Bank Math

PrepBank · পাতা ১৩৫ / ১৬১ · ১৩,৪০১–১৩,৫০০ / ১৬,১২৪

১৩,৪০১.

There are three dice each of them having faces with a number from 1 to 6. These dices are rolled. Find the number of possible outcomes such that at least one of the dice shows the number 3.

ক
49
খ
65
গ
91
ঘ
100

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: There are three dice each of them having faces with a number from 1 to 6. These dices are rolled. Find the number of possible outcomes such that at least one of the dice shows the number 3.

Solution:
মোট উপায় = ৬ × ৬ × ৬
= ২১৬

কোন ছক্কায় ৩ না আসার উপায় = ৫ × ৫ × ৫
= ১২৫

কমপক্ষে একটি ৩ আসার উপায় = ২১৬ - ১২৫
= ৯১

১৩,৪০২.

In a box, there are 8 red, 7 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor red?

ক
ক) 2/5
খ
খ) 3/4
গ
গ) 7/20
ঘ
ঘ) 1/4

সঠিক উত্তর: ঘ

ঘ) 1/4

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1/4

ঘ

ব্যাখ্যা

Question: In a box, there are 8 red, 7 blue and 5 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor red?

Solution:
Total number of balls = (8 + 7 + 5) = 20.

Let E = event that the ball drawn is neither blue nor red
= event that the ball drawn is green.
n(E) = 5
P(E) =n(E)/n(S) = 5/20 = 1/4

১৩,৪০৩.

The ratio between two numbers is 7 : 9. If 25% of the smaller number is added to 30% of the larger number, the result is 178. What is the greater number?

ক
180
খ
270
গ
360
ঘ
450

সঠিক উত্তর: গ

360

উত্তর

সঠিক উত্তর: গ

360

গ

ব্যাখ্যা

Question: The ratio between two numbers is 7 : 9. If 25% of the smaller number is added to 30% of the larger number, the result is 178. What is the greater number?

Solution:
Let the numbers be 7x and 9x.
Then,
25% of the smaller = 0.25 × 7x = 1.75x
30% of the larger = 0.30 × 9x = 2.7x

According to the question,
1.75x + 2.7x = 178
⇒ 4.45x = 178
⇒ x = 178/4.45
∴ x = 40

∴ The greater number is (9 × 40) = 360

১৩,৪০৪.

In ΔPQS above, if PQ =3 and PS = 4, then PR =?

ক
9/4
খ
12/5
গ
16/5
ঘ
15/4
ঙ
20/3

সঠিক উত্তর: খ

12/5

উত্তর

সঠিক উত্তর: খ

12/5

খ

ব্যাখ্যা

Question:

In ΔPQS above, if PQ =3 and PS = 4, then PR =?

Solution:
Hypotenuse = QS = √(3² + 4²) = √(9 + 16) = √25 = 5

The area of the triangle PQS is, area = (1/2) × PQ × PS = (1/2) × 3 × 4 = 6

But the area can be found in another way too:
area = (1/2) × PR × QS = (5/2) × PR
⇒ (5/2) × PR = 6
⇒ PR = (6 × 2)/5
∴ PR = 12/5

১৩,৪০৫.

A, B and C can do a piece of work in 12, 18 and 36 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

ক
18 days
খ
15 days
গ
12 days
ঘ
9 days

সঠিক উত্তর: ঘ

9 days

উত্তর

সঠিক উত্তর: ঘ

9 days

ঘ

ব্যাখ্যা

Question: A, B and C can do a piece of work in 12, 18 and 36 days respectively. In how many days can A do the work if he is assisted by B and C on every third day?

Solution:
A's 2 day's work = (1/12) × 2 = 1/6 part
(A + B + C)' s 1 day's work = (1/12 + 1/18 + 1/36) = 6/36 = 1/6 part

Work done in 3 days = (1/6 + 1/6) = 2/6 = 1/3 part

Now,
1/3 part work is done in 3 days.
∴ Whole work will be done in (3 × 3) = 9 days

১৩,৪০৬.

In a football championship, there are 15 matches. If each team plays one match with every other team, the number of teams is-

ক
5
খ
6
গ
7
ঘ
8

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In a football championship, there are 15 matches. If each team plays one match with every other team, the number of teams is-

Solution:
Let n be the number of teams.
ⁿC₂ = 15
⇒ n!/{2! × (n - 2)!} = 15
⇒ {n(n - 1)(n - 2)!}/{2! × (n - 2)!} = 15
⇒ n(n - 1)/2 = 15
⇒ n(n - 1) = 30
⇒ n2 - n - 30 = 0
⇒ n - 6n + 5n - 30 = 0
⇒ n(n - 6) + 5(n - 6) = 0
⇒ (n - 6)(n + 5)
∴ n = 6 [Negative value is not acceptable]

১৩,৪০৭.

A man is need of money for 90 days he asked to Bank. The Bank charged taka 156 at 8%. What was the amount asked for?

ক
ক) 3,690
খ
খ) 4,960
গ
গ) 7,800
ঘ
ঘ) 7,950

সঠিক উত্তর: গ

গ) 7,800

উত্তর

সঠিক উত্তর: গ

গ) 7,800

গ

ব্যাখ্যা

এখানে,
আসল P = ?
হার r = 8%
=8/100 = 2/25
সময় n = 90 দিন
= 3 মাস
= 3/12 বছর
= 1/4 বছর

মুনাফা I = 156 টাকা
আমরা জানি
I = Pnr
Pnr = I
P = I/nr
= 156/{(1/4) × (2/25)}
= 7,800

১৩,৪০৮.

A solid body is made up of a cylinder of radius r and height r, a cone of base radius r and height r fixed to the cylinder's one base and a hemisphere of radius r to its other base. The total volume of the body (given r = 2) is :

ক
ক) 8π
খ
খ) 16π
গ
গ) 32π
ঘ
ঘ) 64π

সঠিক উত্তর: খ

খ) 16π

উত্তর

সঠিক উত্তর: খ

খ) 16π

খ

ব্যাখ্যা

Total volume of the body :
= Volume of the cylinder + Volume of the cone + Volume of the hemisphere
= πr².r + (1/3)πr².r + (2/3)πr³
= 2πr³
= 2π × (2)³
= 16π.

১৩,৪০৯.

How many number between 1000 and 5000 are exactly divisible by 225 ?

ক
17
খ
18
গ
19
ঘ
20

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: How many numbers between 1000 and 5000 are exactly divisible by 225?

Solution:
225 × 5 = 1125
.
.
.
225 × 22 = 4950

numbers between 1000 and 5000 are exactly divisible by 225 = 22 - 5 + 1
= 18

১৩,৪১০.

A father said to his son, “At the time of your birth, I was exactly as old as you are now". If the father's current age is 42 years, what is the son’s age 5 years back?

ক
16 years
খ
19 years
গ
21 years
ঘ
24 years

সঠিক উত্তর: ক

16 years

উত্তর

সঠিক উত্তর: ক

16 years

ক

ব্যাখ্যা

Question: A father said to his son, “At the time of your birth, I was exactly as old as you are now". If the father's current age is 42 years, what is the son’s age 5 years back?

Solution:
Let the son's present age be = x years.

According to the question,
(42 - x) = x
⇒ x + x = 42
⇒ 2x = 42
⇒ x = 42/2
⇒ x = 21

Son's age 5 years ago = (21 - 5) years = 16 years

১৩,৪১১.

A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

ক
ক) 400 kg
খ
খ) 560 kg
গ
গ) 600 kg
ঘ
ঘ) 640 kg

সঠিক উত্তর: গ

গ) 600 kg

উত্তর

সঠিক উত্তর: গ

গ) 600 kg

গ

ব্যাখ্যা

Question: A merchant has 1000 kg of sugar, part of which he sells at 8% and the remaining at 18% profit. He gains 14% on the whole. Find the quantity of sugar that he sold at 18% profit.

Solution:
Let
The cost price of sugar be tk. x per kg
Then Total cost price = Tk.1000x
The sugar sold at 8% gain by y kg
The sugar sold at 18% gain by (1000 - y) kg

Now
(108xy/100) + {118x(1000 - y)/100} = (114/100) × 1000x
(108y/100) + 1180 - (118y/100) = 1140
1180 - 1140 = (118y/100) - (108y/100)
40 = 10y/100
40 = y/10
y = 400

The sugar sold at 18% gain by (1000 - 400) kg
= 600 kg

১৩,৪১২.

A solid metal sphere of radius 9 cm is melted and recast into solid cones of radius 9 cm and height 4 cm. How many cones can be made?

ক
9
খ
13
গ
15
ঘ
11

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: A solid metal sphere of radius 9 cm is melted and recast into solid cones of radius 9 cm and height 4 cm. How many cones can be made?

Solution:
দেওয়া আছে,
গোলকের ব্যাসার্ধ, R = 9 cm
∴ গোলকের আয়তন, V_গোলক = 4/3πR³= 4/3π(9)³
= 4/3π(729)
= 972π ঘন সেমি।

আবার,
দেওয়া আছে,
কোণকের ব্যাসার্ধ, r = 9 cm এবং উচ্চতা, h = 4 cm
∴ কোণকের আয়তন, V_কোণক = 1/3πr²h
= 1/3π(9)²(4)
= 1/3π(81)(4)
= 108π ঘন সেমি।

∴ কোণকের সংখ্যা = (V_গোলক)/(V_কোণক)
= 972π/108π
= 9

সুতরাং, মোট 9টি কোণ তৈরি করা যাবে।

১৩,৪১৩.

Ratio of speed of boat in still water and speed of stream is 4 : 3. Boat covers 20 km upstream in 4 hours and x km in 3 hours downstream. Find the value of x?

ক
60 km
খ
85 km
গ
90 km
ঘ
100 km
ঙ
105 km

সঠিক উত্তর: ঙ

105 km

উত্তর

সঠিক উত্তর: ঙ

105 km

ঙ

ব্যাখ্যা

Question: Ratio of speed of boat in still water and speed of stream is 4 : 3. Boat covers 20 km upstream in 4 hours and x km in 3 hours downstream. Find the value of x?

Solution:
ধরি, স্থির পানিতে নৌকার গতিবেগ = 4k কিমি/ঘন্টা
এবং স্রোতের গতিবেগ = 3k কিমি/ঘন্টা।

স্রোতের প্রতিকূলে (Upstream) নৌকার গতিবেগ = (4k - 3k) কিমি/ঘন্টা
= 1k কিমি/ঘন্টা।
স্রোতের অনুকূলে (Downstream) নৌকার গতিবেগ = (4k + 3k) কিমি/ঘন্টা
= 7k কিমি/ঘন্টা।

প্রশ্ন অনুযায়ী,
স্রোতের প্রতিকূলে 20 কিমি যেতে সময় লাগে 4 ঘন্টা।
অতএব, স্রোতের প্রতিকূলে গতিবেগ = 20 কিমি/4 ঘন্টা
= 5 কিমি/ঘন্টা।
সুতরাং, 1k = 5
⇒ k = 5

এখন, স্রোতের অনুকূলে নৌকার গতিবেগ = 7k = 7 × 5 = 35 কিমি/ঘন্টা।
∴ স্রোতের অনুকূলে 3 ঘন্টায় অতিক্রান্ত দূরত্ব, x = 35 কিমি/ঘন্টা × 3 ঘন্টা
= 105 কিমি।

১৩,৪১৪.

A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

ক
ক) 4 hours
খ
খ) 5 hours 45 minutes
গ
গ) 4 hours 30 minutes
ঘ
ঘ) 4 hours 45 minutes

সঠিক উত্তর: ঘ

ঘ) 4 hours 45 minutes

উত্তর

সঠিক উত্তর: ঘ

ঘ) 4 hours 45 minutes

ঘ

ব্যাখ্যা

Question: A man takes 6 hours 15 minutes in walking a distance and riding back to starting place. He could walk both ways in 7 hours 45 minutes. The time taken by him to ride back both ways is:

Solution:
Time taken in walking both the ways = 7 hours 45 minutes - - - - - - - - (1)
Time taken in walking one way and riding back = 6 hours 15 minutes - - - - - - - - (2)

By the equation (2) × 2 - (1), we have,
Time taken by the man in riding both ways = 12 hours 30 minutes - 7 hours 45 minutes
= 4 hours 45 minutes.

১৩,৪১৫.

Among 90 students, the average marks in science is 72. If the 60 girls scored an average of 75, determine the average score of the remaining 30 boys.

ক
54
খ
60
গ
66
ঘ
56

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Among 90 students, the average marks in science is 72. If the 60 girls scored an average of 75, determine the average score of the remaining 30 boys.

Solution:
Let, the average marks of the boys = k
Total marks of 90 students = 90 × 72 = 6480
Total marks of 60 girls = 60 × 75 = 4500

According to the question,
4500 + 30k = 6480
⇒ 30k = 6480 - 4500
⇒ 30k = 1980
⇒ k = 1980/30
⇒ k = 66

∴ Average marks of the remaining 30 boys = 66.

১৩,৪১৬.

Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 12 hours. Another pipe alone can fill two tanks in -

ক
30 hours
খ
36 hours
গ
18 hours
ঘ
24 hours

সঠিক উত্তর: ঘ

24 hours

উত্তর

সঠিক উত্তর: ঘ

24 hours

ঘ

ব্যাখ্যা

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 12 hours. Another pipe alone can fill two tanks in -

Solution:
let the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/12 + 1/X
= (X + 12)/12X

Atq,
12X/(X + 12) = 6
x = 12 hours.

to fill two tanks it will take = 24 hours

১৩,৪১৭.

Shakil has to divide his rectangular field into two parts from one corner to the other using a fence. If the area of the field is 540m² and the length of the field is 36m then what will be the length of the fence needed?

ক
33 m
খ
35 m
গ
37 m
ঘ
39 m

সঠিক উত্তর: ঘ

39 m

উত্তর

সঠিক উত্তর: ঘ

39 m

ঘ

ব্যাখ্যা

Question: Shakil has to divide his rectangular field into two parts from one corner to the other using a fence. If the area of the field is 540m² and the length of the field is 36m then what will be the length of the fence needed?

Solution:
Breadth of the field = 540/36 = 15 m

the length of the fence = diagonal of the field
= √(15² + 36²)
= √1521
= 39 m

১৩,৪১৮.

On Sundays, a museum attracts around 510 visitors, while on weekdays, it has about 240. Calculate the average daily visitors in a 30-day month starting on a Sunday.

ক
280
খ
285
গ
290
ঘ
300

সঠিক উত্তর: খ

285

উত্তর

সঠিক উত্তর: খ

285

খ

ব্যাখ্যা

Question: On Sundays, a museum attracts around 510 visitors, while on weekdays, it has about 240. Calculate the average daily visitors in a 30-day month starting on a Sunday.

Solution:
Since, the month begins with a Sunday, so there will be 5 Sundays and 25 other days in this month.

Total visitors in Sundays = 5 × 510 = 2550
Total visitors in other days = 25 × 240 = 6000

∴ Total visiotors in the whole month = (2550 + 6000) = 8550

∴ Average number of visitors per day of the month = 8550/30 = 285

১৩,৪১৯.

A man takes 50 minutes to cover a certain distance at a speed of 6km/hr. If he walks with a speed of 10km/hr, he covers the same distance in -

ক
15 minutes
খ
30 minutes
গ
40 minutes
ঘ
25 minutes

সঠিক উত্তর: খ

30 minutes

উত্তর

সঠিক উত্তর: খ

30 minutes

খ

ব্যাখ্যা

Question: A man takes 50 minutes to cover a certain distance at a speed of 6km/hr. If he walks with a speed of 10km/hr, he covers the same distance in -

Solution:
distance = speed × time
= (6 × 50/60)
= 5km

time = distance/ speed
= 5/10
= 1/2 hour
= 30 minutes

১৩,৪২০.

A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is-

ক
1 : 5
খ
1 : 6
গ
1 : 4
ঘ
1 : 7

সঠিক উত্তর: ঘ

1 : 7

উত্তর

সঠিক উত্তর: ঘ

1 : 7

ঘ

ব্যাখ্যা

Question: A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is-

Solution:
let, new mixture is 12 liters

old mixture = 12 × (1/4) = 3 liters
sugar syrup = 9 liters

new sugar syrup = 9 + (3/2) = 10.5

ratio of lemon juice and sugar syrup = 1.5 : 10.5
= 15 : 105
= 1 : 7

১৩,৪২১.

Monir started a business investing Tk. 9000. After five months, Amir joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Amir in the profit?

ক
ক) TK. 2280
খ
খ) TK. 2520
গ
গ) TK. 2380
ঘ
ঘ) TK. 2240

সঠিক উত্তর: গ

গ) TK. 2380

উত্তর

সঠিক উত্তর: গ

গ) TK. 2380

গ

ব্যাখ্যা

Question: Monir started a business investing Tk. 9000. After five months, Amir joined with a capital of Tk. 8000. If at the end of the year, they earn a profit of Tk. 6970, then what will be the share of Amir in the profit?

Solution:
Now as per the question,
Monir invested for 12 months
and Amir invested for (12 - 5) = 7 months.

So
Monir : Amir = (9000 × 12) : (8000 × 7)
= 108000 : 56000
= 108 : 56
= 27 : 14

Amir Ratio in profit will be = 6970 × (14/41)
= Tk. 2380

১৩,৪২২.

In how many ways 6 cows and 5 goats can be serial in a row so that they are alternate.

ক
86400
খ
34560
গ
17280
ঘ
43200

সঠিক উত্তর: ক

86400

উত্তর

সঠিক উত্তর: ক

86400

ক

ব্যাখ্যা

Question: In how many ways 6 cows and 5 goats can be serial in a row so that they are alternate.

Solution:
Let,
The Arrangement be,
C G C G C G C G C

6 cows can be serial in = 6! Ways
= 720

5 goat can be serial in = 5! Ways
= 120

Required number of ways,
= 720 × 120
= 86400

১৩,৪২৩.

Out of 5 men and 3 women, a committee of three members is to be formed so that it has 1 women and 2 men. In how many different ways can it be done?

ক
ক) 20
খ
খ) 25
গ
গ) 28
ঘ
ঘ) 30

সঠিক উত্তর: ঘ

ঘ) 30

উত্তর

সঠিক উত্তর: ঘ

ঘ) 30

ঘ

ব্যাখ্যা

Required number of ways
=(³C₁× ⁵C₂)
= 3 × 10
= 30

১৩,৪২৪.

Consider three mixtures- the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

ক
The same amount of water and liquid B
খ
The same amount of liquids B and C
গ
More water than liquid B
ঘ
More water than liquid A

সঠিক উত্তর: গ

More water than liquid B

উত্তর

সঠিক উত্তর: গ

More water than liquid B

গ

ব্যাখ্যা

Question: Consider three mixtures- the first having water and liquid A in the ratio 1 : 2, the second having water and liquid B in the ratio 1 : 3, and the third having water and liquid C in the ratio 1 : 4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4 : 3 : 2. Then the resulting mixture has

Solution:
Mixtures A, B, & C are mixed in the ratio 4 : 3 : 2
Let the volumes = 4k, 3k, 2k respectively

Assume k = 60 [LCM(3, 4 & 5) = 60]
Volume of Liquid A = 8k/3 = 160
Volume of Liquid B = 9k/4 = 135
Volume of Liquid C = 8k/5 = 96
Volume of water = (4k/3) + (3k/4) + (2k/5)
= 80 + 45 + 24
= 149

There is more water than Liquid B

১৩,৪২৫.

8 liters Cold drink was added to a 20 liters mixture of water and alcohol such that the ratio of alcohol to that of cold drink and water is 1 : 3. Find the amount of alcohol in the solution.

ক
6 liters
খ
7 liters
গ
14 liters
ঘ
13 liters

সঠিক উত্তর: খ

7 liters

উত্তর

সঠিক উত্তর: খ

7 liters

খ

ব্যাখ্যা

Question: 8 liters Cold drink was added to a 20 liters mixture of water and alcohol such that the ratio of alcohol to that of cold drink and water is 1 : 3. Find the amount of alcohol in the solution.

Solution:
Let,
Quantity of alcohol A
Quantity of water W
Quantity of cold drinks C = 8 liters

We have a 20 liters mixture of alcohol and water.
⇒ A + W = 20
∴ W = 20 - A ................(1)

ATQ,
A : (W + C) = 1 : 3
⇒ A/(W + 8) = 1/3
⇒ 3A = W + 8
⇒ W = 3A - 8 ................(2)

From (1) and (2)
3A - 8 = 20 - A
⇒ 4A = 28
⇒ A = 7

∴ 7 liters of alcohol is present in the mixture.

১৩,৪২৬.

If 9 batsman have an average score of 56 on a match, and one of those batsman scored a 88 on the match, what is the average score on this match for the other 8 batsman?

ক
ক) 51
খ
খ) 52
গ
গ) 53
ঘ
ঘ) 54

সঠিক উত্তর: খ

খ) 52

উত্তর

সঠিক উত্তর: খ

খ) 52

খ

ব্যাখ্যা

Question: If 9 batsman have an average score of 56 on a match, and one of those batsman scored a 88 on the match, what is the average score on this match for the other 8 batsman?

Solution:
9 জন ব্যাটসম্যানের গড় রান = 56
9 জন ব্যাটসম্যানের মোট রান = 56 × 9 = 504

8 জন ব্যাটসম্যানের মোট রান = 504 - 88 = 416

8 জন ব্যাটসম্যানের গড় রান = 416/8 = 52

১৩,৪২৭.

On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5?

ক
0
খ
1
গ
2
ঘ
4
ঙ
None of these

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

প্রশ্ন: On dividing a number by 5, we get 3 as remainder. What will be the remainder when the square of this number is divided by 5?

সমাধান:
Let the number be x and on dividing x by 5, we get m as quotient and 3 as remainder.
∴ x = 5m + 3
⇒ x²= (5m + 3)²
= (25m² + 30m + 9)
= 5(5m² + 6m + 1) + 4

∴ On dividing x² by 5, we get 4 as remainder.

১৩,৪২৮.

90 is 75 percent of which number given below?

ক
ক) 110
খ
খ) 80
গ
গ) 100
ঘ
ঘ) 120

সঠিক উত্তর: ঘ

ঘ) 120

উত্তর

সঠিক উত্তর: ঘ

ঘ) 120

ঘ

ব্যাখ্যা

ধরি ,
x এর 75% = 90
x এর 75/100 = 90
3x/4 = 90
x = (90 × 4)/3 = 120

১৩,৪২৯.

How many triangles are there in the following figure.

ক
17
খ
19
গ
20
ঘ
21

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: How many triangles are there in the following figure.

Solution:

△AEF, △BEP, △EOP, △BPD, △OPD, △ODQ, △OQF, △CFQ, △CDQ, △BEO, △BED, △BOD, △DEO, △CFO, △CDO, △CFD, △DFO, △BCO, △DEF and △ABC
There are 20 triangles.

১৩,৪৩০.

The first term in a sequence is 1 and second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 21th term in the sequence?

ক
ক) 2
খ
খ) 3
গ
গ) 1
ঘ
ঘ) 5

সঠিক উত্তর: খ

খ) 3

উত্তর

সঠিক উত্তর: খ

খ) 3

খ

ব্যাখ্যা

Question: The first term in a sequence is 1 and second term is 5. From the third term on each term is the average (arithmetic mean) of all preceding terms. What is the 21th term in the sequence?

Solution:
The first term = 1
Second term = 5
Third term =(1 + 5)/2 = 3
Fourth term =(1 + 5 + 3)/4 = 3
Fifth term =(1 + 5 + 3 + 3)/4 = 3

We always get an average of 3 for all the sum of all precedings terms.
So, the 21th term would be 3 and the sequence would be
1, 5, 3, 3, 3, 3, 3,.............3.

১৩,৪৩১.

What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years?

ক
Tk. 3125
খ
Tk. 4225
গ
Tk. 3425
ঘ
Tk. 3225

সঠিক উত্তর: ঘ

Tk. 3225

উত্তর

সঠিক উত্তর: ঘ

Tk. 3225

ঘ

ব্যাখ্যা

Question: What would be the compound interest accrued on an amount of Tk 10000 at the rate of 15% per annum in 2 years?

Solution:
Compound Principal = 10000(1 + 15/100)2
= 10000 × (115/100)2
= (10000 × 115 × 115)/(100 × 100)
= 13225

Compound interest = 13225 - 10000 = Tk. 3225

১৩,৪৩২.

2√3 + √3 =

ক
ক) 6
খ
খ) 2√6
গ
গ) 3√3
ঘ
ঘ) 4√6

সঠিক উত্তর: গ

গ) 3√3

উত্তর

সঠিক উত্তর: গ

গ) 3√3

গ

ব্যাখ্যা

2√3 + √3 = √3 + √3 + √3 = 3√3

১৩,৪৩৩.

What is the probability of getting 53 Tuesdays in a leap year?

ক
1/366
খ
2/7
গ
53/366
ঘ
1/7

সঠিক উত্তর: খ

2/7

উত্তর

সঠিক উত্তর: খ

2/7

খ

ব্যাখ্যা

Question: What is the probability of getting 53 Tuesdays in a leap year?

Solution:
1 year = 365 days . A leap year has 366 days
A year has 52 weeks. Hence there will be 52 Tuesdays for sure.
52 weeks = 52 x 7 = 364 days
366 – 364 = 2 days

In a leap year there will be 52 Tuesdays and 2 days will be left.

These 2 days can be:
1. Sunday, Monday
2. Monday, Tuesday
3. Tuesday, Wednesday
4. Wednesday, Thursday
5. Thursday, Friday
6. Friday, Saturday
7. Saturday, Sunday

Of these total 7 outcomes, the favourable outcomes are 2.

Hence, the probability of getting 53 days = 2/7

১৩,৪৩৪.

If 10 men or 20 boys can make 100 footballs in 10 days, then how many footballs will be made by 8 men and 4 boys in 20 days?

ক
ক) 400
খ
খ) 300
গ
গ) 200
ঘ
ঘ) 100

সঠিক উত্তর: গ

গ) 200

উত্তর

সঠিক উত্তর: গ

গ) 200

গ

ব্যাখ্যা

Question: If 10 men or 20 boys can make 100 footballs in 10 days, then how many footballs will be made by 8 men and 4 boys in 20 days?

Solution:
here,
10 men = 20 boys
8 men = (2 × 8) boys
= 16 boys
if 20 boys can make 100 footballs in 10 days,

8 men and 4 boys or, (16 + 4) = 20 boys can make in 20 days = (100 × 2) = 200 footballs

১৩,৪৩৫.

The compound interest on a certain sum for 2 year at 10% per annum is Tk. 525. The simple interest on the same sum for double the time at half the rate percent per annum is

ক
ক) Tk.400
খ
খ) Tk.500
গ
গ) Tk.600
ঘ
ঘ) Tk.800

সঠিক উত্তর: খ

খ) Tk.500

উত্তর

সঠিক উত্তর: খ

খ) Tk.500

খ

ব্যাখ্যা

Let the sum be Tk. P.
Then,[p(1+10/100)²-p]=525
Sum =Tk.2500
S.I.= Tk.(2500×5×4)/100
= Tk. 500

১৩,৪৩৬.

Find the greatest number that will divide 45, 93 and 185 so as to leave the same remainder in each case.

ক
ক) 5
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 2

সঠিক উত্তর: খ

খ) 4

উত্তর

সঠিক উত্তর: খ

খ) 4

খ

ব্যাখ্যা

Question: Find the greatest number that will divide 45, 93 and 185 so as to leave the same remainder in each case.

Solution:
Here,
93 - 45 = 48
185 - 93 = 92
185 - 45 = 140

So, the required number = H.C.F of 48, 92 and 140
= 4

১৩,৪৩৭.

At what rate percent per annum will a sum of Tk. 64,000 amount to Tk. 85,184 in 3 years at compound interest?

ক
5%
খ
7.5%
গ
8.5%
ঘ
10%

সঠিক উত্তর: ঘ

10%

উত্তর

সঠিক উত্তর: ঘ

10%

ঘ

ব্যাখ্যা

Question: At what rate percent per annum will a sum of Tk. 64,000 amount to Tk. 85,184 in 3 years at compound interest?

Solution:
Given that,
Principal, P = Tk. 64,000
Amount, C = Tk. 85,184
Time, n = 3 years

We know,
C = P(1 + r)ⁿ⇒ 85,184 = 64,000 × {1 + (r/100)}³
⇒ 85,184/64,000 = {1 + (r/100)}³
⇒ 1.331 = {1 + (r/100)}³⇒ (1.1)³ = {1 + (r/100)}³

∴ 1 + (r/100) = 1.1
⇒ r/100 = 0.1
∴ r = 10%

১৩,৪৩৮.

The second term of a geometric progression is 10 and the fifth term is 80. What is the common ratio?

ক
3
খ
5
গ
4
ঘ
2

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The second term of a geometric progression is 10 and the fifth term is 80. What is the common ratio?

Solution:
Let the first term = a
Common ratio = r

We know,
n term of geometric progression = ar^{n - 1}
∴ Second term = ar = 10
And fifth term = ar⁴ = 80

Now, divide the second equation by the first. Then we get,
(ar⁴)/(ar) = 80/10
⇒ r³ = 8
⇒ r³ = 2³
∴ r = 2

So the common ratio is 2.

১৩,৪৩৯.

A clock gains (moves ahead) 10 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

ক
36 days
খ
54 days
গ
72 days
ঘ
80 days

সঠিক উত্তর: গ

72 days

উত্তর

সঠিক উত্তর: গ

72 days

গ

ব্যাখ্যা

Question: A clock gains (moves ahead) 10 minutes each day. How many days will it take to reach a point where the clock will indicate the correct time?

Solution:
একটি ঘড়িকে পুনরায় সঠিক সময় দেখাতে হলে তাকে 12 ঘণ্টা সময় এগিয়ে যেতে হবে।
কারণ একটি 12 ঘণ্টার ঘড়িতে যখন সঠিক সময় থেকে 12 ঘণ্টা এগিয়ে যাবে, তখন এটি আবার সঠিক সময় নির্দেশ করবে।

12 ঘণ্টা = 12 × 60 মিনিট = 720 মিনিট

এখন, যেহেতু ঘড়িটি প্রতিদিন 10 মিনিট করে সময় এগিয়ে যায়,

10 মিনিট সময় এগিয়ে যায় 1 দিনে
∴ 720 মিনিট সময় এগিয়ে যাবে = (1/10) × 720 দিনে
= 72 দিনে

সুতরাং, 72 দিন পর ঘড়িটি আবার সঠিক সময় দেখাবে।

১৩,৪৪০.

700 ml of a mixture contains water and milk in the ratio 2 : 8. How much water must be added to the mixture so that the ratio of water and milk becomes 3 : 8?

ক
70 ml
খ
75 ml
গ
60 ml
ঘ
65 ml

সঠিক উত্তর: ক

70 ml

উত্তর

সঠিক উত্তর: ক

70 ml

ক

ব্যাখ্যা

Question: 700 ml of a mixture contains water and milk in the ratio 2 : 8. How much water must be added to the mixture so that the ratio of water and milk becomes 3 : 8?

Solution:
Milk in the 700 ml of mixture = 700 × (8/10) = 560 ml

So, water in the mixture would be = 700 - 560 = 140 ml

Let water to be added = x ml

Now,
(140 + x)/560 = 3/8
1120 + 8x = 1680
8x = 1680 - 1120
8x= 560
x = 560/8 = 70 ml

১৩,৪৪১.

A retailer marked the price of a television at Taka 8000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

ক
Taka 6600
খ
Taka 5800
গ
Taka 6000
ঘ
Taka 6800

সঠিক উত্তর: ঘ

Taka 6800

উত্তর

সঠিক উত্তর: ঘ

Taka 6800

ঘ

ব্যাখ্যা

Question: A retailer marked the price of a television at Taka 8000 and gave a discount of 15%. Calculate the selling price and the amount of discount.

Solution:

Marked Price of the television = Taka 8000
Discount Percentage = 15%
Discount Amount = Discount Percentage × Marked Price = 15% × Taka 8000 = Taka 1200
Selling Price = Marked Price - Discount Amount = Taka 8000 - Taka 1200 = Taka 6800

১৩,৪৪২.

If sin(θ - 30°) = 1/2, then what is the value of cosθ?

ক
0
খ
1/2
গ
√3/2
ঘ
1

সঠিক উত্তর: খ

1/2

উত্তর

সঠিক উত্তর: খ

1/2

খ

ব্যাখ্যা

Question: If sin(θ - 30°) = 1/2, then what is the value of cosθ?

Solution:
দেয়া আছে,
sin(θ - 30°) = 1/2
⇒ θ - 30° = 30°
⇒ θ = 60°

এখন,
cosθ
= cos60°
= 1/2

১৩,৪৪৩.

10 years ago, the age of father was thrice the age of his son. Ten years after, the father's age will be twice that of his son. The ratio of their present ages is?

ক
ক) 7 : 3
খ
খ) 5 : 2
গ
গ) 4 : 5
ঘ
ঘ) 3: 6

সঠিক উত্তর: ক

ক) 7 : 3

উত্তর

সঠিক উত্তর: ক

ক) 7 : 3

ক

ব্যাখ্যা

Let the present age of father and son be x and y years respectively.
10 years ago, father's age was (x-10) years and son's age was (y-10) years
According to the question
(x-10) = 3(y-10)
⇒ x-10 = 3y-30
⇒ 3y - x = 20
After 10 years,
Age of father will be (x + 10) years and that of son will be (y + 10) years
Again, (x + 10) = 2(y + 10)
x + 10 = 2y + 20
x - 2y=10
From 3y - x = 20 and x - 2y=10,
we get y = 30 and x = 70
Thus ratio of father and son's age is 70 : 30 = 7 : 3
-------------------------------------------------------------------------------
১০ বছর আগে, পিতার বয়স পুত্রের বয়সের ৩ গুণ ছিল। ১০ বছর পর, পিতার বয়স পুত্রের বয়সের দ্বিগুন হবে। তাদের বর্তমান বয়সের অনুপাত কত?

পিতা ও পুত্রের বর্তমান বয়স যথাক্রমে x ও y বছর হলে,
(x - 10) = 3(y - 10)
⇒ x - 10 = 3y - 30
⇒ 3y - x = 20
এবং (x + 10) = 2(y + 10)
x + 10 = 2y + 20
x - 2y=10
সুতরাং y = 30 and x = 70
তাদের বর্তমান বয়সের অনুপাত 70 : 30 = 7 : 3

১৩,৪৪৪.

What is the slope of the line perpendicular to the line y = - 5x + 9?

ক
ক) 5
খ
খ) -5
গ
গ) 1/5
ঘ
ঘ) -1/5

সঠিক উত্তর: গ

গ) 1/5

উত্তর

সঠিক উত্তর: গ

গ) 1/5

গ

ব্যাখ্যা

প্রশ্ন: What is the slope of the line perpendicular to the line y = - 5x + 9?

সমাধান:
আমরা জানি,
y = mx + c

দেয়া আছে,
y = - 5x + 9
y = - 5x + 9 কে y = mx + c এর সহিত তুলনা করে পাই,
m = - 9
ঢাল m = - 5

y = - 5x + 9 রেখার লম্ব রেখার ঢাল = - 1/- 5 = 1/5

১৩,৪৪৫.

C and D together can complete a task in 6 days. C alone can do it in 10 days. How many days would it take D to do this job alone?

ক
10
খ
15
গ
12
ঘ
18

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: C and D together can complete a task in 6 days. C alone can do it in 10 days. How many days would it take D to do this job alone?

Solution:
C একা ১০ দিনে কাজটি করতে পারে।
∴ C এর একদিনের কাজ = 1/10

C ও D একসাথে ৬ দিনে কাজটি শেষ করে।
∴ তাদের একদিনের সম্মিলিত কাজ = 1/6

তাহলে, D এর একদিনের কাজ = 1/6 - 1/10
= (10 - 6)/60
= 4/60
= 1/15

অর্থাৎ, D এক দিনে কাজ করে 1/15 অংশ।
∴ পুরো কাজ শেষ করতে D এর সময় = 1 ÷ (1/15) = 15 দিন

১৩,৪৪৬.

In a seminar, the number of participants in Bangla, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated; and all of them being in the same subject.

ক
20
খ
21
গ
22
ঘ
23

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: In a seminar, the number of participants in Bangla, English and Mathematics are 60, 84 and 108 respectively. Find the minimum number of rooms required, where in each room the same number of participants are to be seated; and all of them being in the same subject.

Solution:
HCM of 60, 84 and 108 = 12

Minimum number of rooms required = (60/12) + (84/12) + (108/12)
= 5 + 7 + 9
= 21

১৩,৪৪৭.

ক
18
খ
12
গ
10
ঘ
15

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question:

Solution:
আমরা জানি, কোনো বর্গ ম্যাট্রিক্সের প্রধান কর্ণের ভুক্তিগুলোর সমষ্টিকে ওই ম্যাট্রিক্সের ট্রেস (trace) বলা হয়।

প্রদত্ত ম্যাট্রিক্সটির প্রধান কর্ণের ভুক্তিগুলো হলো: 2, 5, 8.
অতএব, A ম্যাট্রিক্সের ট্রেস, Tr(A) = 2 + 5 + 8 = 15

∴ ম্যাট্রিক্সটির ট্রেস, Tr(A) = 15

১৩,৪৪৮.

By selling 33 metres of cloth, one gains the selling price of 11 metres. Find the gain percent

ক
ক) 45%
খ
খ) 40%
গ
গ) 50%
ঘ
ঘ) 35%

সঠিক উত্তর: গ

গ) 50%

উত্তর

সঠিক উত্তর: গ

গ) 50%

গ

ব্যাখ্যা

Here,
The selling price of 11m cloth is obtained as profit.
(S.P. of 33 m cloth) – (C.P. of 33 m cloth)= S.P pf 11 m cloth
The selling price of 22 m cloth = Cost Price of 33 m of cloth

Let the cost of each metre be Tk. 100.

Therefore,
the cost price of 22 m cloth = 22 × 100 = Tk. 2200 and
S.P. of 22 m cloth = Tk. 3300
Profit = 3300 - 2200 = 1100

Profit% = {(1100/2200) × 100}%
= 50%

১৩,৪৪৯.

A man travels first 150 km of his journey at 80 km/hr. Due to bad weather he travels the next 150 km of his journey at 60 km/hr. What is his average speed for the first 300 km of his journey?

ক
60.6 km/hr
খ
63.6 km/hr
গ
66.6 km/hr
ঘ
68.6 km/hr

সঠিক উত্তর: ঘ

68.6 km/hr

উত্তর

সঠিক উত্তর: ঘ

68.6 km/hr

ঘ

ব্যাখ্যা

Question: A man travels first 150 km of his journey at 80 km/hr. Due to bad weather he travels the next 150 km of his journey at 60 km/hr. What is his average speed for the first 300 km of his journey?

Solution:
Total distance = 300 km
The total time taken to cover the first 300 km is the sum of the time taken to cover the first 150 km and the next 150 km.

Total time = 150/80 + 150/60 hour
= 15/8 + 15/6
= (45 + 60)/24
= 105/24
= 35/8 hour

Average Speed = 300/(35/8) km/hr
= 68.57 km/hr
≈ 68.6 km/hr

১৩,৪৫০.

What will be the least number which when halved will be exactly divisible by 12, 18, 21 and 30?

ক
ক) 930
খ
খ) 1800
গ
গ) 2520
ঘ
ঘ) 3010

সঠিক উত্তর: গ

গ) 2520

উত্তর

সঠিক উত্তর: গ

গ) 2520

গ

ব্যাখ্যা

Question: What will be the least number which when halved will be exactly divisible by 12, 18, 21 and 30?

Solution:
12 = 2 × 2 × 3
18 = 2 × 3 × 3
21 = 3 × 7
30 = 2 × 3 × 5

L.C.M. of 12, 18, 21 30 = 2 × 3 × 2 × 3 × 7 × 5 = 1260
Required number = 1260 × 2 = 2520

১৩,৪৫১.

If 3 men or 4 women can construct a wall in 44 days, then the number of days that 8 men and 4 women take to construct it is____?

ক
ক) 12 days
খ
খ) 14 days
গ
গ) 16 days
ঘ
ঘ) 18 days
ঙ
ঙ) None of these

সঠিক উত্তর: ক

ক) 12 days

উত্তর

সঠিক উত্তর: ক

ক) 12 days

ক

ব্যাখ্যা

Question: If 3 men or 4 women can construct a wall in 44 days, then the number of days that 8 men and 4 women take to construct it is____?

Solution:
৩ জন পুরুষ = ৪ জন মহিলা
১ জন পুরুষ = ৪/৩ জন মহিলা
৮ জন পুরুষ = (৪ × ৮)/৩ জন মহিলা
= ৩২/৩ জন মহিলা

এখন,
৮ জন পুরুষ + ৪ জন মহিলা = (৩২/৩) জন মহিলা + ৪ জন মহিলা = ৪৪/৩ জন মহিলা

৪ জন মহিলা কাজ করে ৪৪ দিনে
১ জন মহিলা কাজ করে ৪৪ × ৪ দিনে
৪৪/৩ জন মহিলা কাজ করে (৪৪ × ৪ × ৩)/৪৪ দিনে
= ১২ দিন

১৩,৪৫২.

In a certain country, a person born every 8 seconds and a person dies every 12 seconds. Therefore, the birth and death rates amount for a population growth rate of one person every-

ক
12 seconds
খ
18 seconds
গ
20 seconds
ঘ
24 seconds
ঙ
None

সঠিক উত্তর: ঘ

24 seconds

উত্তর

সঠিক উত্তর: ঘ

24 seconds

ঘ

ব্যাখ্যা

Question: In a certain country, a person born every 8 seconds and a person dies every 12 seconds. Therefore, the birth and death rates amount for a population growth rate of one person every-

Solution:
Let,
x be the number of seconds for the birth of every new person.

We know,
Birth rate - Death rate = Population growth

ATQ,
⇒ 1 person/8 seconds - 1 person/12 seconds = 1 person/x seconds
⇒ (3 - 2) person/24 seconds = 1 person/x seconds
⇒ 1 person/24 seconds = 1 person/x seconds
∴ x = 24 seconds

১৩,৪৫৩.

A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog is equal to 4 leaps of the hare. Compare their speeds:

ক
16 : 15
খ
18 : 17
গ
19 : 18
ঘ
20 : 19

সঠিক উত্তর: ক

16 : 15

উত্তর

সঠিক উত্তর: ক

16 : 15

ক

ব্যাখ্যা

Question: A dog takes 4 leaps for every 5 leaps of a hare but 3 leaps of the dog is equal to 4 leaps of the hare. Compare their speeds:

Solution:
খরগোশের 5 লাফ নিতে সময় লাগে t s
কুকুরের 4 লাফ নিতে সময় লাগে t s

খরগোশ 4 লাফে যায় x কিমি
5 লাফে যাবে 5x/4 কিমি

কুকুর 3 লাফে যায় x কিমি
4 লাফে যাবে 4x/3 কিমি

বেগের অনুপাত = (4x/3)/t : (5x/4)/t
= (4/3) : (5/4)
= 16 : 15

১৩,৪৫৪.

You toss a coin AND roll a die. What is the probability of getting a tail and a 4 on the die?

ক
ক) 1/2
খ
খ) 1/6
গ
গ) 1/8
ঘ
ঘ) 1/12

সঠিক উত্তর: ঘ

ঘ) 1/12

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1/12

ঘ

ব্যাখ্যা

Probability of getting a tail when a single coin is tossed
=1/2
Probability of getting 4 when a die is thrown
=1/6
Required probability,
=1/2 × 1/6
=1/12

১৩,৪৫৫.

A train running at the speed of 60 km/hr crosses a pole in 10 seconds. What is the length of the train?

ক
ক) 160 meter
খ
খ) 165.87 meter
গ
গ) 166.67 meter
ঘ
ঘ) 155.56 meter

সঠিক উত্তর: গ

গ) 166.67 meter

উত্তর

সঠিক উত্তর: গ

গ) 166.67 meter

গ

ব্যাখ্যা

Question: A train running at the speed of 60 km/hr crosses a pole in 10 seconds. What is the length of the train?

Solution:
In 3600 seconds the train covered 60000 meter
∴ In 10 seconds the train covered (60000 × 10)/3600 meter
= 166.67 meter

∴ The length of the train is 166.67 meter.

১৩,৪৫৬.

What is the sum of two consecutive even numbers, the difference of whose squares is 84?

ক
ক) 34
খ
খ) 38
গ
গ) 42
ঘ
ঘ) 46

সঠিক উত্তর: গ

গ) 42

উত্তর

সঠিক উত্তর: গ

গ) 42

গ

ব্যাখ্যা

Let the numbers be x and x + 2.
Then, (x + 2)² - x² = 84
⇒ 4x + 4 = 84
⇒ 4x = 80
⇒ x = 20.
∴ The required sum
= x + (x + 2)
= 2x + 2
= 42

১৩,৪৫৭.

The product of two numbers is 4107. If the L.C.M of these numbers is 111, then the H.C.F is:

ক
28
খ
37
গ
49
ঘ
43
ঙ
None of the above

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The product of two numbers is 4107. If the L.C.M of these numbers is 111, then the H.C.F is:

Solution:
product of two numbers = H.C.F × L.C.M
⇒ 4107 = 111 × H.C.F
⇒ H.C.F = 4107/111
= 37

Therefore, the H.C.F is = 37

১৩,৪৫৮.

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

ক
564
খ
645
গ
735
ঘ
756

সঠিক উত্তর: ঘ

756

উত্তর

সঠিক উত্তর: ঘ

756

ঘ

ব্যাখ্যা

Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Solution:

Ways in which at least 3 men are selected;

⇒ 3 men + 2 women

⇒ 4 men + 1 woman

⇒ 5 men + 0 woman

Number of ways = ⁷C₃ × ⁶C₂ + ⁷C₄ × ⁶C₁ + ⁷C₅ × ⁶C₀

= 35 ×15 + 35 × 6 + 21

= 735 + 21

= 756

∴ The required No. of ways = 756

১৩,৪৫৯.

A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 9√2 cm, then what is the area of the triangle?

ক
72√3 cm²
খ
84√3 cm²
গ
36√3 cm²
ঘ
144√3 cm²

সঠিক উত্তর: গ

36√3 cm²

উত্তর

সঠিক উত্তর: গ

36√3 cm²

গ

ব্যাখ্যা

Question: A square and an equilateral triangle have equal perimeters. If the diagonal of the square is 9√2 cm, then what is the area of the triangle?

Solution:
Let the side of the square be a cm
Then, its diagonal
√2a = 9√2
⇒ a = 9

Perimeter of the square
= 4a
= 4 × 9
= 36 cm

and also perimeter of the equilateral triangle = 36 cm

Each side of the triangle
= 36/3
= 12

Area of the triangle
= (√3/4) × (12)²
= 36√3 cm²

১৩,৪৬০.

The ratio between a two-digit number and the sum of the digit of that number is 4 : 1. If the digit in the unit’s place is 3 more than the digit in the ten’s place, what is the number.

ক
ক) 27
খ
খ) 36
গ
গ) 42
ঘ
ঘ) 48

সঠিক উত্তর: খ

খ) 36

উত্তর

সঠিক উত্তর: খ

খ) 36

খ

ব্যাখ্যা

Let the ten’s digit be x.
Then, unit’s digit = (x+3).
Sum of the digits = x + (x +3) = 2x + 3.
Number = 10x + (x+3) = 11x + 3.
(11x + 3)/(2x + 3) = 4/1
11x + 3 = 8x + 12
11x - 8x = 12 - 3
3x = 9
x = 3
Hence, Required number = 11x + 3 = 36.

১৩,৪৬১.

If f(x) = x/(x - 2) then value of f^{- 1}(2)?

ক
ক) 2
খ
খ) 3
গ
গ) 4
ঘ
ঘ) 5

সঠিক উত্তর: গ

গ) 4

উত্তর

সঠিক উত্তর: গ

গ) 4

গ

ব্যাখ্যা

Question: If f(x) = x/(x - 2) then value of f^{- 1}(2)?

সমাধান:
ধরি,
y = f(x) = x/(x - 2)

এখন,
x/(x - 2) = y
বা, x = y(x - 2)
বা, x = xy - 2y
বা, x - xy = - 2y
বা, x(1 - y) = - 2y
বা, x = (- 2y)/(1 - y)
∴ x = 2y/(y - 1)
তাহলে,
f^{- 1}(y) = 2y/(y - 1)
f^{- 1}(2) = (2 × 2)/(2 - 1) = 4

১৩,৪৬২.

ক
9
খ
5
গ
13
ঘ
11

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Problem:

Solution :

১৩,৪৬৩.

If a + b = m, a² + b² = n and a³ + b³ = p³ then, m³ + 2p³ = ?

ক
mn
খ
1/3mn
গ
3mn
ঘ
3/mn

সঠিক উত্তর: গ

3mn

উত্তর

সঠিক উত্তর: গ

3mn

গ

ব্যাখ্যা

Solution: If a + b = m, a² + b² = n and a³ + b³ = p³ then, m³ + 2p³ = ?

Solution:
m³ + 2p³
= (a + b)³ + 2(a³ + b³)
= a³ + 3a²b + 3ab² + b³ + 2a³ + 2b³
= 3a³ + 3a²b + 3ab² + 3b³
= 3(a³ + a²b + ab² + b³)
= 3{a²(a + b) + b²(a + b)}
= 3(a + b)(a²+b²)
= 3mn

১৩,৪৬৪.

What is the difference between the compound interests on Tk. 5000 for 1 year at 4% per annum compound yearly and half yearly?

ক
ক) 2
খ
খ) 3
গ
গ) 2(1/2)
ঘ
ঘ) 4

সঠিক উত্তর: ক

ক) 2

উত্তর

সঠিক উত্তর: ক

ক) 2

ক

ব্যাখ্যা

Interest compounded half yearly = 5000(1 + 2/100)²
= 5000(102/100)²
= 5000(1.02)² .........(i)

As we know, A = P(1 + R/100)^t
Interest compound yearly = 5000(1 + 4/100)¹
= 5000(104/100)
= 5000(1.04) ............(ii)

From (i) and (ii)
Required difference = 5000(1.02)² - 5000(1.04)¹
= 5000(1.0404) - 5000(1.04)
= 5202 - 5200
= 2.

১৩,৪৬৫.

Jabir was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one-third of my age". What is the age of Jabir?

ক
58 years
খ
44 years
গ
54 years
ঘ
64 years

সঠিক উত্তর: গ

54 years

উত্তর

সঠিক উত্তর: গ

54 years

গ

ব্যাখ্যা

Question: Jabir was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one-third of my age". What is the age of Jabir?

Solution:
Let the age of Jabir = x years
Then,
⇒ 3(x + 3) - 3(x - 3) = x
⇒ 3x + 9 - 3x + 9 = x
⇒ x = 18

ATQ,
x/3 = 18
∴ x = 18 × 3 = 54 years

∴ The age of Jabir is 54 years.

১৩,৪৬৬.

What must be the side of a square so that its area may be equal to the area of an isosceles triangle with the base and equal sides as 12 m and 10 m respectively?

ক
48 m
খ
12 m
গ
12√3 m
ঘ
4√3 m

সঠিক উত্তর: ঘ

4√3 m

উত্তর

সঠিক উত্তর: ঘ

4√3 m

ঘ

ব্যাখ্যা

Question: What must be the side of a square so that its area may be equal to the area of an isosceles triangle with the base and equal sides as 12 m and 10 m respectively?

Solution:
area of an isosceles triangle = (12/4)(4× 10² - 12²)
= 3 √(400 - 144)
= 3 √256
= 3 ×16
= 48 m

Area of square = 48 = a²
⇒ a = √(16 × 3)
⇒ a = 4√3 m

১৩,৪৬৭.

A grocer wishes to sell a mixture of two variety of pulses worth Tk.16 per KG. In what ratio must he mix the pulses to reach this selling price, when cost of one variety of pulses is Tk.14 per KG and the other is Tk.24 per KG?

ক
ক) 4 : 1
খ
খ) 3 : 4
গ
গ) 5 : 2
ঘ
ঘ) 3 : 7

সঠিক উত্তর: ক

ক) 4 : 1

উত্তর

সঠিক উত্তর: ক

ক) 4 : 1

ক

ব্যাখ্যা

প্রশ্ন: A grocer wishes to sell a mixture of two variety of pulses worth Tk.16 per KG. In what ratio must he mix the pulses to reach this selling price, when cost of one variety of pulses is Tk.14 per KG and the other is Tk.24 per KG?

সমাধান:
ধরি,
১৪ টাকার ডাল ছিল ক কিলোগ্রাম
২৪ টাকার ডাল ছিল খ কিলোগ্রাম

শর্তমতে,
১৪ক + ২৪খ = (ক + খ)১৬
বা, ১৪ক + ২৪খ = ১৬ক + ১৬খ
বা, ২৪খ - ১৬খ = ১৬ক - ১৪ক
বা, ৮খ = ২ক
বা, খ/ক = ২/৮
বা, ক/খ = ৮/২
∴ ক : খ = ৮ : ২ = ৪ : ১

১৩,৪৬৮.

Which of the following is the largest?

ক
14/18
খ
15/25
গ
3/4
ঘ
12/14

সঠিক উত্তর: ঘ

12/14

উত্তর

সঠিক উত্তর: ঘ

12/14

ঘ

ব্যাখ্যা

Question: Which of the following is the largest?

Solution:
14/18 = 7/9 = 0.78
15/25 = 3/5 = 0.6
3/4 = 0.75
12/14 = 6/7 = 0.86

১৩,৪৬৯.

The angle between the minute hand and the hour hand of a clock when the time is 4:20, is -

ক
ক) 10°
খ
খ) 20°
গ
গ) 15°
ঘ
ঘ) 30°

সঠিক উত্তর: ক

ক) 10°

উত্তর

সঠিক উত্তর: ক

ক) 10°

ক

ব্যাখ্যা

Question: The angle between the minute hand and the hour hand of a clock when the time is 4:20, is -

Solution:
কোণ = ।11M - 60H।/2
= ।(11 × 20) - (60 × 4)।/2
= ।220 - 240। /2
= 10°

১৩,৪৭০.

By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

ক
22
খ
20
গ
18
ঘ
16

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: By Selling 45 lemons for Tk. 40, a man loses 20%. How many should he sell for Tk..24, to gain 20% in the transaction?

Solution:
SP per Lemons = 40/45
= Tk. 0.88.
Let, CP was Tk. X per Lemons.
SP = CP - 20% of CP
⇒ 0.88 = 0.8X
⇒ X = Tk. 1.11

To get 20% profit,
SP = 1.11 + 20% of 1.11 = Tk.1.33

Thus, he can sell = 24/1.33
= 18 Lemons in Tk. 24.

১৩,৪৭১.

P's age 3 years ago was three times the present age of Q. At present R's age is twice the age of Q. Also R is 12 years younger than P. What is the present age of R?

ক
18 years
খ
30 years
গ
9 years
ঘ
12 years

সঠিক উত্তর: ক

18 years

উত্তর

সঠিক উত্তর: ক

18 years

ক

ব্যাখ্যা

Question: P's age 3 years ago was three times the present age of Q. At present R's age is twice the age of Q. Also R is 12 years younger than P. What is the present age of R?

Solution:
Let the present age of Q be a years
Three years ago P's age = 3a years
Then, present age of P is (3a + 3)
R's present age = 2a

According to question
(3a + 3) - 2a = 12
a = 9 year

∴ Present age of R = 2a = 2 × 9 = 18 years

১৩,৪৭২.

There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

ক
17% loss
খ
17% profit
গ
23.3% loss
ঘ
15% profit

সঠিক উত্তর: ঘ

15% profit

উত্তর

সঠিক উত্তর: ঘ

15% profit

ঘ

ব্যাখ্যা

Question: There is a shopkeeper whose claim is that he sells a certain product at a cost of Tk 23/kg, which actually costs him Tk 25/kg. The shopkeeper says that he is taking the loss to let his customers get a better deal. When examined thoroughly, the constabulary find that the shopkeeper is actually using an 800 gms weight in place of a 1 kg weight. How much does he gain or lose?

Solution:
Selling price of 0.8 kg = 23 taka

Selling price of 1 kg = 23/0.8 taka
= 115/4 taka
= 28.75 taka

∴ Percentage profit = {(28.75 - 25)/25} × 100%
= (3.75/25) × 100%
= 15%

১৩,৪৭৩.

1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

ক
45%
খ
52%
গ
48%
ঘ
42%

সঠিক উত্তর: গ

48%

উত্তর

সঠিক উত্তর: গ

48%

গ

ব্যাখ্যা

Question: 1200 boys and 800 girls appeared in an examination. If 60% of the boys and 40% of the girls passed the examination, what is the percentage of candidates who failed in the examination?

Solution:
Number of students failed = 40% of boys (1200) + 60% of girls (800)
= (40 × 1200)/100 + (60 × 800)/100
= 480 + 480
= 960

Total number of students = 1200 + 800 = 2000

∴ Percentage of candidates failed = (960/2000) × 100
= 48%

১৩,৪৭৪.

A pair of articles was bought for Tk. 35.70 at a discount of 15%. What must be the marked price of each of the articles?

ক
ক) Tk. 42
খ
খ) Tk. 36
গ
গ) Tk. 21
ঘ
ঘ) Tk. 18

সঠিক উত্তর: গ

গ) Tk. 21

উত্তর

সঠিক উত্তর: গ

গ) Tk. 21

গ

ব্যাখ্যা

Question: A pair of articles was bought for Tk. 35.70 at a discount of 15%. What must be the marked price of each of the articles?

Solution:
Selling price =Tk. 35.70
Discount = 15%.

Let the M.P be 100%.
The selling price will be 100% - 15% = 85%
⇒ 85% = 35.70
⇒ 100% = 35.70 × (100/85)
⇒ 100% = Tk. 42

∴ The Marked price is Tk. 42 .
The marked price of each of the articles = 42/2 = 21Tk.

১৩,৪৭৫.

A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?

ক
10 months
খ
8 months
গ
6 months
ঘ
4 months

সঠিক উত্তর: ক

10 months

উত্তর

সঠিক উত্তর: ক

10 months

ক

ব্যাখ্যা

Question: A and B are partners in a business. A contributes 1/4 of the capital for 15 months and B received 2/3 of the profit. For how long B's money was used?

Solution:
Let the total profit be Tk. z
Then,
B's share of profit = Tk. 2z/3,
A's share of profit = Tk. ( z - 2z/3 ) = Tk. z/3

∴ A : B = z/3 : 2z/3 = 1 : 2

Let the total capital be Tk. X and suppose B's money was used for n months.
Then,
{(X/ 4) × 15}/{(3X/4) × n) = 1/2
⇒ 15/3n = 1/2
⇒ 3n = 30
⇒ n = 10

∴ B's money was used for 10 months.

১৩,৪৭৬.

If -1 < p < 0, then which of the following is the biggest?

ক
p²
খ
1/p²
গ
p + 1
ঘ
p/2

সঠিক উত্তর: খ

1/p²

উত্তর

সঠিক উত্তর: খ

1/p²

খ

ব্যাখ্যা

Question: If -1 < p < 0, then which of the following is the biggest?

Solution:
let, p = -1/2

p/2 = -1/(2 × 2) = -1/4
p² = (-1/2)2 = 1/4
1/p² = 4
p + 1 = 1/2

১৩,৪৭৭.

A shopkeeper lost 7.5% by selling an article. If he had bought it at 10% less and sold it for tk. 31 more, he would have gained 20%. Find the cost price of the article.

ক
50 tk.
খ
125 tk.
গ
200 tk.
ঘ
300 tk.
ঙ
370 tk.

সঠিক উত্তর: গ

200 tk.

উত্তর

সঠিক উত্তর: গ

200 tk.

গ

ব্যাখ্যা

Let, Cost price be tk. 100,
At the loss of 7.5%, the selling price would be tk. (100-7.5)=92.5
At 10% less Cost price would be tk. (100-10) =90
if he gained 20% the selling price would be tk (90+20% of 90) tk (90+18) Etk. 108
Difference of selling price = tk (108 - 92.50) tk 15.50

So when the difference value is 15.50, then the actual value of difference = 31
when the value is 1, then the actual value = 31/15.50
when the value of CP is 100, then the actual value of CP is = 31/15.50 x 100 = 200 TK

১৩,৪৭৮.

Ten years ago, Ayesha was three times as old as her brother. Now, Ayesha is 10 years older than her brother. What is the present age of the brother?

ক
25 years
খ
18 years
গ
12 years
ঘ
14 years
ঙ
15 years

সঠিক উত্তর: ঙ

15 years

উত্তর

সঠিক উত্তর: ঙ

15 years

ঙ

ব্যাখ্যা

Question: Ten years ago, Ayesha was three times as old as her brother. Now, Ayesha is 10 years older than her brother. What is the present age of the brother?

Solution:
ধরি,
বর্তমানে আয়েশার বয়স x এবং তার ভাইয়ের বয়স y

১০ বছর আগে, আয়েশা তার ভাইয়ের বয়সের তিন গুণ ছিল। অর্থাৎ
⇒ x - 10 = 3(y - 10).......... (১)

আবার,
বর্তমানে আয়েশা তার ভাইয়ের চেয়ে ১০ বছর বড়।
x = y + 10

এখন, x এর মান (১) এ বসিয়ে পাই,
⇒ (y + 10) - 10 = 3(y - 10)
⇒ y = 3y - 30
⇒ y - 3y = - 30
⇒ - 2y = - 30
∴ y = 15

তার ভাইয়ের বর্তমান বয়স 15 বছর।

১৩,৪৭৯.

Arrange the following numbers in ascending order: 105, 78, 92, 64, 119, 50, 83

ক
50, 64, 78, 83, 92, 105, 119
খ
64, 50, 78, 83, 105, 92, 119
গ
119, 105, 92, 83, 78, 64, 50
ঘ
78, 83, 50, 64, 92, 105, 119

সঠিক উত্তর: ক

50, 64, 78, 83, 92, 105, 119

উত্তর

সঠিক উত্তর: ক

50, 64, 78, 83, 92, 105, 119

ক

ব্যাখ্যা

Question: Arrange the following numbers in ascending order: 105, 78, 92, 64, 119, 50, 83

Solution:
Given the series,
105, 78, 92, 64, 119, 50, 83

Now,
Ascending order(ছোট থেকে বড়)
50, 64, 78, 83, 92, 105, 119

১৩,৪৮০.

In a certain code language COMPUTER is written as RFUVQNPC. How will BRAVE be written in that code language?

ক
ETSNR
খ
EWBSB
গ
CTWNB
ঘ
ETQNB

সঠিক উত্তর: খ

EWBSB

উত্তর

সঠিক উত্তর: খ

EWBSB

খ

ব্যাখ্যা

Question: In a certain code language COMPUTER is written as RFUVQNPC. How will BRAVE be written in that code language?

Solution:
Rewrite the word in reverse order ⇒ COMPUTER = RETUPMOC
simply replace the remaining letters in alphabetical order such that: E = F, T = U, U = V, P = Q, M = N, O = P [Without 1st and last letter]
we get, COMPUTER = RFUVQNPC

Similarly, BRAVE = EVARB
now, V = W, A = B, R = S [Without 1st and last letter]
∴ BRAVE = EWBSB

১৩,৪৮১.

A sum of money at simple interest amounts to Tk. 8000 in 3 years and to Tk. 8500 in 4 years. The capital was-

ক
ক) 6500
খ
খ) 6000
গ
গ) 6800
ঘ
ঘ) 6600

সঠিক উত্তর: ক

ক) 6500

উত্তর

সঠিক উত্তর: ক

ক) 6500

ক

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 8000 in 3 years and to Tk. 8500 in 4 years. The capital was-

Solution:
in one year, the simple interest is (8500 - 8000) or, 500
so, in three year the interest is (500 × 3) or, 1500

Hence, the capital was (8000 - 1500) or, 6500 Tk.

১৩,৪৮২.

Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.

ক
56
খ
72
গ
48
ঘ
66

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Find the number of triangles which can be formed by joining the angular points of a polygon of 8 sides as vertices.

Solution:
A triangle needs 3 points.
And a polygon of 8 sides has 8 angular points.

Hence,
Number of triangles formed
= ⁸C₃
= (8 × 7 × 6)/(3 × 2 × 1)
= 56

∴ 56 triangles can be formed by joining the angular points of a polygon of 8 sides as vertices

১৩,৪৮৩.

All distinct permutations of the letters of the word PRIDE are arranged in alphabetical order. What is the rank of the word PRIDE?

ক
72
খ
77
গ
88
ঘ
91
ঙ
95

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Question: All distinct permutations of the letters of the word PRIDE are arranged in alphabetical order. What is the rank of the word PRIDE?

Solution:
Here,
The order of each letter in the dictionary is DEIPR.

Now,
with D in the beginning, the remaining letters can be permuted = 4! ways.
= 24 ways

Similarly,
with E in the beginning, the remaining letters can be permuted = 4! ways.
= 24 ways

Similarly,
with I in the beginning, the remaining letters can be permuted = 4! ways.
= 24 ways

Now,
with P in the beginning and R in the second position,
the remaining letters are D, E, I.

Before R, there are D, E, I.

So permutations = 3 × 3!
= 3 × 6
= 18

Now,
with P and R fixed, the remaining letters are D, E, I.

Before I, there are D, E.

So permutations = 2 × 2!
= 2 × 2
= 4

Finally,
add the word itself.

Hence, the rank of the word PRIDE
= 24 + 24 + 24 + 18 + 4 + 1
= 95

১৩,৪৮৪.

If the total surface area of a hemisphere is 81π sq. cm, then its radius is-

ক
ক) 4√3
খ
খ) 2√3 cm
গ
গ) 5√3cm
ঘ
ঘ) 3√3 cm

সঠিক উত্তর: ঘ

ঘ) 3√3 cm

উত্তর

সঠিক উত্তর: ঘ

ঘ) 3√3 cm

ঘ

ব্যাখ্যা

প্রশ্ন: If the total surface area of a hemisphere is 81π sq. cm, then its radius is-

সমাধান:

ধরি
গোলকের ব্যাসার্ধ r cm

প্ৰশ্নমতে,
3πr²= 81π
বা, r² = 27
বা, r² =(3√3)²
বা, r = 3√3

১৩,৪৮৫.

The average age of A and B was 18 years five years ago. Now, the average age of A, B, and C is 24 years. What will C's age be in five years?

ক
31 years
খ
33 years
গ
37 years
ঘ
41 years

সঠিক উত্তর: ক

31 years

উত্তর

সঠিক উত্তর: ক

31 years

ক

ব্যাখ্যা

Question: The average age of A and B was 18 years five years ago. Now, the average age of A, B, and C is 24 years. What will C's age be in five years?
(৫ বছর আগে A এবং B-এর গড় বয়স ছিল ১৮ বছর। বর্তমানে, A, B, এবং C-এর গড় বয়স ২৪ বছর। ৫ বছর পর C-এর বয়স কী হবে?)

Solution:
5 বছর আগে A ও B এর বয়সের যোগফল = 18 × 2 = 36 years.
A ও B এর বর্তমান বয়সের যোগফল = 5 + 5 + 36 = 46 years.
A, B ও C এর বর্তমান বয়সের যোগফল = 24 × 3 = 72 years.

∴ C এর বর্তমান বয়স = 72 - 46 = 26 years.

∴ 5 বছর পর C এর বয়স = 26 + 5 = 31 years.

১৩,৪৮৬.

Anik travels 35 kilometers (km) partly at 4km /h and partly at 5 km/h. If he covers the distance at 5 km/h he could cover 2 km more in the same time. The time taken to cover the whole distance at original rate is-

ক
ক) 4hr 30 min
খ
খ) 5hr 24 min
গ
গ) 7hr 24 min
ঘ
ঘ) 9 hr 24 min
ঙ
ঙ) None

সঠিক উত্তর: গ

গ) 7hr 24 min

উত্তর

সঠিক উত্তর: গ

গ) 7hr 24 min

গ

ব্যাখ্যা

Suppose, he traveled at 4 km/h for p hours and @5 km/h for q hours.
So, 4p+5q = 35 -------- (i)
According to the question,
5(p+q) = 35+2
⇒ 5p + 5q = 37 -------- (ii)
Solving these two equations, we get,
p = 2, q = 27/5
So, total time taken = 2 + 27/5 = 37/5 hr = 7hr + 2×60/5 min = 7 hr 24 min.

১৩,৪৮৭.

The present worth of Tk.169 due in 2 years at 4% per annum compound interest is:

ক
ক) 144.75
খ
খ) 148.5
গ
গ) 15.25
ঘ
ঘ) 156.25

সঠিক উত্তর: ঘ

ঘ) 156.25

উত্তর

সঠিক উত্তর: ঘ

ঘ) 156.25

ঘ

ব্যাখ্যা

সুদাসল = 169 টাকা
সময় n = 2 বছর
মুনাফার হার r = 4% = 4/100 = 1/25
আসল P = ?

আমরা জানি
C = P (1 + r)ⁿ
169 = P(1 + 1/25)²
169 = P(26/25)²
P = (169 × 25 × 25)/26× 26
P = 156.25 টাকা

মূল প্রশ্নে সঠিক উত্তর ছিলো না।
আমরা একটি অপশন পরিবর্তন করে সঠিক অপশনটি দিয়েছি।

১৩,৪৮৮.

The volume of two cubes are in the ratio 8 : 27 . The ratio of their surface area is -

ক
ক) 2 : 3
খ
খ) 3 : 2
গ
গ) 7 : 5
ঘ
ঘ) 4 : 9

সঠিক উত্তর: ঘ

ঘ) 4 : 9

উত্তর

সঠিক উত্তর: ঘ

ঘ) 4 : 9

ঘ

ব্যাখ্যা

The ratio of the volume of two cubes = 8 : 27
Let
a and b the sides of the first cube and second cube respectively
Now
a³: b³ = 8 : 27
⇒ a³ : b³ = 2³ : 3³
⇒ a/b = 2/3

Surface area of cubes =6(side)²

6a²/6b² = a²/b²
= 2²/3²
= 4/9
= 4 : 9

১৩,৪৮৯.

The price of a pen is 25% more than the price of a book. The price of a pen holder is 50% more than the price of the book. How much is the price of the pen holder more than the price of the pen?

ক
20%
খ
25%
গ
35%
ঘ
15%

সঠিক উত্তর: ক

20%

উত্তর

সঠিক উত্তর: ক

20%

ক

ব্যাখ্যা

Let price of book = 100tk

Price of pen = 100 + 100 × 25% = 125 tk
Price of pen-holder = 100 + 100 × 50% = 150 tk

Difference is = 150 -125 = 25 tk

∴ Percentage = (25 × 100)/125 = 20%

১৩,৪৯০.

মা ও মেয়ের বর্তমান বয়সের অনুপাত ৭ : ২। ৫ বছর পর তাদের বয়সের অনুপাত হবে ৮ : ৩। ১০ বছর পর মেয়ের বয়স কত হবে?

ক
২০ বছর
খ
৩০ বছর
গ
৩৫ বছর
ঘ
২৫ বছর
ঙ
কোনোটিই নয়

সঠিক উত্তর: ক

২০ বছর

উত্তর

সঠিক উত্তর: ক

২০ বছর

ক

ব্যাখ্যা

প্রশ্ন: মা ও মেয়ের বর্তমান বয়সের অনুপাত ৭ : ২। ৫ বছর পর তাদের বয়সের অনুপাত হবে ৮ : ৩। ১০ বছর পর মেয়ের বয়স কত হবে?

সমাধান:
ধরি,
মায়ের বর্তমান বয়স = ৭ক বছর
মেয়ের বর্তমান বয়স = ২ক বছর

৫ বছর পর,
মায়ের বয়স হবে = ৭ক + ৫
মেয়ের বয়স হবে = ২ক + ৫

প্রশ্নানুসারে,
(৭ক + ৫)/(২ক + ৫) = ৮/৩
⇒ ৩(৭ক + ৫) = ৮(২ক + ৫)
⇒ ২১ক + ১৫ = ১৬ক + ৪০
⇒ ২১ক - ১৬ক = ৪০ - ১৫
⇒ ৫ক = ২৫
∴ ক = ৫

∴ মেয়ের বর্তমান বয়স = ২ক = ২ × ৫ = ১০ বছর
∴ ১০ বছর পর মেয়ের বয়স = ১০ + ১০ = ২০ বছর

১৩,৪৯১.

48.95 - 32.006 =?

ক
ক) 16.089
খ
খ) 16.35
গ
গ) 16.944
ঘ
ঘ) 16.89

সঠিক উত্তর: গ

গ) 16.944

উত্তর

সঠিক উত্তর: গ

গ) 16.944

গ

ব্যাখ্যা

Question: 48.95 - 32.006 =?

Solution:
48.95 - 32.006
= 16.944

১৩,৪৯২.

If the word CLEAR is written as 90847 and SEARP is written as 58476. Find the code for RESALE-

ক
586048
খ
450875
গ
587490
ঘ
785408

সঠিক উত্তর: ঘ

785408

উত্তর

সঠিক উত্তর: ঘ

785408

ঘ

ব্যাখ্যা

Question: If the word CLEAR is written as 90847 and SEARP is written as 58476. Find the code for RESALE-

Solution:
Given,
C = 9
L = 0
E = 8
A = 4
R = 7

and,
S = 5
E = 8
A = 4
R = 7
P = 6

Similarly,
R = 7
E = 8
S = 5
A = 4
L = 0
E = 8

১৩,৪৯৩.

The sum of the numbers is 184. If one-third of the one exceeds one-seventh of the other by 8, find the smaller number.

ক
ক) 72
খ
খ) 44
গ
গ) 64
ঘ
ঘ) 40

সঠিক উত্তর: ক

ক) 72

উত্তর

সঠিক উত্তর: ক

ক) 72

ক

ব্যাখ্যা

Let the numbers be x and (184-x).
Then,
x/3 - (184 -x)/7 = 8
⇒ 7x – 3(184-x) = 168
⇒ 10x = 720
⇒ x = 72.
So, the numbers are 72 and 112.
Hence, a smaller number = 72.

১৩,৪৯৪.

If A and B can complete a piece of work together in 10 days and B alone in 20 days, in how many days can A alone complete the work?

ক
ক) 30 days
খ
খ) 40 days
গ
গ) 60 days
ঘ
ঘ) 20 days

সঠিক উত্তর: ঘ

ঘ) 20 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 20 days

ঘ

ব্যাখ্যা

Question: If A and B can complete a piece of work together in 10 days and B alone in 20 days, in how many days can A alone complete the work?

solution:
A and B complete a work in = 10 days
One day's work of (A + B) = 1/10

B complete the work in = 20 days;
One day's work of B = 1/20

Then, A's one day's work = 1/10 - 1/20
= 1/20

so, A can do the work alone in 20 days.

১৩,৪৯৫.

If 2 is added to the numerator of a fraction, the fraction becomes 1. If 9 is added to the denominator, the fraction becomes 1/2. Find the fraction.

ক
11/13
খ
12/14
গ
13/15
ঘ
9/11

সঠিক উত্তর: ক

11/13

উত্তর

সঠিক উত্তর: ক

11/13

ক

ব্যাখ্যা

Question: If 2 is added to the numerator of a fraction, the fraction becomes 1. If 9 is added to the denominator, the fraction becomes 1/2. Find the fraction.

Solution:
ধরি,
লব x, হর y
শর্তমতে,
(x +2)/y = 1
⇒ x + 2 = y ................(1)

আবার,
x/(y + 9) = 1/2
⇒ 2x = y + 9
⇒ 2x - 9 = y ..................(2)

(1) ও (2) হতে পাই,
2x - 9 = x + 2
⇒ x = 11

x এর মান (1) নং এ বসিয়ে পাই,
11 + 2 = y
⇒ y = 13

∴ ভগ্নাংশটি 11/13

১৩,৪৯৬.

The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is-

ক
ক) 10 years
খ
খ) 15 years
গ
গ) 12 years
ঘ
ঘ) 9 years

সঠিক উত্তর: ঘ

ঘ) 9 years

উত্তর

সঠিক উত্তর: ঘ

ঘ) 9 years

ঘ

ব্যাখ্যা

প্রশ্ন: The average age of three boys is 15 years. If their ages are in ratio 3 : 5 : 7, the age of the youngest boy is-

সমাধান:
The average age of three boys is 15 years
∴ Sum of ages of three boys = 45 years

Their ages are in ratio 3 : 5 : 7
Now,
3x + 5x + 7x = 45
⇒ 15x = 45
∴ x = 3

∴ Age of youngest boy is = 3x
= 3 × 3 years
= 9 years

১৩,৪৯৭.

5.6 can be expressed in terms of percentage as

ক
ক) 56%
খ
খ) 5.6%
গ
গ) 560%
ঘ
ঘ) 0.56%

সঠিক উত্তর: গ

গ) 560%

উত্তর

সঠিক উত্তর: গ

গ) 560%

গ

ব্যাখ্যা

5.6 × 100/100
⇒ (5.6 × 100) × (1/100)
= (5.6 × 100)%
= 560%

∴ 5.6 is 560%.

১৩,৪৯৮.

A mother is 30 times older in comparison to her daughter. After the period of 18 year , the mother's age would be thrice in the comparison of his daughter. In that case tell about the present age of the mother.

ক
32
খ
39
গ
45
ঘ
33
ঙ
40

সঠিক উত্তর: ঙ

উত্তর

সঠিক উত্তর: ঙ

ঙ

ব্যাখ্যা

Let, a daughter’s present age be x year.
In that case mother present age would be = 30x years
30x + 18 = 3 (x + 18)
⇒ 27x = 36
⇒ x = 4/3
∴ So the present age of mother = (30 × 4/3)
= 40 years.

১৩,৪৯৯.

Niloy walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles?

ক
318 minutes
খ
322 minutes
গ
324 minutes
ঘ
328 minutes

সঠিক উত্তর: গ

324 minutes

উত্তর

সঠিক উত্তর: গ

324 minutes

গ

ব্যাখ্যা

Question: Niloy walks at a rate of 10 mph. After every ten miles, he rests for 6 minutes. How much time does he take to walk 50 miles?

Solution:
Niloy needs time = 50/10 = 5 hours
= (5 × 60)
= 300 minutes

He will also rest 4 times after 10, 20, 30 and 40 miles
Total resting time = 4 × 6 = 24 minutes.

Total time = 300 + 24 = 324 minutes

১৩,৫০০.

A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 cm. Find the value of CB.

ক
9 cm
খ
12.5 cm
গ
10.5 cm
ঘ
None of the above

সঠিক উত্তর: গ

10.5 cm

উত্তর

সঠিক উত্তর: গ

10.5 cm

গ

ব্যাখ্যা

Question: A circle of radius 3 cm is drawn inscribed in a right angle triangle ABC, right angled at C. If AC is 10 cm. Find the value of CB.
(ABC ত্রিভুজটা একটা সমকোণ ত্রিভুজ, আর C তে সমকোণ। এখন ত্রিভুজের ভিতরে ৩ সেমি ব্যাসার্ধের একটা বৃত্ত আঁকা হয়েছে। যদি AC এর দৈর্ঘ্য ১০ সেমি হয়, তাহলে CB কত হবে?)

Solution:

(বাহিরের বিন্দু থেকে আঁকা স্পর্শক দুটি সমান হয়)
(x + 7)² = 10² + (x + 3)²
⇒ x² + 14x + 49 = 100 + x² + 6x + 9
⇒ 8x = 60
∴ x = 7.5cm

∴ CB = x + 3 = 7.5 + 3 = 10.5 cm