current how much time will the boat take to travel 22km?

Solution:
Let,
Speed of the boat in still water = S km/h
Speed of the current = W km/h

According to the question,
S + W = 14  …… (i) (Downstream speed)
S − W = 8    …… (ii) (Upstream speed)

Adding equations (i) and (ii):
(S + W) + (S − W) = 14 + 8
⇒ 2S = 22
⇒ S = 11 km/h

So, the boat’s speed in still water is 11 km/h.

Time to travel 22 km in still water = Distance/Speed = 22 / 11 = 2 hours
৪,১৩৯.
A group of workers promise to complete a piece of work in 8 days, but 6 of them do not report for work. If it took the remaining workers 10 days to complete the work, then what was the number of workers originally hired? 
  1. ক
    ক) 25
  2. খ
    খ) 27
  3. গ
    গ) 30
  4. ঘ
    ঘ) 33
ব্যাখ্যা
Question: A group of workers promise to complete a piece of work in 8 days, but 6 of them do not report for work. If it took the remaining workers 10 days to complete the work, then what was the number of workers originally hired? 

Solution: 
Let, the workers promised were = x
The workers worked were = x - 6

[x জনের 8 দিনের করা কাজ = (x - 6) জনের 10 দিনে করা কাজের পরিমাণ একই] 
ATQ,
8x = 10x - 60 
⇒ 10x - 8x = 60
⇒ 2x = 60 
⇒ x = 60/2
∴ x = 30 

∴ The number of workers originally hired was 30
৪,১৪০.
If tanθ = 5/12, then cosecθ = ?
  1. ক
    17/13
  2. খ
    12/5
  3. গ
    12/13
  4. ঘ
    13/5
ব্যাখ্যা

Question: If tanθ = 5/12, then cosecθ = ?

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

∴ লম্ব = 5, ভূমি = 12

∴ অতিভুজ = √(52 + 122)
= √(25+144) = √169 = 13

∴ cosecθ
= অতিভুজ/লম্ব
= 13/5

৪,১৪১.
There are two stations of length 162 meters and 120 meter respectively. A train takes 18 seconds to pass first station and 15 seconds to pass another station. Determine the length of the train.
  1. ক
    ক) 90 m
  2. খ
    খ) 70 m
  3. গ
    গ) 100 m
  4. ঘ
    ঘ) 95 m
ব্যাখ্যা

Let length of the train be x m
Speed of train,
(x+162) / 18 = (x+120) / 15
∴ x = 90 m

৪,১৪২.
Over a span of 9 hours, a man traveled 61 km, part of it on foot at 4 km/hr and part by bike at 9 km/hr. What distance did he walk?
  1. ক
    20 km
  2. খ
    14 km
  3. গ
    16 km
  4. ঘ
    18 km
ব্যাখ্যা

Question: Over a span of 9 hours, a man traveled 61 km, part of it on foot at 4 km/hr and part by bike at 9 km/hr. What distance did he walk?

Solution:
Let the time in which he travelled on foot = x hr
Then the time in which he travelled on bicycle =(9 - x) hr
distance = speed × time
⇒ 4x + 9(9 - x) = 61
⇒ 4x + 81 - 9x = 61
⇒ 5x = 20
⇒ x = 4

∴ The distance travelled on foot = 4 × 4 = 16 km

৪,১৪৩.
On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. The divisor is -
  1. ক
    ক) 279
  2. খ
    খ) 229
  3. গ
    গ) 179
  4. ঘ
    ঘ) 169
ব্যাখ্যা
Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. The divisor is -

Solution: 
Divisor = (Dividend - Remainder)/ Quotient
= (15968 - 37)/89
= 15931/89
= 179
৪,১৪৪.
Which of the following is closest to the value of 999/{100 + (1/999)}?
  1. ক
    0.001
  2. খ
    0.01
  3. গ
    0.1
  4. ঘ
    1
  5. ঙ
    10
ব্যাখ্যা
Question: Which of the following is closest to the value of 999/{100 + (1/999)}?

Solution:
Since it is an approximation, we can say that 1/999 is so small (almost 0.001) that we can neglect the same.

What remains is the simple fraction of 999/100 = 9.99 ≈ 10
The closest answer is 10.
৪,১৪৫.
Suny borrows TK. 10000 for 2 years at 4% p.a. simple interest. He lends it to Maruf at 6% p.a. for 2 years. Find his gain in this transaction per year.
  1. ক
    ক) Tk. 400
  2. খ
    খ) Tk. 250
  3. গ
    গ) Tk. 150
  4. ঘ
    ঘ) Tk. 200
ব্যাখ্যা
Question: Suny borrows TK. 10000 for 2 years at 4% p.a. simple interest. He lends it to Maruf at 6% p.a. for 2 years. Find his gain in this transaction per year.

Solution: 
Interest which has to be paid by Suny = 10000 × 2 × (4/100) Taka
= 800 Taka 

Interest which has to be paid by Maruf = 10000 × 2 × (6/100) Taka
= 1200 Taka

So, gain for Suny after 2 years = 1200 - 800 Taka 
= 400 Taka 
∴ Suny's gain per year = 400/2 = 200 Taka 
৪,১৪৬.
If then what is the value of (3 - 2x) + (3 - 2x)2?
  1. ক
    3
  2. খ
    2
  3. গ
    1
  4. ঘ
    0
ব্যাখ্যা
Question: If  then what is the value of (3 - 2x) + (3 - 2x)2?

Solution:
√(3 - 2x) = 1
⇒ {√(3 - 2x)}2 = 12
⇒ 3 - 2x = 1

∴ (3 - 2x) + (3 - 2x)2 = 1 + 12 = 2
৪,১৪৭.
In a class of 50 students, 20 study History, 25 study Geography, and 10 study both subjects. How many students study neither subject? 
  1. ক
    12 students
  2. খ
    25 students
  3. গ
    15 students
  4. ঘ
    10 students
ব্যাখ্যা

Question: In a class of 50 students, 20 study History, 25 study Geography, and 10 study both subjects. How many students study neither subject?

Solution:
Given that,
Total students = 50
Study History = 20
Study Geography = 25
Study both = 10

Students studying at least one subject = H + G - Both
= 20 + 25 - 10
= 35

Therefore, Students who study neither subject = Total students - at least one subject
= 50 - 35 = 15

∴ 15 students study neither subject.

৪,১৪৮.
A system of equations is shown below:
X + 1= 6
X - m=5
X + p = 4
X - q = 3
What is the value of I+m+p+q?
  1. ক
    ক) 3
  2. খ
    খ) 2
  3. গ
    গ) 6
  4. ঘ
    ঘ) 5
ব্যাখ্যা
We can multiply equation 2 by -1 ad equation 4 by -1, and we have:
x + l = 6
-x + m =- 5
x + p = 4
-x + q = -3

Adding these equations together we have:
l + m + p + q = 2
৪,১৪৯.
Find the value of [2 - 3 × (2 - 3)- 1]- 1.
  1. ক
    1/5
  2. খ
    - 1/5
  3. গ
    5
  4. ঘ
    - 5
ব্যাখ্যা
Question: Find the value of [2 - 3 × (2 - 3)- 1]- 1.
 
Solution: 
[2 - 3 × (2 - 3)- 1]- 1
= [2 - 3 × (- 1)- 1]- 1
= [2 - 3 × (- 1)]- 1
= [2 + 3]- 1
= 5- 1
= 1/5 
৪,১৫০.
In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?
  1. ক
    24
  2. খ
    48
  3. গ
    64
  4. ঘ
    128
ব্যাখ্যা
Question: In an examination paper, there are two groups each containing 4 questions. A candidate is required to attempt 5 questions but not more than 3 questions from any group. In how many ways can 5 questions be selected?

Solution: 
5 questions can be selected in the following ways,
2 questions from the first group and 3 questions from the second group Or 3 questions from the first group and 2 questions from the second group.
= (4C2 × 4C3) + (4C3 × 4C2)
= 24 + 24
= 48
৪,১৫১.
A right triangle has sides 9 cm, 12 cm, and 15 cm. What is its area?
  1. ক
    24 cm2
  2. খ
    34 cm2
  3. গ
    54 cm2
  4. ঘ
    32 cm2
ব্যাখ্যা

Question: A right triangle has sides 9 cm, 12 cm, and 15 cm. What is its area?

Solution:
A right triangle with sides 9 cm, 12 cm, and 15 cm.

We know,
Area = (1/2) × base × height
= (1/2) × 9 × 12
= 54 cm2

So, the area of the right triangle is 54 cm2.

৪,১৫২.
4x + 1 = 32, then x = ?
  1. ক
    ক) 2
  2. খ
    খ) 3
  3. গ
    গ) 3/2
  4. ঘ
    ঘ) 2/3
ব্যাখ্যা

দেওয়া আছে,
4x + 1 = 32
⇒ 22(x + 1) = 25
⇒ 2(x + 1) = 5
⇒ 2x + 2 = 5
⇒ 2x = 5 - 2
⇒ 2x = 3
∴ x = 3/2

৪,১৫৩.
Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?
  1. ক
    2 hrs
  2. খ
    20 min
  3. গ
    40 min
  4. ঘ
    30 min
ব্যাখ্যা
Question: Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour?

Solution:
In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 -  40) km = 20 km at 60 km/hr.

∴ stoppage time = 20/60 hrs
= 1/3 hrs
= 20 min.
৪,১৫৪.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. What is the present age of the mother?
  1. ক
    30 years
  2. খ
    34 years
  3. গ
    38 years
  4. ঘ
    40 years
ব্যাখ্যা
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. What is the present age of the mother?

Solution: 
Let the age of the person’s mother be ‘x years
Age of the person = (2x/5)

After 8 years, age of the person’s mother = ‘x + 8’ years
Age of the person after 8 years = (2x/5) + 8 years

According to question:
(2x/5) + 8 = (1/2)(x + 8)
(2x/5) + 8 = (x/2) + 4
(x/2) -  (2x/5) = 8 - 4
(5x - 4x)/10 = 4
x/10 = 4
x = 40

So, the present age of his mother is 40 years
৪,১৫৫.
A couple has a son and a daughter. The age of the father is five times that of the son and the age of the daughter is one-third of that of her mother. The wife is 8 years younger to her husband and the sister is 4 years older than her brother. The mother's age is?
  1. ক
    44 years
  2. খ
    50 years
  3. গ
    32 years
  4. ঘ
    42 years
ব্যাখ্যা
Question: A couple has a son and a daughter. The age of the father is five times that of the son and the age of the daughter is one-third of that of her mother. The wife is 8 years younger to her husband and the sister is 4 years older than her brother. The mother's age is?

Solution:
ধরি,
ছেলের বয়স = x বছর
পিতার বয়স  = 5x বছর

আবার, ধরি মায়ের বয়স = y বছর
মেয়ের বয়স = y/3 বছর

প্রশ্নমতে,
5x - y = 8 ........... (1)
এবং,
⇒ y/3 - x = 4
⇒ y/3 = x + 4
∴ y = 3x + 12 ...........(2)

(1) নং হতে পাই,
⇒ 5x - y = 8
∴ y = 5x - 8
এখন y এর মান (2) নং এ বসিয়ে পাই
⇒ 5x - 8 = 3x + 12
⇒ 5x - 3x = 12 + 8
⇒ 2x = 20
⇒ x = 20/2
∴ x = 10
∴ পিতার বয়স  = 5x = 5 × 10 = 50 বছর
∴ মায়ের বয়স = 50 - 8 = 42 বছর
৪,১৫৬.
A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is-
  1. ক
    40
  2. খ
    45
  3. গ
    39
  4. ঘ
    37
ব্যাখ্যা
Question: A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is-

Solution:
Let there be x pupils in the class.
Total increase in marks = x × (1/2) = x/2

Here,
x/2 = (83 - 63)
⇒ x/2 = 20 
⇒ x = 40
৪,১৫৭.
Shakil and Rony invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Shakil invested Tk. 40000, then what was the amount invested by Rony?
  1. ক
    ক) Tk. 30000
  2. খ
    খ) Tk. 45000
  3. গ
    গ) Tk. 60000
  4. ঘ
    ঘ) Tk. 75000
ব্যাখ্যা
Question: Shakil and Rony invested in a business and gained a profit which was divided in the ratio of 2 : 3. If Shakil invested Tk. 40000, then what was the amount invested by Rony?

Solution: 
Given ratio = 2 : 3 
Let,
Shakil invested 2x Taka 
Rony invested 3x Taka 

ATQ,
2x = 40000 
∴ x = 20000

∴ Rony invested 3x Taka = 3 × 20000 Taka 
= 60000 Taka 
৪,১৫৮.
A rectangle’s length exceeds its width by 24 meters. If the total perimeter is 208 meters, what is the area?
  1. ক
    2200 square meters
  2. খ
    2520 square meters
  3. গ
    2560 square meters
  4. ঘ
    2740 square meters
ব্যাখ্যা
Question: A rectangle’s length exceeds its width by 24 meters. If the total perimeter is 208 meters, what is the area?

Solution:
মনে করি,
আয়তক্ষেত্রটির দৈর্ঘ্য = x মিটার
প্রস্থ = (x - 24) মিটার

আমরা জানি,
আয়তক্ষেত্রের পরিসীমা = 2(দৈর্ঘ্য + প্রস্থ) 

প্রশ্নমতে,
2(x + x - 24) = 208
⇒ 2(2x - 24) = 208
⇒ 2x - 24 = 208/2
⇒ 2x - 24 = 104
⇒ 2x = 104 + 24
⇒ 2x = 128
⇒ x = 128/2
⇒ x = 64

∴ প্রস্থ = (64 - 24) মিটার = 40 মিটার 

অতএব, আয়তক্ষেত্রের ক্ষেত্রফল = (দৈর্ঘ্য × প্রস্থ) = (64 × 40) বর্গমিটার = 2560 বর্গমিটার
৪,১৫৯.
Unless new reserves are found, the world's supply of coal is being depleted in such a way that with demand continuing to grow at present rate, reserves will be exhausted by the year 2050. What is the best conclusion that can be drawn from the above paragraph?
  1. ক
    ক) It is the time to search for alternative.
  2. খ
    খ) New reserves of coal would be found before 2050.
  3. গ
    গ) Demand for coal is growing fast.
  4. ঘ
    ঘ) World's coal reserve is declining .
ব্যাখ্যা
বিশ্বের কয়লার সরবরাহ এমনভাবে হ্রাস পাচ্ছে যে বর্তমান হারে চাহিদা বৃদ্ধি অব্যাহত থাকলে এবং নতুন মজুদ পাওয়া না গেলে, মজুদ 2050 সালের মধ্যে শেষ হয়ে যাবে। এক্ষেত্রে আমাদের করণীয় হলো।
কয়লার বিকল্প ব্যবস্থা খুঁজে বের করা। কারণ নতুন কয়লার মজুদ আমরা নাও পেতে পারি। তাই এমন উৎস খোঁজা উচিত যা অফুরন্ত। যেমন: নবায়নযোগ্য শক্তি (সূর্য শক্তি, জল শক্তি, বায়ু শক্তি, বায়োমাস ইত্যাদি।)

তাই সঠিক উত্তর হবে, ক।
৪,১৬০.
A man, his wife and daughter worked in a garden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to women is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings is mounted to Tk. 105, then find the daily wage of the daughter.
  1. ক
    Tk. 9
  2. খ
    Tk. 13
  3. গ
    Tk. 10
  4. ঘ
    Tk. 15
  5. ঙ
    None
ব্যাখ্যা
Question: A man, his wife and daughter worked in a garden. The man worked for 3 days, his wife for 2 days and daughter for 4 days. The ratio of daily wages for man to women is 5 : 4 and the ratio for man to daughter is 5 : 3. If their total earnings is mounted to Tk. 105, then find the daily wage of the daughter.

Solution:
Assume that the daily wages of man, women and daughter are Tk 5x, Tk 4x, Tk 3x respectively.
Multiply (no. of days) with (assumed daily wage) of each person to calculate the value of x.
[3 × (5x)] + [2 × (4x)] + [4 × (3x)] = 105
⇒ 15x + 8x + 12x = 105
⇒ 35x = 105
⇒ x = 3
Hence, man's daily wage = 5x = 5 × 3 = Tk. 15
Wife's daily wage = 4x = 4 × 3 = Tk. 12
Daughter's daily wage = 3x = 3 × 3 = Tk. 9
৪,১৬১.
Monir buys Tk. 40 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?
  1. ক
    ক) Tk. 32
  2. খ
    খ) Tk. 30
  3. গ
    গ) Tk. 34
  4. ঘ
    ঘ) None of the above
ব্যাখ্যা
Question: Monir buys Tk. 40 shares in a company which pays 10% dividend. If the man gets 12.5% on his investment, at what price did he buy the shares?

Solution:
Dividend on 40 share = 10%
∴ Dividend on 1 share = (10 × 40)/100
= Tk. 4

Tk. 12.50 is an income on an investment of Tk. 100
Tk. 4 is an income on an investment of = (100 × 4)/12.50
= (100 × 4 × 10)/125
= Tk. 32
৪,১৬২.
A man can row 9 km/hr in still water and he finds that it takes him twice as long to row up as to row down the river. Find the rate of the stream
  1. ক
    ক) 2 km/hr.
  2. খ
    খ) 3 km/hr.
  3. গ
    গ) 4 km/hr.
  4. ঘ
    ঘ) 5 km/hr.
ব্যাখ্যা
Question: A man can row 9 km/hr in still water and he finds that it takes him twice as long to row upstream as to row downstream the river. Find the rate of the stream.

Solution: 
Let, the speed of the current be x km/hr
Thus upstream speed = (9 - x) km/h and
downstream speed = (9 + x) km/hr

Let distance traveled be y

Then,
y/(9 - x) = 2y/(9 + x)
1/(9 - x) = 2/(9 + x)
9 + x = 18 - 2x
x + 2x = 18 - 9
3x = 9
x = 3 

the speed of the current be 3 km/hr.
৪,১৬৩.
Three varieties of rice costing Tk. 30, Tk, 50. and Tk. 20 are mixed in the ratio 3 : 2 : 4 in terms of weight. A retailer sells the mixture at Tk. 33 per kg. What percentage of profit does he make?
  1. ক
    ক) 5%
  2. খ
    খ) 10%
  3. গ
    গ) 9%
  4. ঘ
    ঘ) None
ব্যাখ্যা
Question: Three varieties of rice costing Tk. 30, Tk, 50. and Tk. 20 are mixed in the ratio 3 : 2 : 4 in terms of weight. A retailer sells the mixture at Tk. 33 per kg. What percentage of profit does he make?

Solution:
Assume the trader bought 3 kg, 2 kg and 4 kg of the three varieties.
Total weight = (3 + 2 + 4) kg = 9 kg
C.P. of 9 kg = Tk. (3 × 30 + 2 × 50 + 4 × 20) = Tk.270.
S.P. of 9 kg = Tk.(9 × 33) = TK. 297.

∴ Profit = {(297−270)/270} × 100) %
= 10%
৪,১৬৪.
A merchant purchases a wrist watch for tk 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price of the watch is
  1. ক
    500 tk
  2. খ
    550 tk
  3. গ
    600 tk
  4. ঘ
    650 tk
ব্যাখ্যা
Question: A merchant purchases a wrist watch for tk 450 and fixes its list price in such a way that after allowing a discount of 10%, he earns a profit of 20%. Then the list price of the watch is

Solution:
Here ,
Cost Price = tk 450 and discount on marked price = 10%
If the marked price of watch be y, then
y × (90/100) = (450 × 120)/100
⇒ y = (450 × 120)/90
∴ y = 600
৪,১৬৫.
In triangle △ABC, If AB = BC and ∠B = 70°, ∠A will be:
  1. ক
    ক) 70°
  2. খ
    খ) 10°
  3. গ
    গ) 55°
  4. ঘ
    ঘ) 130°
ব্যাখ্যা

If AB = BC, then ∠A =  ∠C
As we know, ∠A +  ∠B + ∠C = 180°
Or, A +  70° + ∠A = 180°
Or, 2∠A = 180° - 70° = 110°
So, ∠A = 55°

৪,১৬৬.
If x and y are both odd numbers, which of the following must be ab even number?
  1. ক
    xy + 4
  2. খ
    x + y
  3. গ
    x + y + 1
  4. ঘ
    None of these
ব্যাখ্যা
Question: If x and y are both odd numbers, which of the following must be ab even number?

Solution:
ধরি,
x = 3 এবং y = 5
ক) xy + 4 = (3 × 5) + 4 = 19 ; যা বিজোড়
খ) x + y = 3 + 5 = 8  ; যা জোড়
গ) x + y + 1 = 3 + 5 + 1 = 9  ; যা বিজোড়

∴ x + y সব সময় জোড়।
৪,১৬৭.
Arrange the words given below in a meaningful sequence. 1. Boil, 2. Serve, 3. Wash, 4. Chop, 5. Cook
  1. ক
    2, 5, 1, 4, 3
  2. খ
    3, 4, 1, 5, 2
  3. গ
    1, 4, 2, 5, 3
  4. ঘ
    5, 1, 3, 2, 4
ব্যাখ্যা
Question: Arrange the words given below in a meaningful sequence.
1. Boil, 2. Serve, 3. Wash, 4. Chop, 5. Cook

Solution:
Wash ⇒ Chop ⇒ Boil ⇒ Cook ⇒ Serve
3 ⇒ 4 ⇒ 1 ⇒ 5 ⇒ 2
৪,১৬৮.
PQR ত্রিভুজের ∠QPR = ৮০°, PQ = PR  হলে ∠PQR = ?
  1. ক
    ৫০°
  2. খ
    ৮০°
  3. গ
    ৯০°
  4. ঘ
    ১২০°
  5. ঙ
    কোনটিই নয়
ব্যাখ্যা
প্রশ্ন: PQR ত্রিভুজের ∠QPR = ৮০°, PQ = PR  হলে ∠PQR = ?

সমাধান:

যেহেতু, PQ = PR 
∠PQR = ∠PRQ
কিন্তু, ∠QPR = ৮০°

∠PQR + ∠PRQ + ∠QPR = ১৮০°
⇒ ∠PQR + ∠PRQ = ১৮০° - ৮০°
⇒ ২∠PQR = ১০০°
∴ ∠PQR = ৫০°
৪,১৬৯.
In a business partnership, Ajay and Vijay invested Tk. (1400 + x) and Tk. (1800 + 2x). After 12 months, Vijay’s profit amounted to Tk. 3200 out of a total Tk. 5600. Calculate Ajay’s starting investment.
  1. ক
    Tk.1500
  2. খ
    Tk.2000
  3. গ
    Tk.1800
  4. ঘ
    Tk.1600
  5. ঙ
    Tk.2020
ব্যাখ্যা

Question: In a business partnership, Ajay and Vijay invested Tk. (1400 + x) and Tk. (1800 + 2x). After 12 months, Vijay’s profit amounted to Tk. 3200 out of a total Tk. 5600. Calculate Ajay’s starting investment.

Solution:
Ratio of profit share = Ajay : Vijay
⇒ (1400 + x) : (1800 + 2x) = (5600 - 3200) : 3200
⇒ (1400 + x) /(1800 + 2x) = (5600-3200)/3200
⇒ (1400 + x) /(1800 + 2x) = 2400 / 3200
⇒ (1400 + x) /(1800 + 2x) = 3 / 4
⇒ 5600 + 4x = 5400 + 6x
⇒ 6x - 4x = 5600 - 5400
⇒ 2x = 200
∴ x= 100

∴ Initial investment of Ajay = 1400 + 100 = Tk.1500

৪,১৭০.
If A = {1, 2, 3} and B = Ø, what is the value of (A U B)?
  1. ক
    {1, 2, 3}
  2. খ
    {1, 2, 3, Ø}
  3. গ
    {2, 3, Ø}
  4. ঘ
    Ø
ব্যাখ্যা

Question: If A = {1, 2, 3} and B = Ø, what is the value of (A U B)?

Solution:
দেওয়া আছে,
A = {1, 2, 3}
এবং B = Ø
যেকোনো সেট A এবং ফাঁকা সেট (Ø) এর সংযোগ (union) হলো A 

∴ (A ∪ B) = {1, 2, 3} ∪ Ø
= A
= {1, 2, 3}

৪,১৭১.
ABCD is a rectangle. If its length is decreased by 5 meter and the width is increased by 3 meter, the area decreases by 9 square meters. If its length is increased by 3 meter and the width is increased by 2 meter, the area increases by 67 square meters. What is the width of ABCD?
  1. ক
    ক) 9 meter
  2. খ
    খ) 17 meter
  3. গ
    গ) 18 meter
  4. ঘ
    ঘ) 22 meter
ব্যাখ্যা
Question: ABCD is a rectangle. If its length is decreased by 5 meter and the width is increased by 3 meter, the area decreases by 9 square meters. If its length is increased by 3 meter and the width is increased by 2 meter, the area increases by 67 square meters. What is the width of ABCD?

Solution:
ধরি
আয়তক্ষেত্রের দৈর্ঘ্য = x মিটার
আয়তক্ষেত্রের প্রস্থ = y মিটার

১ম শর্তমতে
(x - 5)(y + 3) = xy - 9
xy - 5y + 3x - 15= xy - 9
3x - 5y = 6     ......................(1)

২য় শর্তমতে
(x + 3)(y + 2) = xy + 67
xy + 3y + 2x + 6 = xy + 67
2x + 3y = 61 ........................(2)

(1) × 2 -  (2) × 3 ⇒
6x - 10y - 6x - 9y = 12 - 183
- 19y = - 171
y = 171/19
y = 9

অতএব
আয়তক্ষেত্রের প্রস্থ = 9 মিটার
৪,১৭২.
Country : President :: State : ?
  1. ক
    ক) Governor
  2. খ
    খ) M.P
  3. গ
    গ) Legislator
  4. ঘ
    ঘ) Minister
ব্যাখ্যা
As President is the nominal head of a country, similarly Governer is the nominal head of a State.
৪,১৭৩.
Aman, Belal, and Dipto are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Aman withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Belal is -
  1. ক
    Tk. 1240
  2. খ
    Tk. 1420
  3. গ
    Tk. 1550
  4. ঘ
    Tk. 1600
ব্যাখ্যা
Question: Aman, Belal, and Dipto are partners in a business. Their shares are in the proposition of (1/3) : (1/4) : (1/5). Aman withdraws half of his capital after 15 months and after another 15 months, a profit of Tk. 4340 is divided. The share of Belal is -

Solution: 
প্রাথমিক বিনিয়োগের অনুপাত = (1/3) : (1/4) : (1/5)
 = 20 : 15 : 12 

বিনিয়োগ যথাক্রমে 20x, 15x, 12x

A : B : C = (20x × 15) + (10x × 15) : (15x × 30) : (12x × 30)
= 450x : 450x : 360x
= 5 : 5 : 4

বেলালের শেয়ার = (5/14) × 4340
= 1550 টাকা 
৪,১৭৪.
If x2 + y2 = 13 and xy = 6, then (x + y)3 is-
  1. ক
    125
  2. খ
    512
  3. গ
    729
  4. ঘ
    216
ব্যাখ্যা
Question: If x2 + y2 = 13 and xy = 6, then (x + y)3 is-

Solution:
Given that,
x2 + y2 = 13 and xy = 6
⇒ (x + y)2 = x2 + y2 + 2xy
⇒ (x + y)2 = 13 + (2 × 6)
⇒ (x + y)2 = 13 + 12
⇒ (x + y)2 = 25 = 52
∴ x + y = 5

Now,
(x + y)3 = 53 = 125
৪,১৭৫.
If 26 August of a certain year was Tuesday, what day was 29 September of that year?
  1. ক
    Sunday
  2. খ
    Monday
  3. গ
    Wednesday
  4. ঘ
    Tuesday
ব্যাখ্যা

Question: If 26 August of a certain year was Tuesday, what day was 29 September of that year?

Solution:
From 26 August to 29 September,
= 6 + 29 days
= 35 days

The same weekday repeats after every 7 days (or multiples of 7).

So, the 36th day would be Tuesday again.
Therefore, the 35th day (29 September) was Monday.

৪,১৭৬.
If the diameter of a sphere is 6 m, its hemisphere will have a volume of?
  1. ক
    9π cubic meters
  2. খ
    18π cubic meters
  3. গ
    54 cubic meters
  4. ঘ
    27π cubic meters
  5. ঙ
    None of these
ব্যাখ্যা
Question: If the diameter of a sphere is 6 m, its hemisphere will have a volume of?

Solution:
Given that,
Diameter of the sphere = 6 m
Radius of the sphere = 6/2 = 3

We know that,
The volume of a hemisphere is, V = (2/3)πr3
= (2/3) × π × (3)3
= 18π cubic meters
৪,১৭৭.
The pairs of equations 9x + 3y + 12 = 0 and 18x + 6y + 26 = 0 have-
  1. ক
    ক) Unique solution
  2. খ
    খ) Exactly two solutions
  3. গ
    গ) Infinitely many solutions
  4. ঘ
    ঘ) No solution
  5. ঙ
    ঙ) Exactly three solutions
ব্যাখ্যা

Given,
9x + 3y + 12 = 0 and 18x + 6y + 26 = 0
a1/a2 = 9/18 = 1/2
b1/b2 = 3/6 = 1/2
c1/c2 = 12/26 = 6/13
Since, a1/a2 = b1/b2 ≠ c1/c2

So, the pairs of equations are parallel and the lines never intersect each other at any point, therefore there is no possible solution.

৪,১৭৮.
An officer was appointed on maximum daily wages on contract money of Tk. 6720. But on being absent for some days, he was paid Tk. 5600. For how many days was he absent?
  1. ক
    5 days
  2. খ
    4 days
  3. গ
    3 days
  4. ঘ
    2 days
  5. ঙ
    1 day
ব্যাখ্যা

Question: An officer was appointed on maximum daily wages on contract money of Tk. 6720. But on being absent for some days, he was paid Tk. 5600. For how many days was he absent?

Solution:
Maximum daily wages of the officers = H.C.F of Tk. 6720 and Tk. 5600

H.C.F of 6720 & 5600 = 1120

Maximum daily wage = Tk. 1120
Total days appointed = 6720 ÷ 1120 = 6 days
​
​Absent days = 6 − 5 = 1 day

৪,১৭৯.
Simple interest on a certain sum at the rate of 5.5% p.a. for 4 years and 6 years differs by BDT 220. The sum is?
  1. ক
    Tk. 3600
  2. খ
    Tk. 2400
  3. গ
    Tk. 1800
  4. ঘ
    Tk. 2000
ব্যাখ্যা
Question: Simple interest on a certain sum at the rate of 5.5% p.a. for 4 years and 6 years differs by BDT 220. The sum is?

Solution:
Given that,
Rate of interest, r = 5.5%
Difference in simple interest for 6 years and 4 years = 220
Time difference, n = 6 - 4 = 2 years

We know that,
I = (P × r × n)/100
⇒ 220 = (P × 5.5 × 2)/100
⇒ 11 × P = 22000
⇒ P = 22000/11
∴ P = 2000
∴ The sum is Tk. 2000.
৪,১৮০.
If doubling a number and adding 16 to the result gives the same answer as multiplying the number by 8 and taking away 8 from the product, the number is:
  1. ক
    4
  2. খ
    6
  3. গ
    8
  4. ঘ
    12
ব্যাখ্যা
Question: If doubling a number and adding 16 to the result gives the same answer as multiplying the number by 8 and taking away 8 from the product, the number is:

Solution:
Let the number be a
ATQ,
2a + 16 = 8a - 8
⇒ 16 + 8 = 8a - 2a
⇒ 6a = 24
∴ a = 4
৪,১৮১.
Among 100 students, the average marks in English is 78. If the 60 girls scored an average of 84, determine the average score of the remaining boys.
  1. ক
    72.5
  2. খ
    67
  3. গ
    68
  4. ঘ
    69
ব্যাখ্যা

Question: Among 100 students, the average marks in English is 78. If the 60 girls scored an average of 84, determine the average score of the remaining boys.

Solution:
ধরি,
ছাত্রদের গড় নম্বর = x 

100 জন শিক্ষার্থীর মোট নম্বর = 100 × 78 = 7800 
এবং 60 জন ছাত্রীর মোট নম্বর = 60 × 84 = 5040

প্রশ্নমতে,
5040 + (100 - 60)x = 7800
⇒ 5040 + 40x = 7800
⇒ 40x= 7800 - 5040
⇒ 40x = 2760
⇒ ক = 2760/40 
⇒ ক = 69

∴ 40 জন ছাত্রের গড় নম্বর = 69

৪,১৮২.
What is the value of (1/3)log10125 - 2log104 + log1032 + log101
  1. ক
    0
  2. খ
    1
  3. গ
    1/3
  4. ঘ
    1/2
ব্যাখ্যা
Question: What is the value of (1/3)log10125 - 2log104 + log1032 + log101

Solution:
(1/3)log10125 - 2log104 + log1032 + log101
= (1/3)log1053 - 2log1022 + log1025 + 0
= log105 - 4log102 + 5log102
= log105 + log102
= log1010
= 1
৪,১৮৩.
A trader mixes 26 kg of fertilizer at tk 20 per kg with 30 kg of fertilizer of other variety at tk 36 per kg and sells the mixture at tk 30 per kg. His profit percent is:
  1. ক
    5%
  2. খ
    6%
  3. গ
    8%
  4. ঘ
    9%
ব্যাখ্যা
Question: A trader mixes 26 kg of fertilizer at tk 20 per kg with 30 kg of fertilizer of other variety at tk 36 per kg and sells the mixture at tk 30 per kg. His profit percent is:

Solution:
Cost price of 56 kg fertilizer = (26 × 20) + (30 × 36) tk
= 520 + 1080 tk
= 1600 tk

Selling price of 56 kg rice = 56 × 30 tk
= 1680 tk

Profit = 1680 - 1600 tk = 80 tk
∴ Gain = (80/1600) ×100
= 5%
৪,১৮৪.
If the sum of A and B is 40, and if C = 32, what is average value of A, B and C?
  1. ক
    ক) 24
  2. খ
    খ) 26
  3. গ
    গ) 28
  4. ঘ
    ঘ) 30
ব্যাখ্যা
Question: If the sum of A and B is 40, and if C = 32, what is average value of A, B and C?

Solution: 
average value of A, B and C is = (A + B + C)/3
= (40 + 32)/3
= 72/3
= 24
৪,১৮৫.
In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
  1. ক
    3300
  2. খ
    2300
  3. গ
    2700
  4. ঘ
    2400
ব্যাখ্যা
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:

Solution: 
Number of valid votes = 80% of 7500
= 6000

Valid votes polled by other candidate = 45% of 6000
= (45/100) x 6000
= 2700
৪,১৮৬.
While covering a distance of 24 km, a man noticed that after walking for 1 hour and 40 minutes, the distance covered by him was 5/7 of the remaining distance. What was his speed in meters per second?
  1. ক
    ক) 1(1/3) m/s
  2. খ
    খ) 1 (2/3) m/s
  3. গ
    গ) 1 m/s
  4. ঘ
    ঘ) 2 (1/3) m/s
ব্যাখ্যা

Let,
The speed is x km/hr.
Then,
Distance covered in 1 hr. 40 min
i.e., 1(2/3) hrs. = 5x/3 km.
Remaining Distance = {24 - (5x/3)}
∴ 5x/3 = 5/7{24 - (5x/3)
⇒ 5x/3 = 5/7{(72 - 5x)/3}
⇒ 7x = 72 - 5x
⇒ 12x = 72
⇒ x = 72/12
⇒ x = 6.
Hence, Speed = 6 km/hr
= {6 × (5/18)} m/s
= 5/3 m/s
= 1(2/3) m/s.

৪,১৮৭.
Which number when added to each of the numbers 24, 32 and 42 would make the sums to be in continued proportion?
  1. ক
    4
  2. খ
    5
  3. গ
    6
  4. ঘ
    8
ব্যাখ্যা
Question: Which number when added to each of the numbers 24, 32 and 42 would make the sums to be in continued proportion?

Solution:
Let the number to be added is x.
∴(24 + x) / (32 + x) = (32 + x) / (42 + x).
⇒ (24 + x)(42 + x) = (32 + x)2
⇒ 1008 + 66x + x2 = 1024 + 64x + x2
⇒ 2x = 16
∴ x = 8
৪,১৮৮.
If LOAD = DAOL, then ROAD = ?
  1. ক
    RDAO
  2. খ
    RADO
  3. গ
    OARD
  4. ঘ
    DAOR
ব্যাখ্যা

Question: If LOAD = DAOL, then ROAD = ?

Solution:
LOAD = DAOL এর L আর D এবং O আর A নিজেদের মধ্যে স্থান পরিবর্তন করেছে।

একইভাবে,
ROAD শব্দের R আর D এবং O আর A নিজেদের মধ্যে স্থান পরিবর্তন করেছে।

∴ ROAD = DAOR

৪,১৮৯.
A team of 6 players is to be selected from 8 batsmen and 5 bowlers. How many ways can this be done if exactly 4 batsmen must be selected?
  1. ক
    600
  2. খ
    700
  3. গ
    900
  4. ঘ
    450
ব্যাখ্যা

Question: A team of 6 players is to be selected from 8 batsmen and 5 bowlers. How many ways can this be done if exactly 4 batsmen must be selected?

Solution:
এখানে, একটি দল গঠন করতে হলে,  4 জন ব্যাটসম্যান এবং 2 জন বোলার নির্বাচন করতে হবে।

8 জন ব্যাটসম্যান থেকে 4 জন ব্যাটসম্যান নির্বাচন করার উপায়:
8C4 = 8!/{4! (8 - 4)!} 
= (8 × 7 × 6 × 5)/(4 × 3 × 2 × 1)
= 70 টি

5 জন বোলার থেকে 2 জন বোলার নির্বাচন করার উপায়:
5C2 = 5!/{2! (5 - 2)!}
= (5 × 4)/(2 × 1)
= 10 টি

সুতরাং, মোট সম্ভাব্য উপায় = 70 × 10 = 700 টি।

অতএব, দল গঠনের মোট উপায় হলো 700 টি।

৪,১৯০.
P and Q are two alloys of gold and copper prepared by mixing metals in the ratio 7:2 and 7:11 respectively. If equal amounts of both alloys are melted to form a third alloy R, then the ratio of gold and copper in R will be -
  1. ক
    7 : 5
  2. খ
    7 : 11
  3. গ
    7 : 13
  4. ঘ
    5 : 13
  5. ঙ
    5 : 9
ব্যাখ্যা

Question: P and Q are two alloys of gold and copper prepared by mixing metals in the ratio 7:2 and 7:11 respectively. If equal amounts of both alloys are melted to form a third alloy R, then the ratio of gold and copper in R will be - 
​
​Solution: 
Alloy P (Gold:Copper) = 7:2
Gold fraction in P = 7/9
Copper fraction in P = 2/9
​
​Alloy Q (Gold:Copper) = 7:11
Gold fraction in Q = 7/18
Copper fraction in Q = 11/18
​
Let, 1 kg of each alloy is mixed; 
Gold in Alloy R = 7/9 + 7/18 = 21/18
​
​Copper in Alloy R = 2/9 + 11/18 = 15/18 
​
​∴ The ratio of Gold:Copper in R = (21/18) : (15/18)
= 21 : 15
= 7 : 5

৪,১৯১.
A train with a length of 150m long, takes 30 seconds to cross a 500m long bridge. How much time will the train take to cross a 370m long platform?
  1. ক
    18 sec
  2. খ
    24 sec
  3. গ
    30 sec
  4. ঘ
    36 sec
ব্যাখ্যা
Question:  A train with a length of 150m long, takes 30 seconds to cross a 500m long bridge. How much time will the train take to cross a 370m long platform?

Solution:
Length of the train = 150 m
Length of the bridge = 500 m
∴ Total length = (500 + 150)m
= 650m

∴ Speed of the train =650/30 ​m/sec
= 65/3 m/sec

Now total length of the train and new bridge = (370 + 150)m
= 520m

∴ Time taken = (520 × 3​)/65 sec
= 24 sec
৪,১৯২.
A person standing on a railway platform noticed that a train took 15 seconds to completely pass through the platform which was 80 m long and it took 9 seconds in passing him. What is the speed of the train in km/hr?
  1. ক
    ক) 46 km/hr 
  2. খ
    খ) 48 km/hr 
  3. গ
    গ) 50 km/hr 
  4. ঘ
    ঘ) 52 km/hr 
ব্যাখ্যা
Question: A person standing on a railway platform noticed that a train took 15 seconds to completely pass through the platform which was 80 m long and it took 9 seconds in passing him. What is the speed of the train in km/hr?

Solution:
Let the length of the train be x meters
Then, the train covers x meters in 9 seconds
and (x + 80) meters in 15 seconds 

ATQ,
x/9 = (x + 80)/15  [ উভয় পাশেই ১ সেকেন্ডের গতিবেগ নেওয়া হয়েছে ] 
⇒ 15x = 9x + 720
⇒ 15x - 9x = 720
⇒ 6x = 720
⇒ x = 720/6
∴ x = 120

So, the length of the train is 120 m

∴ Speed of the train = (120/9) m/sec = 40/3 m/sec 

Speed of the train in km/hr = (40/3) × (3600/1000) km/hr 
= (40/3) × (36/10) km/hr
= 48 km/hr
৪,১৯৩.
A number divided by 13 leaves a remainder of 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65?
  1. ক
    30
  2. খ
    40
  3. গ
    5
  4. ঘ
    9
ব্যাখ্যা
Question: A number divided by 13 leaves a remainder of 1 and if the quotient, thus obtained, is divided by 5, we get a remainder of 3. What will be the remainder if the number is divided by 65?

Solution: 
ধরি, 
ভাগফল = k
ভাগফলকে 5 দিয়ে ভাগ করলে ভাগশেষ হবে 3.
k কে 5 দ্বারা ভাগ করলে ভাগফল হবে = m

∴ k = 5m + 3

এই ভাগফলের সাথে 13 গুণ করে সাথে 1 যোগ করলে সংখ্যাটি পাওয়া যবে।

∴ সংখ্যাটি = 13(5m + 3) + 1
= 65m + 40

এই সংখ্যাটিকে 65 দ্বারা ভাগ করলে ভাগশেষ হবে 40
৪,১৯৪.

What is the perimeter of the figure above?
  1. ক
    380
  2. খ
    360
  3. গ
    330
  4. ঘ
    300
  5. ঙ
    230
ব্যাখ্যা
Question:

What is the perimeter of the figure above?

Solution:

Apply the Pythagorean theorem
We get: 602 + x2 = 1002
⇒ 3600 + x2 = 10000
⇒ x2 = 6400
∴ x = 80

∴ Perimeter = 60 + 70 + 100 + 80 + 70 = 380
৪,১৯৫.
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
  1. ক
    ক) 720
  2. খ
    খ) 520
  3. গ
    গ) 700
  4. ঘ
    ঘ) 750
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6)
= 720.

৪,১৯৬.
A product is sold at a profit of 20%. If the cost price is increased by 10% and sale price by Tk. 26, then the percentage of the profit reduce by 5%, cost price is -
  1. ক
    ক) 200
  2. খ
    খ) 250
  3. গ
    গ) 320
  4. ঘ
    ঘ) 400
ব্যাখ্যা
ধরি,
পণ্যটির ক্রয়মূল্য x  টাকা 

20% লাভে, 
বিক্রয়মূল্য = (120 × x)/100 টাকা 
                  =6x/5 টাকা 

10% খরচ বৃদ্ধিতে,
নতুন ক্রয়মূল্য = (110 × x)/100 
                       = 11x/10 টাকা 

নতুন বিক্রয়মূল্য = (6x/5) + 26  টাকা
                         =  (6x+130)/5

নতুন লাভ= {(6x+130)/5} -(11x/10)
                  = (2(6x+130) -11x)/10
                  = (12x-11x+260)/10
                  = (x+260)/10 
প্রশ্নমতে,
15 =[{(x+260)/10} × 100]/(11x/10)
15 =(x + 260)×10 × 10/11x
11x × 15 = 100(x+260)
165x = 100x + 26000
165x - 100x = 26000
65x = 26000
x = 26000/65 = 2000/5= 400 TK

পণ্যটির ক্রয়মূল্য 400 টাকা
৪,১৯৭.
Two trains are running in the same direction on parallel tracks. The first train is 200 meters long and is moving at a speed of 15 meters per second. The second train is 250 meters long and is moving at 10 meters per second. How much time will the faster train take to completely overtake the slower one?
  1. ক
    82 seconds
  2. খ
    65 seconds
  3. গ
    90 seconds
  4. ঘ
    70 seconds
ব্যাখ্যা
Question: Two trains are running in the same direction on parallel tracks. The first train is 200 meters long and is moving at a speed of 15 meters per second. The second train is 250 meters long and is moving at 10 meters per second. How much time will the faster train take to completely overtake the slower one?

Solution:
Given that,
Length of faster train = 200 m
Length of slower train = 250 m
Speed of faster train = 15 m/s
Speed of slower train = 10 m/s

Since both trains are moving in the same direction, their relative speed
= (15 - 10)m/s
= 5 m/s

To completely overtake, the faster train must cover the length of both trains
= 200 + 250 = 450 m

We know that,
Time = Distance/Speed = 450​/5 = 90 seconds
So the faster train will take 90 seconds to overtake the slower one.
৪,১৯৮.
12 marbles are selected at random from a large collection of white, red, green and yellow marbles. The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color?
  1. ক
    ক) 34/91
  2. খ
    খ) 23/91
  3. গ
    গ) 36/91
  4. ঘ
    ঘ) 33/91
ব্যাখ্যা
Question: 12 marbles are selected at random from a large collection of white, red, green and yellow marbles. The number of marbles of each color is unlimited. Find the probability that the selection contains at least one marble of each color?

Solution:
এখানে, মোট মার্বেল সংখ্যা = 12

12টি মার্বেল নির্বাচন করার মোট উপায় = 12 + 4 - 1C4 - 1 = 15C3 = 455

আবার,
প্রত্যেক রঙের কমপক্ষে 1টি মার্বেল নির্বাচনের উপায় = 12 - 1C4 - 1
= 11C3
= 165

∴ নির্ণেয় সম্ভাব্যতা = 165/455
= 33/91
৪,১৯৯.
What percent of 50 is 15?
  1. ক
    30%
  2. খ
    35%
  3. গ
    70%
  4. ঘ
    300%
ব্যাখ্যা
Question: What percent of 50 is 15?

Solution:
15 = x% of 50
⇒ 15 = (x/100) × 50
⇒ x = 1500/50 = 30%
৪,২০০.
A train running at the speed of 66 km/h crosses a pole in 15 seconds. What is the length of the train?
  1. ক
    275 m
  2. খ
    250 m
  3. গ
    235 m
  4. ঘ
    220 m
ব্যাখ্যা
Question: A train running at the speed of 66 km/h crosses a pole in 15 seconds. What is the length of the train?

Solution:
Given,
Speed = 66 km/h
= (66 × 5/18) m/sec
= 55/3 m/sec

So the length of the train = (55/3 × 15) m
= 275 m