Bank Math

PrepBank · পাতা ৩১ / ১৬১ · ৩,০০১–৩,১০০ / ১৬,১২৪

৩,০০১.

Painting : Frame :: Book :?

ক
Cover
খ
Pages
গ
Money
ঘ
Writer

ব্যাখ্যা

Question: Painting : Frame :: Book :?

Solution:
We know, Cover is used to protect book in same way a frame is use to protect painting.

৩,০০২.

If January 1, 2025 is on a Wednesday, what day will January 1, 2027 fall on?

ক
Sunday
খ
Wednesday
গ
Friday
ঘ
Saturday

ব্যাখ্যা

Question: If January 1, 2025 is on a Wednesday, what day will January 1, 2027 fall on?

Solution:
Except for a leap year, the first and last days of every year fall on the same day of the week. In a leap year, one extra day must be added.

The year 2025 is not a leap year.
If January 1st, 2025, is a Wednesday, then the last day of the year will also be a Wednesday.

January 1st, 2026, will be a Thursday.
The last day of 2026 will also be a Thursday.

January 1st, 2027, will be a Friday.

৩,০০৩.

A circle and a rectangle have the same perimeter. The sides of the rectangle are 36 cm and 52 cm. what is the area of the circle?

ক
2412 sq.cm
খ
2426 sq.cm
গ
2448 sq.cm
ঘ
2464 sq.cm

ব্যাখ্যা

Question: A circle and a rectangle have the same perimeter. The sides of the rectangle are 36 cm and 52 cm. what is the area of the circle?

Solution:
Perimeter of the rectangle =2(36 + 52)
= 176 cm

∴ Circumference of circle = 176 cm
⇒ 2πr = 176
⇒ r = 176/2π
⇒ r = (176 × 7)/(2 × 22)
∴ r = 28 cm

∴ Area of circle = πr²
= (22/7) × (28)²
= 2464 sq.cm

৩,০০৪.

If 6 and x have the same mean as 2, 4 and 24, what is the value of x?

ক
ক) 5
খ
খ) 10
গ
গ) 14
ঘ
ঘ) 36
ঙ
ঙ) 29

ব্যাখ্যা

Question: If 6 and x have the same mean as 2, 4 and 24, what is the value of x?

Solution:
Mean of 2, 4 and 24 = (2 + 4 + 24)/3
= 30/3
= 10

Now, mean of 6 and x = (6 + x)/2
ATQ,
(6 + x)/2 = 10
⇒ 6 + x = 10×2
⇒ x = 20 - 6
∴ x = 14

৩,০০৫.

From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

ক
4 km/h
খ
5 km/h
গ
6 km/h
ঘ
7 km/h
ঙ
8 km/h

ব্যাখ্যা

Question: From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours. If A traveled with 2/3 of his speed and B traveled with double of his speed, they would have met after 5 hours. The speed of A is:

Solution:
Let the speed of A = x km/h and that of B = y km/h
ATQ,
(x × 6) + (y × 6) = 60
⇒ 6x + 6y = 60
⇒ 6(x + y) = 60
⇒ x + y = 10 .......... (1)

And, (2x/3) × 5 + (2y × 5) = 60
⇒ (10x/3) + 10y = 60
⇒ (10x + 30y)/3 = 60
⇒ 10x + 30y = 180
⇒ 10(x + 3y) 180
⇒ x + 3y = 18 .......... (2)

From equation (1) × 3 - (2)
3x + 3y = 30
⇒ x + 3y = 18
⇒ 2x = 12
∴ x = 6 km/h

৩,০০৬.

What is the value of 1 + {tan²A/(1 + secA)} ?

ক
cosecA
খ
cosA
গ
sinA
ঘ
secA

ব্যাখ্যা

Question: What is the value of 1 + {tan²A/(1 + secA)} ?

Solution:
1 + {tan²A/(1 + secA)}
= 1 + {(sce²A - 1)/(1 + secA)}
= {(1 + secA) + (sce²A - 1)}/(1 + secA)
= (1 + secA + sce²A - 1)/(1 + secA)
= (secA + sce²A)/(1 + secA)
= secA(1 + secA)/(1 + secA)
= secA

৩,০০৭.

The price of a t-shirt is Tk. 50. If you buy more than 3 shirts, you will get 12% discount. How much do you have to pay if you buy 8 shirts?

ক
Tk. 370
খ
Tk. 350
গ
Tk. 352
ঘ
Tk. 358

ব্যাখ্যা

Question: The price of a t-shirt is Tk. 50. If you buy more than 3 shirts, you will get 12% discount. How much do you have to pay if you buy 8 shirts?

Solution:
The price of 1 t-shirt 50
∴ The price of 8 t-shirt (50 × 8)
= 400

If price 100 then have to be paid 88
If price 1 then have to be paid 88/100
If price 400 then have to be paid (88 × 400)/100
= 352

৩,০০৮.

A and B can do a piece of work in 20 days and 30 days respectively. They began to work together but A leaves after some time, and B completed the remaining work in 10 days. After how many days did A leave?

ক
5 days
খ
8 days
গ
7 days
ঘ
10 days

ব্যাখ্যা

Question: A and B can do a piece of work in 20 days and 30 days respectively. They began to work together but A leaves after some time, and B completed the remaining work in 10 days. After how many days did A leave?

Solution:
Work done by B in 10 days = (1/30 × 10) part
= 10/30
= 1/3 part

Remaining work = 1 - 1/3 = 2/3 part

(A + B)'s 1 day's work = (1/20 + 1/30) part
= (3/60 + 2/60) = 5/60
= 1/12 part

Now, 1/12 part work is done by (A + B) in 1 day
∴ 1 part work is done by (A + B) in 12 days

∴ 2/3 part work is done by (A + B) in = 12 × (2/3) = 8 days

∴

৩,০০৯.

A train starts from a place A at 8 : 00 a.m. and arrives at another place B at 1 : 30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

ক
165
খ
175
গ
150
ঘ
135

ব্যাখ্যা

Question: A train starts from a place A at 8 : 00 a.m. and arrives at another place B at 1 : 30 p.m. on the same day. If the speed of the train is 30 km/hr, then what will be the distance (in km) covered by the train?

Solution:
সকাল ৮ : ০০ টা থেকে দুপুর ১ : ৩০ টা পর্যন্ত
মোট সময় = ৫ ঘণ্টা ৩০ মিনিট = ৫.৫ ঘণ্টা

∴ ট্রেনের মোট অতিক্রান্ত দূরত্ব = ৩০ × ৫.৫ কিলোমিটার
= ১৬৫ কিলোমিটার

৩,০১০.

The difference in Taka between simple and compound interest at 10% annually on a sum of Tk. 8,000 after 2 years is:

ক
Tk. 12.5
খ
Tk. 34
গ
Tk. 54
ঘ
Tk. 80

ব্যাখ্যা

Question: The difference in Taka between simple and compound interest at 10% annually on a sum of Tk. 8,000 after 2 years is:

Solution:
Given that,
Principal, P = Tk. 8,000
Rate, r = 10%
Time, n = 2 years

We know that,
Simple Interest = Pnr/100
= (8000 × 2 × 10)/100
= 1600 Tk.

And Compound Interest = P(1 + r/100)ⁿ - P
= 8000(1 + 10/100)² - 8000
= 8000(11/10)² - 8000
= 8000(1.21) - 8000
= 9680 - 8000
= 1680 Tk.

∴ Difference = 1680 - 1600 = 80 Tk.
The difference between compound and simple interest is Tk. 80.

৩,০১১.

A dice is thrown. What is the probability that the number shown on the dice is even number ?

ক
ক) 1/4
খ
খ) 1/6
গ
গ) 1/3
ঘ
ঘ) 1/2

ব্যাখ্যা

Question: A dice is thrown. What is the probability that the number shown on the dice is even number ?

Solution:
When a dice is thrown once.
The total number of outcomes is 6 (1, 2, 3, 4, 5, and 6)
Even numbers = 3 (2, 4, 6)

Probability = No of Favorable Outcomes/Total no of Outcomes
P(Even numbers) = 3/6
= 1/2

∴ The required probability is 1/2

৩,০১২.

The product of two co-prime numbers is 342. Then their LCM is =?

ক
272
খ
342
গ
552
ঘ
756

ব্যাখ্যা

Question: The product of two co-prime numbers is 342. Then their LCM is =?

Solution:
We know,
If the HCF of two or more numbers is 1, then two or more numbers are co-prime numbers.
HCF of co-prime number is always = 1

Now,
Product of number = LCM × HCF
⇒ LCM × 1 = 342
⇒ LCM = 342

৩,০১৩.

Mr. Danny spends Tk.10000 monthly on average for the first four months and Tk.12000 monthly for the next eight months and saves Tk.26000 a year. His average monthly income is-

ক
ক) TK. 12500
খ
খ) TK. 14500
গ
গ) TK. 13500
ঘ
ঘ) TK.14000
ঙ
ঙ) TK.13800

ব্যাখ্যা

Total annual income
= TK (10000 X 4 + 12000 X 8 + 26000)
= TK. 162000
Average monthly income = TK 16200012 = TK. 13500

৩,০১৪.

Anik and Shuvo are working on a special assignment. Anik needs 6 hours to type 32 pages on a computer and Shuvo needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 110 pages?

ক
ক) 7 hour 30 minutes
খ
খ) 8 hour 15 minutes
গ
গ) 7 hour 15 minutes
ঘ
ঘ) 8 hour 30 minutes

ব্যাখ্যা

Pages typed by Anik in 1 hour = 32/6 = 16/3
Pages typed by Shuvo in 1 hour = 40/5 = 8

Pages typed by Anik and Shuvo in 1 hour = 16/3 + 8 = 40/3
Time taken to type 110 pages when Anik and Shuvo work together = 110 × 3 /40 = 33/4
= 8 (1/4) hours = 8 hour 15 minutes.

৩,০১৫.

The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

ক
372
খ
388
গ
400
ঘ
420
ঙ
None of these

ব্যাখ্যা

Question: The product of two numbers is 9375 and the quotient, when the larger one is divided by the smaller, is 15. The sum of the numbers is:

Solution:
Let, the numbers be x and y and x is greater than y.

As given,
xy = 9375 ....(i)
And, x/y = 15
⇒ x = 15y

∴ From equation (i),
15y × y = 9375
⇒ y² = 9375/15
⇒ y² = 625
⇒ y = √625
⇒ y = 25

∴ x = (15 × 25) = 375

So, the requried solution is = x + y
= 375 + 25
= 400

৩,০১৬.

A 240 m long train passed a pole in 24 seconds. How long will it take to pass a 650 m long platform?

ক
ক) 89 sec
খ
খ) 91 sec
গ
গ) 96 sec
ঘ
ঘ) 99 sec

ব্যাখ্যা

Train’s speed = 240/24 = 10 m/s
The train has to cover = (240 + 650) = 890 m.
∴ Required time = 890/10 = 89 seconds

৩,০১৭.

An article when sold at a gain of 5% yields Tk. 15 more than when sold at a loss of 5%. Its cost price would be -

ক
Tk 130
খ
Tk 150
গ
Tk 120
ঘ
Tk 110
ঙ
Tk 115

ব্যাখ্যা

At 5% profit, selling price = 100 + 5 = 105 tk
At 5% loss, selling price = 100 - 5 = 95 tk
Difference between selling price = 105 - 95 = 10 tk
When the difference 10, buying price is 100 tk
∴ When the difference is 15, buying price is (100 × 15)/10 tk
= 150 tk

৩,০১৮.

ACT, EGG, INK, ______ What is the next term in the series?

ক
EGG
খ
OLD
গ
TOY
ঘ
JOY

ব্যাখ্যা

Question: ACT, EGG, INK, ______ What is the next term in the series?

Solution:
In the English alphabet, there are five vowels (A, E, I, O, U).
Here, 1st position starts with A, 2nd position starts with E, 3rd position starts with I,

∴ the 4th position will start with O. So, the correct answer is OLD.

৩,০১৯.

30% of 10 is 10% of which?

ক
ক) 30
খ
খ) 60
গ
গ) 40
ঘ
ঘ) 600

ব্যাখ্যা

30% of 10 = 10% of z
⇒(30/100)×10=(10/100)×z
⇒3=z/10
So,z=30

৩,০২০.

Find the missing number-

ক
12
খ
28
গ
9
ঘ
13

ব্যাখ্যা

Question: Find the missing number-

Solution:
প্রথম চিত্রে,
(19 + 16)/5 = 35/5 = 7

দ্বিতীয় চিত্রে,
(24 + 16)/5 = 40/5 = 8

তৃতীয় চিত্রে,
(26 + 19)/5 = 45/5 = 9

৩,০২১.

If 2x - 3y = 6, then 6y - 4x = ?

ক
ক) -12
খ
খ) -6
গ
গ) 6
ঘ
ঘ) 12

ব্যাখ্যা

Given, 2x - 3y = 6 .... (i)
Lets (i) × (-2),
So, - 4x + 6y = - 12
Or, 6y - 4x = - 12

৩,০২২.

An umbrella marked at Tk. 80 is sold for Tk. 68. The rate of discount is:

ক
ক) 15%
খ
খ) 12%
গ
গ) 17.5%
ঘ
ঘ) 20%
ঙ
ঙ) 25%

ব্যাখ্যা

Discount = 80 - 68 = 12
Discount Rate = (12/80) × 100
= 15%

৩,০২৩.

The average of 7 consecutive odd numbers is 33. What is the average of the first and last numbers?

ক
ক) 31
খ
খ) 32
গ
গ) 33
ঘ
ঘ) 35

ব্যাখ্যা

Question: The average of 7 consecutive odd numbers is 33. What is the average of the first and last numbers?

Solution:

The middle number is = 33
So, the other numbers are = 27, 29, 31, 33, 35, 37, 39

The average of the first and last numbers is = (27 + 39)/2 = 66/2 = 33

৩,০২৪.

How many prime numbers are there between 110 and 120?

ক
0
খ
1
গ
3
ঘ
2

ব্যাখ্যা

Question: How many prime numbers are there between 110 and 120?

Solution:
The numbers from 110 to 120 are,
111, 112, 113, 114, 115, 116, 117, 118, 119

Now let's check which of these are prime numbers (divisible only by 1 and themselves).
111 = 3 × 37 = not prime
112 = even = not prime
113 = prime (only divisible by 1 and 113)
114 = even = not prime
115 = ends with 5 = divisible by 5 = not prime
116 = even = not prime
117 = 9 × 13 = not prime
118 = even = not prime
119 = 7 × 17 = not prime

∴ Only one number is prime 113

৩,০২৫.

To fill a tank, 28 buckets of water are required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four-fifth of its present?

ক
35
খ
28
গ
25
ঘ
None of the above

ব্যাখ্যা

Question: To fill a tank, 28 buckets of water are required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to four-fifth of its present?

Solution:

ধরি,
বালতির ধারণক্ষমতা x
ট্যাঙ্কের ধারণক্ষমতা 28x

আবার,
বালতির নতুন ধারণক্ষমতা (4x/5)

∴ প্রয়োজনীয় বালতির সংখ্যা = 28x/(4x/5)
= 28x × (5/4x)
= (7 × 5) টি
= 35 টি

৩,০২৬.

If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of 1/(log_{x + z}y) + 1/(log_{x - z}y).

ক
1
খ
2
গ
3
ঘ
4
ঙ
None of these

ব্যাখ্যা

Question: If x, y and z are the sides of a right angled triangle, where ‘z’ is the hypotenuse, then find the value of 1/(log_{x + z}y) + 1/(log_{x - z}y).

Solution:
Here x, y and z are the sides of a right angled triangle, so z² = x² + y².

ঋণাত্মক সংখ্যার লগারিদম হয় না বিধায়, সঠিক উত্তর: ঙ) None of these

৩,০২৭.

In a certain language ICEBERG is coded as GCEBERI, how is ICHNITE coded in that language?

ক
ECINHIT
খ
ECINHTI
গ
ECHNITI
ঘ
EHCNIIT

ব্যাখ্যা

Question: In a certain language ICEBERG is coded as GCEBERI, how is ICHNITE coded in that language?

Solution:
ICEBERG ⇔ GCEBERG
I ⇒ C ⇒ E ⇒ B ⇒ E ⇒ R ⇒ G
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
G ⇒ C ⇒ E ⇒ B ⇒ E ⇒ R ⇒ G

Here,
Letters of 1st and 7th position inter-change their position.
Letters of 3rd and 5th position also inter-change their position.
And the letters of even number position remain same.

I ⇒ C ⇒ H ⇒ N ⇒ I ⇒ T ⇒ E
1 ⇒ 2 ⇒ 3 ⇒ 4 ⇒ 5 ⇒ 6 ⇒ 7
E ⇒ C ⇒ I ⇒ N ⇒ H ⇒ T ⇒ I

∴ ICHNITE ⇔ ECINHTI

৩,০২৮.

A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is = ?

ক
ক) 1523
খ
খ) 1451
গ
গ) 1641
ঘ
ঘ) 1712

ব্যাখ্যা

LCM of 30, 36, 80 = 720
Number = 720 × K + 11 (K = 2)
Then the number = 720 × 2 + 11
= 1440 + 11
= 1451

৩,০২৯.

Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?

ক
90 km
খ
95 km
গ
100 km
ঘ
110 km

ব্যাখ্যা

Question: Two stations A and B are on a straight line. One train starts from A at 7 a.m. and travels towards B at 20 Kmph. Another train starts from B at 8 a.m. and travel towards A at a speed of 25 kmph. If they meet at 10 a.m., what is the distance between two stations A and B?

Solution:
train started at 7 a.m. traveled for (10 - 7) = 3 hour
so in 3 hour at 20 kmph, the train travelled (20 × 3) = 60 km

train started at 8 a.m. traveled for (10 - 8) = 2 hour
so in 2 hour at 25 kmph, the train travelled (25 × 2) = 50 km

∴ The distance between two station A and B is = (60 + 50) km
= 110 km

৩,০৩০.

The diameters of two cones are equal, If their slant heights be in the ratio of 5 : 7 then find the ratio of their Curved surface areas.

ক
5 : 1
খ
2 : 7
গ
5 : 7
ঘ
5 : 3

ব্যাখ্যা

Question: The diameters of two cones are equal, If their slant heights be in the ratio of 5 : 7 then find the ratio of their Curved surface areas.

Solution:
Given,
l₁ / l₂= 5/7
Now, curved surface area of first cone
= πrl₁
and curved surface area of second cone
= πrl₂
Therefore, Ratio
= πrl₁ / πrl₂
= l₁ / l₂
= 5 : 7

৩,০৩১.

'Boat is to sea', therefore 'Plane is to _____'

ক
ক) Fly
খ
খ) Air
গ
গ) Sky
ঘ
ঘ) Float

ব্যাখ্যা

Question: 'Boat is to sea', therefore 'Plane is to _____'

Solution:
নৌকা সমুদ্র দিয়ে চলাচল করে।
তেমনি উড়োজাহাজ আকাশে যাতায়াত করে।

৩,০৩২.

(0.01 × 0.001 × 0.1 × 10⁶) is equal to:

ক
1
খ
10
গ
20
ঘ
100

ব্যাখ্যা

Question: (0.01 × 0.001 × 0.1 × 10⁶) is equal to:

Solution:
Given expression,
(0.01 × 0.001 × 0.1 × 10⁶)
= (1/100) × (1/1000) × (1/10) × 10⁶
= 10⁶/10⁶
= 10^{(6 - 6)}
= 10⁰
= 1

৩,০৩৩.

The average of 80 numbers is 42. When 5 more numbers are included, the average of 85 numbers becomes 45. Find the average of 5 numbers.

ক
ক) 45
খ
খ) 48
গ
গ) 75
ঘ
ঘ) 93

ব্যাখ্যা

Question: The average of 80 numbers is 42. When 5 more numbers are included, the average of 85 numbers becomes 45. Find the average of 5 numbers.

Solution:
Sum of 80 numbers= 80 × 42 = 3360
Now, Sum of 85 numbers = 85 × 45 = 3825
Hence, the sum of 5 numbers = 3825 - 3360 = 465
Average of five numbers = 465/5 = 93

৩,০৩৪.

The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father is -

ক
ক) 35 years
খ
খ) 40 years
গ
গ) 30 years
ঘ
ঘ) 25 years

ব্যাখ্যা

ধরি
পিতার বর্তমান বয়স = ৭x বছর
পুত্রের বর্তমান বয়স = ২x বছর
প্রশ্নমতে,
(৭x + ১০)/(২x + ১০) = ৯/৪
২৮x + ৪০ = ১৮x + ৯০
২৮x - ১৮x = ৯০ - ৪০
১০x = ৫০
x = ৫

পিতার বর্তমান বয়স = (৭ × ৫)বছর = ৩৫ বছর

৩,০৩৫.

A cylinder has a radius of 50 cm and a height of 100 cm. Find the volume of the cylinder.

ক
196250 cm³
খ
3140000 cm³
গ
785000 cm³
ঘ
7850 cm³
ঙ
None of these

ব্যাখ্যা

Question: A cylinder has a radius of 50 cm and a height of 100 cm. Find the volume of the cylinder.

Solution:
We know the volume of a cylinder is given by the formula = πr²h, where r is the radius of the cylinder and h is the height.

Therefore, putting the values, we get,
V = πr²h
= 3.14 × 50² × 100
= 785000 cm³

৩,০৩৬.

If log_x(144) = 4 then x = ?

ক
2√3
খ
4
গ
3
ঘ
3√2

ব্যাখ্যা

Question: If log_x(144) = 4 then x = ?

Solution:
Given that,
log_x(144) = 4
⇒ x⁴ = 144
⇒ x⁴ = (2√3)⁴
∴ x = 2√3

৩,০৩৭.

A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is-

ক
5.15 kmph
খ
4.4 kmph
গ
4.25 kmph
ঘ
4.14 kmph

ব্যাখ্যা

Question: A and B take part in 100 m race. A runs at 5 kmph. A gives B a start of 8 m and still beats him by 8 seconds. The speed of B is-

Solution:

A's speed = 5 × (5/18) m/sec = 25/18 m/sec.

Time taken by A to cover 100 m = 100 × (18/25) sec = 72 sec.
∴ Time taken by B to cover 92 m = (72 + 8) = 80 sec.

B's speed = (92/80) ×(18/5) kmph = 4.14 kmph.

৩,০৩৮.

A certain amount of money earning simple interest becomes 7/5th of the initial amount in 4 years. What is the interest rate?

ক
ক) 4%
খ
খ) 6%
গ
গ) 8%
ঘ
ঘ) 10%

ব্যাখ্যা

Questtion: A certain amount of money earning simple interest becomes 7/5th of the initial amount in 4 years. What is the interest rate?

Solution:
মনেকরি
আসল P = 100 টাকা
মুনফা- আসল A = 100 এর 7/5 = 140 টাকা
মুনাফা I = 140 - 100 = 40 টাকা
সময় n = 4 বছর
মুনাফার হার r = ?

আমরাজানি
I = Pnr
r = I/Pn
= (40 × 100)/(100 × 4)
= 10%

৩,০৩৯.

The volume of a sphere is the same as the volume of a right circular cylinder whose radius is 4 cm and height is 18 cm. What is the radius of the sphere?

ক
6 cm
খ
8 cm
গ
10 cm
ঘ
14 cm

ব্যাখ্যা

Question: The volume of a sphere is the same as the volume of a right circular cylinder whose radius is 4 cm and height is 18 cm. What is the radius of the sphere?

Solution:
ধরি, গোলকের ব্যাসার্ধ = r₁
এবং বেলনের ব্যাসার্ধ = r₂

দেওয়া আছে,
বেলনের ব্যাসার্ধ, r₂ = 4 সেমি
বেলনের উচ্চতা, h = 18 সেমি

আমরা জানি,
গোলকের আয়তন = (4/3)πr₁³
বেলনের আয়তন = πr₂²h

প্রশ্নমতে,
গোলকের আয়তন = বেলনের আয়তন
(4/3)πr₁³ = πr₂²h
⇒ (4/3)r₁³ = (4)² × 18
⇒ (4/3)r₁³ = 16 × 18
⇒ 4r₁³ = 16 × 18 × 3
⇒ r₁³ = (16 × 18 × 3)/4
⇒ r₁³ = 4 × 18 × 3
⇒ r₁³ = 216
⇒ r₁ = 6

∴ গোলকের ব্যাসার্ধ = 6 সেমি

৩,০৪০.

On February 5, 1998, it was Thursday. The day of the week on February 5, 1997, was-

ক
Wednesday
খ
Monday
গ
Friday
ঘ
Sunday

ব্যাখ্যা

Question: On February 5, 1998, it was Thursday. The day of the week on February 5, 1997, was-

Solution:
1997 was an ordinary year, it had 1 odd day. So, the day on February 5, 1998, would be one day beyond the day on February 5, 1997.

∴ Thursday on February 5, 1998, would be one day beyond the day on February 5, 1997, so the day on February 5, 1997, was Wednesday.

৩,০৪১.

A bus is running at 60 km/hr speed. How far the bus will travel in 3 min. 30 sec.?

ক
5 km
খ
4.5 km
গ
3.5 km
ঘ
4 km

ব্যাখ্যা

Question: A bus is running at 60 km/hr speed. How far the bus will travel in 3 min. 30 sec.?

Solution:
3 min. 30 sec. = 180 + 30 sec. = 210 sec.

In 3600 sec. the bus travels 60 km.
∴ In 210 sec. the bus travels (60 × 210)/3600 km.
= 3.5 km.

৩,০৪২.

If x = 2 then the value of x³ + 27x² + 243x + 631 is -

ক
ক) 1222
খ
খ) 1232
গ
গ) 1133
ঘ
ঘ) 1233

ব্যাখ্যা

Question: If x = 2 then the value of x³ + 27x² + 243x + 631 is -

Solution:
Given,
x = 2
Now,
x³ + 27x² + 243x + 631
= x³ + 3 . x² . 9 + 3 . x . 9² + 9³ - 98
= (x + 9)³ - 98
= (2 + 9)³ - 98
= 1331 - 98
= 1233

৩,০৪৩.

If (x - 1) is an odd number, what are the two other odd numbers nearest to it?

ক
x, x - 1
খ
x - 3, x + 5
গ
x - 3, x + 1
ঘ
x, x - 2

ব্যাখ্যা

Question: If (x - 1) is an odd number, what are the two other odd numbers nearest to it?

Solution:
(x - 1) is an odd number

The previous odd number = x - 1 - 2 = x - 3
The next odd number = x - 1 + 2 = x + 1

So, the two required odd numbers are: x - 3, x + 1

৩,০৪৪.

A rectangular hall measures 10 meters in length and 6 meters in width. If carpeting costs Tk. 15 per square meter, what will be the total cost to carpet the entire hall?

ক
Tk. 700
খ
Tk. 900
গ
Tk. 1000
ঘ
Tk. 500

ব্যাখ্যা

Question: A rectangular hall measures 10 meters in length and 6 meters in width. If carpeting costs Tk. 15 per square meter, what will be the total cost to carpet the entire hall?

Solution:
Area of the hall = Length × Width
= 10 × 6 = 60 m²

Cost of carpet = Area × Cost per m²
= 60 × 15
= Tk. 900

৩,০৪৫.

A fraction’s numerator is cut down by 25%, and its denominator grows by 250%. If this produces a fraction of 6/5, what is the original fraction?

ক
49/5
খ
32/9
গ
24/5
ঘ
28/5

ব্যাখ্যা

Question: A fraction’s numerator is cut down by 25%, and its denominator grows by 250%. If this produces a fraction of 6/5, what is the original fraction?

Solution:
Let the numerator is x and the denominator is y

x is decreased by 25%.

so, new numerator = x - 25% of x
= x - x/4 = 3x/4 = 0.75x

y is increased by 250%

so, new denominator = y + 250% of y
= y + 2.5y
= 3.5y

ATQ,
0.75x / 3.5y = 6/5
x/y = (6 × 3.5)/(5 × 0.75)
= 28/5

৩,০৪৬.

There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

ক
Tk. 4250
খ
Tk. 3972
গ
Tk. 3886
ঘ
Tk. 3735

ব্যাখ্যা

Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of 12,000 after 3 years at the same rate?

Solution:
Let,
the simple interest rate = r%

Given,
60% increase in an amount in 6 years at simple interest
∴ If P = Tk. 100, then I = Tk. 60

Then,
I = Pnr/100
⇒ I/P = nr/100
⇒ 60/100 = 6r/100
⇒ 0.6 = 6r/100
⇒ r = 10%

Now,
P = Tk. 12000
n = 3 years
r = 10%

We know,
The compound interest = P(1 + r)ⁿ - P
= 12000 (1.1)³ - 12000
= 12 × 1331 - 12000
= 15972 - 12000
= Tk. 3972

৩,০৪৭.

The ratio of the ages of a father and his son is 8 : 3 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What was the father's present age?

ক
56 years
খ
96 years
গ
78 years
ঘ
66 years

ব্যাখ্যা

Question: The ratio of the ages of a father and his son is 8 : 3 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What was the father's present age?

Solution:
ধরি, পিতার বর্তমান বয়স = 8x বছর
এবং পুত্রের বর্তমান বয়স = 3x বছর

ছয় বছর আগে,
পিতার বয়স = 8x − 6 বছর
পুত্রের বয়স = 3x − 6 বছর

প্রদত্ত শর্ত,
(8x − 6)/(3x − 6) = 3/1
9x - 18 = 8x - 6
9x - 8x = 18 - 6
x = 12

∴ পিতার বর্তমান বয়স = 8x = 8 × 12 = 96 বছর

৩,০৪৮.

The L.C.M of 1/3, 5/6, 2/9, 4/27 is?

ক
10/27
খ
1/54
গ
24/7
ঘ
20/3

ব্যাখ্যা

Question: The L.C.M of 1/3, 5/6, 2/9, 4/27 is?

Solution:
L.C.M of 1, 5, 2, 4 is 20
H.C.F of 3, 6, 9, 27 is 3

We know,
Required L.C.M = L.C.M of 1, 5, 2, 4/H.C.F of 3, 6, 9, 27
= 20/3

৩,০৪৯.

If x + y = 7 and x - y =3, then x²- y² =

ক
ক) -4
খ
খ) 4
গ
গ) 10
ঘ
ঘ) 21

ব্যাখ্যা

x² - y²
= (x + y)(x - y)
= 7 × 3
= 21

৩,০৫০.

What is the ratio of one third of 7/15 and two third of the same number?

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

ব্যাখ্যা

Question: What is the ratio of one third of 7/15 and two third of the same number?

Solution:
one third of 7/15 is {(1/3) × (7/15)} = 7/45
two third of 7/15 is {(2/3) × (7/15)} = 14/45

ratio = 7/45 : 14/45 = 1 : 2

৩,০৫১.

The sum of two numbers is 21 and the sum of their squares is 333. The product of two numbers is -

ক
ক) 40
খ
খ) 49
গ
গ) 54
ঘ
ঘ) 58

ব্যাখ্যা

Let, the numbers be x and y
According to the question, x + y = 21 ......(i) and x² + y² = 333 ......(ii)
∴ (x + y)² = x² + y² + 2xy
⇒ (21)² = 333 + 2xy
⇒ 441 = 333 + 2xy
⇒ 2xy = 108
⇒ xy = 54

৩,০৫২.

Find the value of
is -

ক
ক) 1/2
খ
খ) 1/3
গ
গ) 1/4
ঘ
ঘ) - 1/4

ব্যাখ্যা

Question: Find the value of
is -

Solution:
এখানে,

= 1/4

৩,০৫৩.

12 buckets of water fill a tank when the capacity of each tank is 13.5 litres How many buckets will be needed to fill the same tank, if the capacity of each bucket is 9 liters.

ক
8
খ
18
গ
16
ঘ
4

ব্যাখ্যা

ট্যাংকের ধারণক্ষমতা = 12 × 13.5 = 162
দেয়া আছে, প্রতিটি বাকেটের ধারণক্ষমতা = ৯ লিটার
মোট বাকেট লাগবে = 162/9 = 18 টি
উত্তরঃ 18 টি

৩,০৫৪.

A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

ক
38 years
খ
40 years
গ
43 years
ঘ
45 years

ব্যাখ্যা

Question: A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

Solution:
Let the age of son = x years
∴ Age of mother would be = 2x years

As per question 20 years ago;
10 (x - 20) = 2x - 20
⇒ 10x - 200 = 2x - 20
⇒ 10x - 2x = - 20 + 200
⇒ 8x = 180
⇒ x = 180/8
∴ x = 22.5

∴ Mother's age is = 2 × 22.5 = 45 years

৩,০৫৫.

If the height of a tringle is increased by 60% and its base is decreased by 30%, what will be the effect on its area?

ক
12% Increase
খ
12% decrease
গ
112% increase
ঘ
No change

ব্যাখ্যা

Question: If the height of a tringle is increased by 60% and its base is decreased by 30%, what will be the effect on its area?

Solution:
ধরি,
ত্রিভুজের উচ্চতা = 10 একক
ভূমি = 10 একক
∴ ত্রিভুজের ক্ষেত্রফল = (1/2) × 10 × 10 = 50 বর্গ একক

আবার,
উচ্চতা 60% বৃদ্ধি করলে নতুন উচ্চতা = 10 + 10 এর 60% = 10 + 6 = 16 একক
ভূমি 30% হ্রাস করলে হ্রাসকৃত ভূমি = 10 - 10 এর 30% = 10 - 3 = 7 একক

∴ নতুন ত্রিভুজের ক্ষেত্রফল = (1/2) × 16 × 7 = 56 বর্গ একক

∴ ক্ষেত্রফল বৃদ্ধি পেয়েছে = (56 - 50) বর্গ একক = 6 বর্গ একক

এখন, ক্ষেত্রফল,
50 বর্গ এককে বৃদ্ধি পেয়েছে = 6 বর্গ একক
∴ বর্গ এককে বৃদ্ধি পেয়েছে = 6/50 বর্গ একক
∴ 100 বর্গ এককে বৃদ্ধি পেয়েছে = (6 × 100)/50 = 12 বর্গ একক

সুতরাং,
ক্ষেত্রফল বৃদ্ধি পেয়েছে = 12%

৩,০৫৬.

A milkman mixed some water with milk to gain 25% by selling the mixture at the cost price. The ratio of water and milk is respectively -

ক
1 : 10
খ
1 : 5
গ
1 : 4
ঘ
2 : 5

ব্যাখ্যা

Question: A milkman mixed some water with milk to gain 25% by selling the mixture at the cost price. The ratio of water and milk is respectively -

Solution:
ধরি,
১ লিটার দুধের ক্রয়মূল্য ১০০ টাকা
২৫% লাভে মিশ্রনের বিক্রয়মূল্য = (১০০ + ২৫) = ১২৫ টাকা

১০০ টাকার দুধ = ১ লিটার
১২৫ টাকার দুধ = (১২৫/১০০) = ৫/৪ লিটার।

কিন্তু মিশ্রনে দুধের পরিমান ১ লিটার।
∴ পানির পরিমান = (৫/৪) - ১ = ১/৪ লিটার।

∴ পানি : দুধ = ১/৪ : ১
= ১ : ৪

৩,০৫৭.

At what angle the hands of a clock are inclined at 15 minutes past 5?

ক
67.5°
খ
72.5°
গ
58.5°
ঘ
69.5°

ব্যাখ্যা

Question: At what angle the hands of a clock are inclined at 15 minutes past 5?

Solution:
Hours hand moves in 15 past.
5 from 12 p.m = (5 + 15/60) hours = 21/4 hours
Angle of hours hand = (360/12) × (21/4)
= 157.5°

Minutes hands makes angle of = (360/60) × 15
= 90°

Angle between hours and minutes hands = (157.5° - 90°)
= 67.5°

৩,০৫৮.

The volume of a cone is 300π cubic centimeters. If the radius of its base is 6 cm, what is the height of the cone?

ক
10 cm
খ
25 cm
গ
30 cm
ঘ
12 cm

ব্যাখ্যা

Question: The volume of a cone is 300π cubic centimeters. If the radius of its base is 6 cm, what is the height of the cone?

solution:
দেওয়া আছে,
কোণকের আয়তন, V = 300π ঘন সে.মি.
ভূমির ব্যাসার্ধ, r = 6 সে.মি.
ধরি, কোণকের উচ্চতা = h সে.মি.

আমরা জানি,
কোণকের আয়তন, V = 1/3 × π × r² × h
∴ 300π = 1/3 × π × 6² × h
⇒ 300 = 1/3 × 36 × h (π উভয় পক্ষ থেকে বাদ দিয়ে)
⇒ 300 = 12h
⇒ h = 300 / 12
∴ h = 25 সে.মি.

অতএব, কোণকটির উচ্চতা = 25 সে.মি.

৩,০৫৯.

The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is:

ক
5 : 2
খ
3 : 2
গ
1 : 2
ঘ
1 : 1

ব্যাখ্যা

Question: The ratio of the surface area of a sphere and the curved surface area of the cylinder circumscribing the sphere is:

Solution:
Let the radius of the sphere be r
Then, the radius of the cylinder = r
Height of the cylinder = 2r
Surface area of sphere = 4πr²

Surface area of the cylinder = 2πr(2r) = 4πr²

∴ Required ratio
= 4πr² : 4πr²
= 1 : 1

৩,০৬০.

X, Y, and Z started a business by investing Tk. 150000, Tk. 250000 and Tk. 100,000 respectively. Find the share of Y, out of an annual profit of Tk. 100,000.

ক
Tk. 30000
খ
Tk. 40000
গ
Tk. 50000
ঘ
Tk. 60000

ব্যাখ্যা

Question: X, Y, and Z started a business by investing Tk. 150000, Tk. 250000 and Tk. 100,000 respectively. Find the share of Y, out of an annual profit of Tk. 100,000.

Solution:
Ratio of shares of A, B and C = Ratio of their investment
X : Y : Z = 150000 : 250000 : 100000
= 3 : 5 : 2

∴ Total parts = 3 + 5 + 2 = 10

∴ Share of Y = Tk. [(100000 × 5)/ 10] = 50000

৩,০৬১.

Two bicycles start at the same time from points A and B, moving toward each other. If the distance between A and B is 125 km and their speeds are 14 km/h and 11 km/h respectively then after how much time will they meet each other?

ক
3.5 hours
খ
4.5 hours
গ
5 hours
ঘ
2.5 hours

ব্যাখ্যা

Question: Two bicycles start at the same time from points A and B, moving toward each other. If the distance between A and B is 125 km and their speeds are 14 km/h and 11 km/h respectively then after how much time will they meet each other?

Solution:
Given,
The distance between A and B = 125 km
Speed of 1^st bicycle = 14 km/h
Speed of 2^nd bicycle = 11 km/h

The bicycles are moving toward each other,
So their relative speed = (Speed of 1^st bicycle + Speed of 2^nd bicycle)
= (14 + 11) km/h
= 25 km/h

Time = (Distance ÷ relative speed)
= (125 ÷ 25)
= 5 h

৩,০৬২.

A person incurs a loss of 5% by selling a watch for Tk. 1,140. At what price should the watch be sold to earn 5% profit ?

ক
ক) Tk. 1,580
খ
খ) Tk. 1,180
গ
গ) Tk. 1,260
ঘ
ঘ) Tk. 1,225

ব্যাখ্যা

5% ক্ষতিতে
বিক্রয়মূল্য 95 টাকা হলে ক্রয়মূল্য 100 টাকা
বিক্রয়মূল্য 1 টাকা হলে ক্রয়মূল্য 100/95 টাকা
বিক্রয়মূল্য 1140 টাকা হলে ক্রয়মূল্য (100 × 1140)/95 টাকা
= 1200 টাকা

5% লাভে
ক্রয়মূল্য 100 টাকা হলে বিক্রয়মূল্য 105 টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য 105/100 টাকা
ক্রয়মূল্য ১ টাকা হলে বিক্রয়মূল্য (105 × 1200)/100 টাকা
= 1260 টাকা

৩,০৬৩.

Which of the following is equivalent to the pair of inequalities 2x - 5 > 3 and x + 4 ≤ 12?

ক
4 ≤ x < 16
খ
1 ≤ x < 4
গ
4 < x ≤ 8
ঘ
4 ≤ x < 8

ব্যাখ্যা

Question: Which of the following is equivalent to the pair of inequalities 2x - 5 > 3 and x + 4 ≤ 12?

Solution:
প্রথম অসমতাটি হলো:
⇒ 2x - 5 > 3
⇒ 2x > 3 + 5
⇒ 2x > 8
⇒ x > 4

দ্বিতীয় অসমতাটি হলো:
⇒ x + 4 ≤ 12
⇒ x ≤ 12 - 4
⇒ x ≤ 8

এখন প্রাপ্ত ফলাফল দুটিকে একত্রে সাজালে পাই:
4 < x এবং x ≤ 8
∴ 4 < x ≤ 8

৩,০৬৪.

Out of 7500 candidates 75% were offered to study in arts and 45% in Business. How many were offered both?

ক
ক) 1000
খ
খ) 1750
গ
গ) 2000
ঘ
ঘ) 1500
ঙ
ঙ) 2500

ব্যাখ্যা

Both offered = (75 + 45)% - 100% = 20%
Numbers of student offered both = 7500 × 20% = 1500

৩,০৬৫.

Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, then the tank shall be filled in:

ক
ক) 4.8 hr
খ
খ) 5 hr
গ
গ) 5.5 hr
ঘ
ঘ) 7 hr

ব্যাখ্যা

Question: Two pipes A and B can fill a tank in 6 hours and 4 hours respectively. If they are opened on alternate hours and if pipe A is opened first, then the tank shall be filled in:

Solution:
নল A ৬ ঘণ্টায় করে ১ অংশ
১ ঘণ্টায় করে ১/৬ অংশ

নল B ৪ ঘণ্টায় করে ১ অংশ
১ ঘণ্টায় করে ১/৪ অংশ

প্রথম ঘণ্টায় নল A, ২য় ঘণ্টায় নল B এভাবে ক্রমান্বয়ে নলগুলো কাজ করে।

দুটি নল একসাথে ২ ঘণ্টায় করে (১/৬) + (১/৪) অংশ
= ৫/১২ অংশ

৪ ঘণ্টায় করে ১০/১২ অংশ

বাকি থাকে ১ - ১০/১২
= ১/৬ অংশ ; যা নল A ১ ঘন্টায় সম্পূর্ণ করে।

সময় লাগবে = ৪ + ১ ঘণ্টা
= ৫ ঘণ্টা

৩,০৬৬.

Robin invests a part of Tk. 12000 in 12% stock at Tk. 120 and the remainder in 15% stock at Tk. 125. If his total dividend per annum is Tk. 1360, how much does he invest in 12% stock at Tk. 120?

ক
ক) Tk. 2500
খ
খ) Tk. 3500
গ
গ) Tk. 4000
ঘ
ঘ) Tk. 1500

ব্যাখ্যা

Let investment in 12% stock be Tk. x
Investment in 15% stock = 12000 – x

According to the question,
12/120 × x + 15/125 × (12000 – x) = 1360
x/10 + 3/25 (12000 – x) = 1360
5x + 72000 – 6x = 1360 × 50
x = 72,000 - 68,000
x = 4,000

৩,০৬৭.

Two cyclists start from P towards M, which is 150 km away, at the same time. The first cyclist moves at 30 km/h while the second cyclist moves at 20 km/h. After reaching M, the first cyclist immediately turns back and meets the second cyclist at L. What is the distance between M and L?

ক
25 km
খ
30 km
গ
35 km
ঘ
40 km

ব্যাখ্যা

Question: Two cyclists start from P towards M, which is 150 km away, at the same time. The first cyclist moves at 30 km/h while the second cyclist moves at 20 km/h. After reaching M, the first cyclist immediately turns back and meets the second cyclist at L. What is the distance between M and L?

Solution:
Speed of first cyclist : Speed of second cyclist :: 30:20 :: 3:2

Let's say the distance from M to La is x km
First cyclist's total distance = 150 + x (to M and back to L)
Second cyclist's distance = 150 - x (from P to L)

As distance is proportional to speed:
(150 + x) : (150 - x) :: 3:2
⇒ 2(150 + x) = 3(150 - x)
⇒ 300 + 2x = 450 - 3x
⇒ 2x + 3x = 450 - 300
⇒ 5x = 150
∴ x = 30
Therefore, L is 30 km away from M.

৩,০৬৮.

A clock is so placed that at 2:00 p.m. the minute hand points towards North-west. In which direction does the hour hand point at 6:00 p.m.?

ক
North-West
খ
North-East
গ
West
ঘ
South-East
ঙ
East

ব্যাখ্যা

If the Minute hand is at 12 which is North-West, then at 6.00 p.m. the hour hand will be pointing at the number 6. Since the numbers 12 and 6 are exactly the opposite. The opposite of the North-West should be South-East. Hence, option D is the correct answer.

৩,০৬৯.

If a rectangle has length m and the width is half of the length, the area of the rectangle is-

ক
ক) m²
খ
খ) 2m²
গ
গ) m²/2
ঘ
ঘ) m²/4

ব্যাখ্যা

Given that
length = m
Width = m/2

The area of the rectangle is = m(m/2) = m²/2

৩,০৭০.

The circumference of the back-sided wheel of a vehicle is 1 m greater than that of the front-side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the back-sided wheel is:

ক
4 m
খ
5 m
গ
6 m
ঘ
7 m

ব্যাখ্যা

Question: The circumference of the back-sided wheel of a vehicle is 1 m greater than that of the front-side wheel. To travel 600 m, the front wheel rotates 30 times more than the back wheel. The circumference of the back-sided wheel is:

Solution:
ধরি, সামনের চাকার পরিধি x m
পেছনের চাকার পরিধি = x + 1 m

600 m যেতে সামনের চাকা ঘোরে 600/x বার
600 m যেতে পেছনের চাকা ঘোরে 600/x + 1 বার

(600/x) - (600/x + 1) = 30
⇒ (x + 1 - x)/x (x + 1) = 30 / 600
⇒ 1/x² + x = 1/20
⇒ x² + x = 20
⇒ x² + x - 20 = 0
⇒ x² + 5x - 4x - 20 = 0
⇒ x (x + 5) - 4 (x + 5) = 0
⇒ (x + 5) (x - 4) = 0

x এর ঋণাত্মক মান গ্রহণযোগ্য নয়।
∴ x - 4 = 0
x = 4

পেছনের চাকার পরিধি = 4 + 1 = 5 m

৩,০৭১.

Salman and Rasel both have the same efficiency of work. If Salman finishes half of the work in 9 days. How much time will Rasel need to finish the rest of the work?

ক
ক) 18 days
খ
খ) 4.5 days
গ
গ) 9 days
ঘ
ঘ) 21 days

ব্যাখ্যা

Question: Salman and Rasel both have the same efficiency of work. If Salman finishes half of the work in 9 days. How much time will Rasel need to finish the rest of the work?

Solution:
যেহেতু সালমান এবং রাসেল উভয়ের দক্ষতা একই, তাদের একটি কাজ করতে একই সময় লাগবে।
তাহলে রাসেলের বাকি অর্ধেক কাজ শেষ করতেও ৯ দিন লাগবে।

৩,০৭২.

The G.C.D. of 1.08, 0.36 and 0.9 is -

ক
ক) 0.36
খ
খ) 0.24
গ
গ) 0.09
ঘ
ঘ) 0.18

ব্যাখ্যা

Question: The G.C.D. of 1.08, 0.36 and 0.9 is -

Solution:
১.০৮ = ১০৮/১০০ = ২৭/২৫
০.৩৬ = ৩৬/১০০ = ৯/২৫
০.৯ = ৯/১০

ভগ্নাংশের গ.সা.গু = ( লব সমূহের গ.সা.গু ) / ( হর সমূহের ল.সা.গু)
= (২৭,৯, ৯ এর গ.সা.গু)/(২৫,২৫,১০ এর ল.সা.গু)
= ৯/৫০
= ০.১৮

৩,০৭৩.

Train A crosses a stationary train B in 50 seconds, and a pole in 30 seconds with the same speed. The length of the train A is 270 meters. What is the length of the stationary train B?

ক
ক) 180 meters
খ
খ) 210 meters
গ
গ) 230 meters
ঘ
ঘ) 250 meters

ব্যাখ্যা

Solution: Train A crosses a stationary train B in 50 seconds, and a pole in 30 seconds with the same speed. The length of the train A is 270 meters. What is the length of the stationary train B?
Solution:
Speed of train A = (270/30) m/sec = 9 m/sec
Let the length of train B be x meters.
Then,
(270 + x)/9 = 50
⇒ 270 + x = 450
⇒ x = 180 meters

৩,০৭৪.

Two pipes A and B can fill the tank in 24 and 36 minutes, respectively. Both the pipes are opened together. After how many minutes should the pipe B be turned off, so that the tank be fill in 18 minutes?

ক
9 minutes
খ
12 minutes
গ
10 minutes
ঘ
16 minutes

ব্যাখ্যা

Question: Two pipes A and B can fill the tank in 24 and 36 minutes, respectively. Both the pipes are opened together. After how many minutes should the pipe B be turned off, so that the tank be fill in 18 minutes?

Solution:
Given that,
Pipe A fills the tank in 24 minutes.
Pipe B fills the tank in 36 minutes.
Total time to fill the tank = 18 minutes.
Now,
LCM of 24 and 36 = 72 (Total capacity of the tank).
Efficiency of pipe A = 72/24 = 3 units/minute.
Efficiency of pipe B = 72/36 = 2 units/minute.

Let,
pipe B be turned off after x minutes.
Pipe A works for 18 minutes.
Pipe B works for x minutes.
Work done by A in 18 minutes = 3 × 18 = 54 units.
Work done by B in x minutes = 2x = 2x units.

Total work done = 54 + 2x = 72
⇒ 2x = 72 - 54
⇒ 2x = 18
⇒ x = 18/2
∴ x = 9

∴ Pipe B should be turned off after 9 minutes.

৩,০৭৫.

If A = {a, b, r, t, s, y} and B = {e, d, f, r, s}, then B - A =

ক
{a, b, t, y}
খ
{r, s}
গ
{e, d, f}
ঘ
{a, b, d, e, f, t, y}

ব্যাখ্যা

Question: If A = {a, b, r, t, s, y} and B = {e, d, f, r, s}, then B - A =

Solution:
B - A = {e, d, f, r, s} - {a, b, r, t, s, y}
= {e, d, f}

৩,০৭৬.

The average weight of 25 students in a class was found to be 48 kg. Later it was discovered that one student's weight was recorded as 35 kg instead of 60 kg. What is the correct average weight of the 25 students?

ক
48 kg
খ
49 kg
গ
50 kg
ঘ
51 kg

ব্যাখ্যা

Question: The average weight of 25 students in a class was found to be 48 kg. Later it was discovered that one student's weight was recorded as 35 kg instead of 60 kg. What is the correct average weight of the 25 students?

Solution:
Given,
The average weight of 25 students in a class was found to be 48 kg
Incorrect sum of the weight of 25 students = (48 × 25) kg
= 1200 kg

Correct sum of the weight of 25 students = (incorrect sum) - (wrongly copied item) + (actual item)
= (1200 - 35 + 60) kg
= 1225 kg

Correct mean = correct sum/number of students
= (1225/25) kg
= 49 kg

∴ Hence, the correct mean weight is 49 kg

৩,০৭৭.

Badhan has 60 kg of 18% sugar solution. How much sugar should he add to make it 40% sugar solution?

ক
20 kg
খ
22 kg
গ
24 kg
ঘ
26 kg

ব্যাখ্যা

Sugar in solution = 60 × 18/100 = 10.8 kg
Water in solution = 60 - 10.8 = 49.2 kg
In 40% sugar solution, if solution is 100 kg, then sugar is 40 kg and water is 60 kg.
According to the question,
(10.8 + y)/49.2 = 40/60
Therefore, y = 22

৩,০৭৮.

100 kg of solution A is mixed with 60 kg of solution B. If solution A has tin and copper in the ratio 1 : 4 and solution B has lead and tin in the ratio 3 : 2, then what is the amount of tin in the new solution?

ক
ক) 70 kg
খ
খ) 36 kg
গ
গ) 44 kg
ঘ
ঘ) 56 kg

ব্যাখ্যা

A তে টিন আছে = (100 এর 1/5)
= 20 kg
A তে কপার আছে = (100 এর 4/5)
= 80 kg
B তে লেড আছে = (60 এর 3/5) = 36kg
B তে টিন আছে =(60 এর 2/5) = 24kg

নতুন মিশ্রণে টিন আছে = (20 + 24)kg = 44 kg

৩,০৭৯.

A train 300 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 300 m long?

ক
ক) 40 sec
খ
খ) 43 sec
গ
গ) 45 sec
ঘ
ঘ) 48 sec

ব্যাখ্যা

Question: A train 300 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 300 m long?

Solution:
Speed = (45 ×1000)/3600 m/s
= 12.5 m/s

Total distance to be covered = (300 + 300) m = 600 m.

∴ Required time = 600/12.5 = 48 sec

৩,০৮০.

A seller bought 60 pens for 600 taka. How many pens does he need to sell for 600 taka to make a profit of 20%?

ক
30
খ
60
গ
40
ঘ
50

ব্যাখ্যা

Question: A seller bought 60 pens for 600 taka. How many pens does he need to sell for 600 taka to make a profit of 20%?

Solution:
Cost price of 60 pens = Tk. 600
Cost price per pen = 600 ÷ 60
= Tk. 10

Since the seller wants 20% profit,
The selling price per pen will be = (10 × 120%) tk
= {10 × (120/100)} tk
= 12 tk

Now, the number of pens the seller can sell = 600/12
= 50

৩,০৮১.

A parallelogram has a base of 12 meters and a height of 8 meters. If the area of the parallelogram is increased by 50%, what will be the new height if the base remains the same?

ক
10 meters
খ
12 meters
গ
14 meters
ঘ
16 meters

ব্যাখ্যা

Question: A parallelogram has a base of 12 meters and a height of 8 meters. If the area of the parallelogram is increased by 50%, what will be the new height if the base remains the same?

Solution:
The area of a parallelogram is given by the formula:
Area = Base × Height
Original Area = 12 meters × 8 meters = 96 square meters

New area after a 50% increase:
New Area = 96 square meters × 1.5 = 144 square meters

New Height = New Area/Base = 144 square meters/12 meters = 12 meters

৩,০৮২.

x + y = 6 এবং 2x = 4 হলে, y এর মান কত?

ক
2
খ
4
গ
6
ঘ
8

ব্যাখ্যা

প্রশ্ন: x + y = 6 এবং 2x = 4 হলে, y এর মান কত?

সমাধান:
2x = 4
⇒ x = 4/2
∴ x = 2

এখন,
x + y = 6
⇒ y = 6 - 2
∴ y = 4

৩,০৮৩.

4,7,8,4 = 26

ক
ক) +,−,×
খ
খ) ×,−,÷
গ
গ) ×,+,−
ঘ
ঘ) +,÷,×
ঙ
ঙ) None of these

ব্যাখ্যা

4×7−8÷4 = 26

৩,০৮৪.

What is the angle between the hour and minute hands of a clock when it is 4 : 20?

ক
15.5°
খ
20°
গ
22.5°
ঘ
10°

ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 4 : 20?

Solution:
We know,
The angle between the hour and minute hands is,
Angle = |11M - 60H|/2
= |(11 × 20) - (60 × 4)|/2
= |220 - 240|/2
= |- 20|/2
= 20/2
= 10°

So the angle between the hour and minute hands at 4 : 20 is 10°.

৩,০৮৫.

If L + M = 2N and N + O = 2L, then-

ক
L = M
খ
L + O = N + M
গ
M + O = N + L
ঘ
L = M + O

ব্যাখ্যা

Question: If L + M = 2N and N + O = 2L, then-

Solution:
Let
L + M = 2N .............(1)
N + O = 2L .............(2)

(1) + (2)⇒
L + M = 2N
N + O = 2L
L + M + N + O = 2N + 2L
⇒ L + M + N + O - L - N = 2N + 2L - L - N
∴ M + O = N + L

৩,০৮৬.

The price of a loaf of bread was increased by 20%. How many leaves can be purchased now by the amount of money used to buy 300 loaves at the earlier price?

ক
ক) 240
খ
খ) 250
গ
গ) 280
ঘ
ঘ) 320

ব্যাখ্যা

ধরি,
প্রতি পিস পাউরুটির পূর্বমূল্য ছিল 100 টাকা
300 পিস পাউরুটির পূর্বমূল্য ছিল = (100 × 300) টাকা
= 30000 টাকা

20% বৃদ্ধিতে ,
প্রতি পিস পাউরুটির বর্তমানমূল্য ছিল = 100 + 20 টাকা
= 120 টাকা
বর্তমান মূল্যে 30000 টাকা দিয়ে পাউরুটি কেনা যাবে = 30000/120 টাকা
= 250 টাকা

৩,০৮৭.

12 women can complete a piece of work in 10 days. 10 men can complete the same work in 8 days. What is the ratio of the work capacity of one man to one woman?

ক
1 : 2
খ
3 : 2
গ
5 : 2
ঘ
10 : 7

ব্যাখ্যা

Question: 12 women can complete a piece of work in 10 days. 10 men can complete the same work in 8 days. What is the ratio of the work capacity of one man to one woman?

Solution:
12 women can complete a piece of work in 10 days.
∴ 1 woman can complete a piece of work in 10 × 12 = 120 days.

∴ 1 Woman's 1 day's work = 1/(12 × 10)
= 1/120
∴ One woman's 1 day's work = 1/120

Similarly,
Men's 1 day's work = 1/(10 × 8) = 1/80
∴ One man's 1 day's work = 1/80

∴ Ratio of capacity of one man to one woman = (1/80) : (1/120)
= 120 : 80
= 3 : 2

৩,০৮৮.

The surface area of a cube is 150 cm². Its volume must be-

ক
ক) 50 cm³
খ
খ) 95 cm³
গ
গ) 100 cm³
ঘ
ঘ) 125 cm³

ব্যাখ্যা

Question: The surface area of a cube is 150 cm². Its volume must be-

Solution:
let, length of one side is a cm
surface area = 6a² cm

⇒ 6a² = 150
⇒ a² = 150/6
⇒ a² = 25
⇒ a = 5 cm

volume = a³
= 5³
= 125 cm³

৩,০৮৯.

The average of five numbers is 16. If one number is excluded, the average becomes 14. The excluded number is -

ক
24
খ
22
গ
23
ঘ
26

ব্যাখ্যা

Question: The average of five numbers is 16. If one number is excluded, the average becomes 14. The excluded number is -

Solution:
The average of five numbers is 16
The sum of five numbers is (16 × 5) = 80

let, the excluded number is x

so,
(80 - x)/4 = 14
or, 80 - x = 56
or x = 80 - 56
∴ x = 24

৩,০৯০.

If a pole 12 m high casts a shadow 4√3 m long on the ground, then the elevation of the sun is -

ক
30°
খ
60°
গ
45°
ঘ
90°

ব্যাখ্যা

Question: If a pole 12 m high casts a shadow 4√3 m long on the ground, then the elevation of the sun is -

Solution:

ধরি,
AB = 12, BC = 4√3

ABC সমকোণী ত্রিভুজ হতে পাই,
tanθ = AB/BC
⇒ tanθ = 12/4√3
⇒ tanθ = 3/√3
⇒ tanθ = (√3 × √3)/√3
⇒ tanθ = √3
⇒ tanθ = tan60°
∴ θ = 60°

So the elevation of the sun is 60°.

৩,০৯১.

The area of a circle is increased by 22 square cm if its radius is increased by 1 cm. The original radius of the circle is -

ক
6 cm
খ
3.5 cm
গ
4 cm
ঘ
3 cm

ব্যাখ্যা

Question: The area of a circle is increased by 22 square cm if its radius is increased by 1 cm. The original radius of the circle is -

Solution:
Let the original radius of the circle be r cm.

ATQ,
π(r + 1)² - πr² = 22
⇒ π{(r + 1)² - r²} = 22
⇒ π(r² + 2r + 1 - r²) = 22
⇒ 2r + 1 = 22/π
⇒ 2r + 1 = (22 × 7)/22
⇒ 2r + 1 = 7
⇒ 2r = 6
∴ r = 3 cm

৩,০৯২.

A box contains 9 blue balls, 6 green balls, and 10 yellow balls. One ball is drawn at random. What is the probability that the ball drawn is neither blue nor yellow?

ক
1/4
খ
6/25
গ
3/5
ঘ
2/25

ব্যাখ্যা

Question: A box contains 9 blue balls, 6 green balls, and 10 yellow balls. One ball is drawn at random. What is the probability that the ball drawn is neither blue nor yellow?

Solution:
Number of blue balls = 9
Number of green balls = 6
Number of yellow balls = 10

∴ Total balls = 9 + 6 + 10 = 25

Let, event E = The ball drawn is neither blue nor yellow, so it must be green.

∴ Number of favorable outcomes = 6

∴ P(E) = 6/25

৩,০৯৩.

The mess charges for 35 students for 24 days in Tk 6300. In how many days will the mess charges be Tk 3375 for 25 students?

ক
16
খ
18
গ
20
ঘ
22

ব্যাখ্যা

Question: The mess charges for 35 students for 24 days in Tk 6300. In how many days will the mess charges be Tk 3375 for 25 students?

Solution:
Let C be the daily mess charge per student.
Given that mess charges for 35 students for 24 days is Tk 6300, the daily cost per student is = 6300/(35 × 24)
= 7.5

Now, to find how many days mess charges will be Tk 3375 for 25 students, we can use the daily cost per student (C):

The total mess charges for 25 students in D days is 3375 = 25 × C × D
⇒ D = 3375/(25 × 7.5)
= 18

৩,০৯৪.

To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

ক
20 days
খ
24 days
গ
30 days
ঘ
32 days

ব্যাখ্যা

Question: To complete a work, A takes 50% more time than B. If together they take 18 days to complete the work, how much time shall B take to do it?

Solution:
Let B takes x days to complete the work
Then A will take 50% more i.e 150% of x days i.e 3/2x days.

So the one day work of A and B together will be
(1/x) +{1/(3/2x)} = 1/18
⇒ (1/x) + (2/3x) = 1/18
⇒ 5/3x = 1/18
⇒ x = 30
∴ B takes 30 days to complete the work.

৩,০৯৫.

The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year child.The average age of the family now is -

ক
ক) 19 years
খ
খ) 23 years
গ
গ) 28.5 years
ঘ
ঘ) 29.3 years

ব্যাখ্যা

Sum of the present age of husband, wife and child
= (23 × 2 + 5 × 2) + 1 = 57 years
∴ Required average = (57/3) years
= 19 years

৩,০৯৬.

If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is-

ক
ক) 5%
খ
খ) 10%
গ
গ) 15%
ঘ
ঘ) 20%

ব্যাখ্যা

Question: If the ratio of cost price and selling price of an article be 10 : 11, the percentage of profit is-

Solution:
⇒ CP = 10x
⇒ SP = 11x
⇒ Profit = 11x - 10x
= x
⇒ Profit% = {x/10x} × 100
=10%

৩,০৯৭.

In a right triangle, the length of one of the legs is 5 and the length of the hypotenuse is 13. What is the length of the other leg?

ক
ক) 4 cm
খ
খ) 6 cm
গ
গ) 8 cm
ঘ
ঘ) 12 cm

ব্যাখ্যা

Question: In a right triangle, the length of one of the legs is 5 cm and the length of the hypotenuse is 13cm . What is the length of the other leg?

Solution:
সমকোণী ত্রিভুজের অতিভুজ = 13
সমকোণ সংলগ্ন এক বাহু = 5
সমকোণ সংলগ্ন অপর বাহু = a

প্রশ্নমতে,
a² + 5² = 13²
⇒ a² + 25 = 169
⇒ a² = 169 - 25
⇒ a² = 144
⇒ a² = 12²
∴ a = 12

∴ সমকোণ সংলগ্ন অপর বাহু = 12 সে.মি.

৩,০৯৮.

A grocer buys some eggs at Tk. 3 each. He finds that 12 of them are broken, but he sells the others at Tk. 4 each and makes a profit of Tk. 96. How many eggs did he buy?

ক
120
খ
132
গ
144
ঘ
118

ব্যাখ্যা

ধরি, মুদি ব্যবসায়ী x টি ডিম কিনেছিল।
প্রশ্নমতে, 4 (x - 12) - 3x = 96
বা, 4x - 48 - 3x = 96
বা, x = 96 + 48
বা, x = 144

৩,০৯৯.

10 women can do a work in 8 days. 8 men can complete the same work in 7 days. What is the ratio between the capacity of a man and a woman?

ক
9 : 7
খ
11 : 5
গ
7 : 3
ঘ
10 : 7

ব্যাখ্যা

Question: 10 women can do a work in 8 days. 8 men can complete the same work in 7 days. What is the ratio between the capacity of a man and a woman?

Question:
(10 × 8) = 80 women can complete the work in 1 day.
∴ 1 woman's 1 day's work = 1/80 part

(8 × 7) = 56 men can complete the work in 1 day.
1 man's 1 day's work = 1/56 part

So, required ratio = 1/56 : 1/80
= (1/56)/(1/80)
= 80/56
= 10/7
= 10 : 7

৩,১০০.

A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?

ক
2
খ
4
গ
21/3
ঘ
6

ব্যাখ্যা

Question: A mechanic repairs 4 cars in 5/3 hours. How many cars can he repair in 50 minutes?

Solution:
Here,
5/3 hours = (5/3) × 60 = 100 minutes

In 100 minutes, he repairs = 4 cars
In 1 minute, he repairs = 4/100
So, in 50 minutes, he repairs = (4 × 50)/100
= 2 cars