Bank Math

PrepBank · পাতা ৩৬ / ১৬১ · ৩,৫০১–৩,৬০০ / ১৬,১২৪

৩,৫০১.

If cosecθ - cotθ = 2/3, then cosecθ + cotθ =?

ক
ক) 1
খ
খ) 0
গ
গ) 3/2
ঘ
ঘ) 1/2

ব্যাখ্যা

Question: If cosecθ - cotθ = 2/3, then cosecθ + cotθ =?

Solution:
cosec²θ - cot²θ = 1
⇒ (cosecθ + cotθ )(cosecθ - cotθ) = 1
⇒ (cosecθ + cotθ )(2/3) = 1
∴ (cosecθ + cotθ )= 3/2

৩,৫০২.

49 × 49 × 49 × 49 = 7^?

ক
4
খ
7
গ
8
ঘ
16

ব্যাখ্যা

Question: 49 × 49 × 49 × 49 = 7^?

Solution:
49 × 49 × 49 × 49 = 7^?
⇒ 7²× 7² × 7² × 7² = 7^?
⇒ 7^{2 + 2 + 2 + 2} = 7^?
⇒ 7⁸ = 7^?
? = 8

৩,৫০৩.

What should be the value of "P" so that the expression (9 − 24x + Px²) becomes a perfect square?

ক
4
খ
6
গ
8
ঘ
16

ব্যাখ্যা

Question: What should be the value of "P" so that the expression (9 − 24x + Px²) becomes a perfect square?

Solution:
(9 − 24x + Px²)
= (3)² − 2 × 3 × 4x + (4x)² + Px² - (4x)²
= (3 - 4x)² + Px² - 16x²

∴ the expression becomes a perfect square if,
Px² - 16x² = 0
⇒ Px² = 16x²
∴ P = 16

৩,৫০৪.

A cube has a total surface area of 384 square units. What is the volume of the cube?

ক
343 cubic units
খ
512 cubic units
গ
729 cubic units
ঘ
1000 cubic units

ব্যাখ্যা

Question: A cube has a total surface area of 384 square units. What is the volume of the cube?

Solution:
Given, total surface area of the cube, S = 384 square units.
We know, surface area of a cube, S = 6a²

According to the question,
6a² = 384
⇒ a² = 384 / 6
⇒ a² = 64
⇒ a² = 8²
⇒ a = 8

Again, we know, volume of the cube, V = a³
= 8³
= 512

Therefore, the volume of the cube is 512 cubic units.

৩,৫০৫.

If a regular square pyramid has a base of side 5 cm and height 45 cm, then what its volume?

ক
ক) 225 cm³
খ
খ) 270 cm³
গ
গ) 350 cm³
ঘ
ঘ) 375 cm³

ব্যাখ্যা

Question: If a regular square pyramid has a base of side 5 cm and height 45 cm, then what its volume?

Solution:
Volume of the square pyramid = (1/3) × a² × h
= (1/3) × 5² × 45 cm³
= 375 cm³

৩,৫০৬.

250 candidates appeared for an examination, of which 50 failed. The pass percentage is-

ক
20%
খ
40%
গ
60%
ঘ
80%

ব্যাখ্যা

Question: 250 candidates appeared for an examination, of which 50 failed. The pass percentage is-

Solution:
Pass = 250 - 50 = 200

pass percentage = (200/250) × 100%
= 80%

৩,৫০৭.

A boat goes 8 km downstream in 16 minutes. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

ক
20 km/hr
খ
18 km/hr
গ
26 km/hr
ঘ
24 km/hr

ব্যাখ্যা

Question: A boat goes 8 km downstream in 16 minutes. The speed of the stream is 4 km/hr. What is the speed of the boat in still water?

Solution:
The speed upstream is = 8/16 km/min
= (8 × 60)/16 km/hr
= 30 km/hr

Let,
The speed of boat in still water is = x km/hr

Now,
x + 4 = 30
⇒ x = 30 - 4
∴ x = 26

৩,৫০৮.

In a zoo, there are Lions and Pigeons. If heads are counted, there are 140 and if legs are counted, there are 440. How many pigeons are there?

ক
ক) 80
খ
খ) 60
গ
গ) 50
ঘ
ঘ) 90

ব্যাখ্যা

Question: In a zoo, there are Lions and Pigeons. If heads are counted, there are 140 and if legs are counted, there are 440. How many pigeons are there?

Solution:
Let, the pigeons have x
So, Loins has = 140 - x

ATQ,
2x + 4(140 - x) =440
⇒ 2x + 560 - 4x = 440
⇒ 2x = 120
⇒ x = 60

৩,৫০৯.

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

ক
50%
খ
45%
গ
40%
ঘ
60%

ব্যাখ্যা

Question: By selling 33 meters of cloth, one gains the selling price of 11 meters. Find the gain percent.

Solution:
Gain = (SP of 33 m) - (CP of 33 m) = SP of 11m
⇒ SP of 22m = CP of 33m

Let
CP of each meter be Tk 1.
Then,
CP of 22 m = Tk. 22.
CP of 33 m = Tk. 33

Hence, SP of 22m = Tk. 33
∴ Gain = 33 - 22 = Tk. 11

∴ %Gain = (11/22) × 100
= 50%

৩,৫১০.

How many triangles are there in the figure bellow?

ক
15
খ
30
গ
45
ঘ
18

ব্যাখ্যা

Total numbers in each row = 1 + 2 + 3 + 4 + 5 = 15
Number of row in the given triangle = 3
Total number of triangles = 15 × 3 = 45

৩,৫১১.

A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

ক
Tk. 90
খ
Tk. 138
গ
Tk. 150
ঘ
Tk. 160

ব্যাখ্যা

Question: A worker was hired for 7 days. Each day, he was paid Tk. 10 more than what he was paid for the previous day of work. The total amount he was paid in the first 4 days of work equaled the total amount he was paid in the last 3 days. What was his starting pay?

Solution:
ধরি,
১ম দিন ছিলো x টাকা

২য় দিন = x + 10
৩য় দিন = (x + 20)
৪র্থ দিন = (x + 30)
৫ম দিন = (x + 40)
৬ষ্ঠ দিন = (x + 50)
৭ম দিন = (x + 60) টাকা

প্রশ্নমতে,
x + (x + 10) + (x + 20) + (x + 30) = (x + 40) + (x + 50) + (x + 60)
⇒ 4x + 60 = 3x + 150
⇒ 4x - 3x = 150 - 60
∴ x = 90

৩,৫১২.

The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

ক
7
খ
23
গ
9
ঘ
11

ব্যাখ্যা

Question: The product of two numbers is 120 and the sum of their squares is 289. The sum of the number is:

Solution:
let the two numbers be x, y

xy = 120
x² + y² = 289

We know
(x + y)² = x² + y² + 2xy
⇒ (x + y)² = 289 + 2 × 120
⇒ (x + y)² = 289 + 240
⇒ (x + y)² = 529
⇒ (x + y)² = 23²
∴ x + y = 23

৩,৫১৩.

A train of 220 m long is moving at 45 km/h. The time taken by the train to cross a tunnel of 260 m long is-

ক
25 sec
খ
35 sec
গ
38 sec
ঘ
40 sec

ব্যাখ্যা

Question: A train of 220 m long is moving at 45 km/h. The time taken by the train to cross a tunnel of 260 m long is-

Solution:
মোট অতিক্রান্ত দূরত্ব = (220 + 260) মিটার
= 480 মিটার

45 কিমি = (45 × 1000) = 45000 মিটার
1 ঘণ্টা = 3600 সেকেন্ড

45000 মিটার অতিক্রম করে 3600 সেকেন্ডে
1 মিটার অতিক্রম করে 3600/45000 সেকেন্ডে
480 মিটার অতিক্রম করে (3600 × 480)/45000 সেকেন্ডে
= 38.4 সেকেন্ডে

কাছাকাছি উত্তর হিসাবে অপশন গ কে সঠিক উত্তর নেওয়া হয়েছে।

৩,৫১৪.

A train 360 metre long runs with a speed of 45 km/hr. What time will it take to pass a platform 140 metre long?

ক
ক) 44 seconds
খ
খ) 40 seconds
গ
গ) 30 seconds
ঘ
ঘ) 38 seconds
ঙ
ঙ) 25 seconds

ব্যাখ্যা

Speed = 45 km/hr = 45 × 5/18
= 25/2 m/s
Distance travelled = Length of the train + Length of the platform
= 360 + 140
= 500 metre.
Time taken to cross the platform = 500/(25/2)
= 40 seconds

৩,৫১৫.

If (x - y)² = 12 and xy = 1, then what is the value of (x² + y²)?

ক
ক) 12
খ
খ) 14
গ
গ) 17
ঘ
ঘ) 18

ব্যাখ্যা

Question: If (x - y)² = 12 and xy = 1, then what is the value of (x² + y²)?

Solution:
x² + y²
= (x - y)² + 2xy
= 12 + 2 × 1
= 12 + 2
= 14

৩,৫১৬.

Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

ক
21 years
খ
12 years
গ
18 years
ঘ
14 years

ব্যাখ্যা

Question: Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

Solution:
Given that,
Sachin is 4 years younger than Rohan
Their ages are in the ratio 7 : 9

Let their ages are,
Sachin = 7x
Rohan = 9x

ATQ,
9x - 7x = 4
⇒ 2x = 4
∴ x = 2

Sachin age is = 7x = 7 × 2 = 14 years

৩,৫১৭.

The sum of three numbers is 360. The ratio of the first number to the second number is 3 : 4 and between the second and third numbers, this ratio is 4 : 5, ﬁnd the second number.

ক
100
খ
120
গ
160
ঘ
200

ব্যাখ্যা

Question: The sum of three numbers is 360. The ratio of the first number to the second number is 3 : 4 and between the second and third numbers, this ratio is 4 : 5, ﬁnd the second number.

Solution:
Given that,
The sum of three numbers is = 360
The ratio of first number to second number is = 3 : 4
The ratio of second number of third number is = 4 : 5

The ratio of first, second and third number = 3 : 4 : 5
Let, the numbers are = 3x, 4x , 5x

ATQ,
3x + 4x + 5x = 360
⇒ 12x = 360
⇒ x = 360/12
⇒ x = 30

∴ The second number is = 4 × 30
= 120

৩,৫১৮.

Due to a 25% increase in the price of salt, a person got 10kg less quantity for Tk. 500 than he was getting before the increase. What was the initial price per kg of salt in Taka?

ক
Tk. 15
খ
Tk. 10
গ
Tk. 5
ঘ
Tk. 20

ব্যাখ্যা

Question: Due to a 25% increase in the price of salt, a person got 10kg less quantity for Tk. 500 than he was getting before the increase. What was the initial price per kg of salt in Taka?

Solution:
25% বৃদ্ধিতে পূ‍‍র্বমূল্য 100 টাকা হলে ব‍‍র্তমান মূল্য 125 টাকা
∴ পূ‍‍র্বমূল্য 500 টাকা হলে ব‍‍র্তমান মূল্য (125 × 500)/100 টাকা
= 625 টাকা

10kg লবণের ব‍‍র্তমান মূল্য = (625 - 500) = 125 টাকা
∴ 1kg লবণের ব‍‍র্তমান মূল্য = 125/10 টাকা
= 12.5 টাকা

ব‍‍র্তমানে 500 টাকায় পাওয়া যায় = 500/12.5 = 40 kg
পূ‍‍র্বে 500 টাকায় পাওয়া যেতো = 40 + 10 = 50 kg
∴ প্রতি কেজি লবণের পূ‍‍র্বমূল্য = 500/50 = 10 টাকা

৩,৫১৯.

Which number is appropriate in place of question mark?

ক
40
খ
42
গ
45
ঘ
50

ব্যাখ্যা

Question: Which number is appropriate in place of question mark?

Solution:
7 + 5 = 12
12 + 6 = 18
18 + 7 = 25
25 + 8 = 33
33 + 9 = 42

৩,৫২০.

A sum of money invested at simple interest becomes 23/10 of itself in 2 years and 6 months. What is the rate of interest per annum?

ক
52%
খ
50%
গ
38%
ঘ
28%

ব্যাখ্যা

Question: A sum of money invested at simple interest becomes 23/10 of itself in 2 years and 6 months. What is the rate of interest per annum?

Solution:
let,
principle = P
interest, I = (23P/10 - P)
= 13P/10
time, n = 2 years 6 months
= 2.5 years
we know,
I = Pnr/100
r = (100 × I)/Pn
= (100 × 13P/10) /P × 2.5
= 52%

৩,৫২১.

At present father and son have a combined age of 83. 10 years ago they had an age ratio of 7 : 2. What is the present age of the son?

ক
18 years
খ
24 years
গ
22 years
ঘ
26 years

ব্যাখ্যা

Question: At present father and son have a combined age of 83. 10 years ago they had an age ratio of 7 : 2. What is the present age of the son?

Solution:
Let,
10 years ago their age were 7p and 2p

ATQ,
7p + 2p + 20 = 83
9p = 63
p = 7

present age of son is = 14 + 10 = 24 years

৩,৫২২.

If (a - 18)² + (b - 12)² + (c - 6)² = 0 then, What is the value of (a + b + c)^1/2 = ?

ক
9
খ
6
গ
12
ঘ
14

ব্যাখ্যা

Question: If (a - 18)² + (b - 12)² + (c - 6)² = 0 then, What is the value of (a + b + c)^1/2 = ?

Solution:
দেওয়া আছে,
(a - 18)² + (b - 12)² + (c - 6)² = 0

আমরা জানি, যেকোনো বর্গের যোগফল শূন্য হলে প্রতিটি বর্গই শূন্য হবে।
সুতরাং,
(a - 18)² = 0
⇒ a - 18 = 0
∴ a = 18

আবার,
(b - 12)² = 0
⇒ b - 12 = 0
∴ b = 12

এবং
(c - 6)² = 0
⇒ c - 6 = 0
∴ c = 6

প্রদত্ত রাশি,
(a + b + c)^1/2
= (18 + 12 + 6)^1/2
= (36)^1/2
= 6

৩,৫২৩.

A train covered first 120 km at a speed of 20 km an hour and then covered the remaining 180 km at a speed of 45 km an hour. Find its average speed.

ক
60 km/hr
খ
30 km/hr
গ
50 km/hr
ঘ
40 km/hr

ব্যাখ্যা

Question: A train covered first 120 km at a speed of 20 km an hour and then covered the remaining 180 km at a speed of 45 km an hour. Find its average speed.

Solution:
Total distance = 120 + 180 = 300 km.

Time taken for the first 120 km = 120/20 = 6 hrs.
Time taken for the next 180 km = 180/45 = 4 hrs.
Total time taken = 6 + 4 = 10 hrs.

Average Speed =Total Distance Travelled/Total Time Taken
= 300/10
= 30 km/hr

৩,৫২৪.

If r sinθ = 3, r cosθ = 4, then find the value of (4 tanθ + 1).

ক
3
খ
2
গ
4
ঘ
1/2

ব্যাখ্যা

Question: If r sinθ = 3, r cosθ = 4, then find the value of (4 tanθ + 1).

Solution:
r sinθ = 3
r cosθ = 4

Now,
(r sinθ)/(r cosθ) = 3/4
⇒ sinθ/cosθ = 3/4
⇒ tanθ = 3/4
⇒ 4 tanθ = 4 × 3/4 = 3
⇒ 4 tanθ + 1 = 3 + 1
∴ 4 tanθ + 1 = 4

৩,৫২৫.

The compound interest on Tk.30000 at 7% per annum is Tk.4347. The period is

ক
ক) 2 year
খ
খ) 2.5 year
গ
গ) 3 year
ঘ
ঘ) 4 year

ব্যাখ্যা

Amount = Tk.(30000+4347) = Tk.34347
let the time be n year
Then,
30000(1+7/100)ⁿ = 34347
(107/100)ⁿ = 34347/30000 = 11449/10000 = (107/100)²
n = 2year

৩,৫২৬.

A, B and C started a business each investing Tk.10000. After 4 month A withdraws Tk.3000, B withdraws Tk.4000, C invest Tk.3000 more At the end of the years, a total profit was Tk.32800. Find the share of C.

ক
Tk. 10000
খ
Tk. 14400
গ
Tk. 17600
ঘ
Tk. 19200

ব্যাখ্যা

Question: A, B and C started a business each investing Tk. 10000. After 4 month A withdraws Tk. 3000, B withdraws Tk.4000, C invest Tk. 3000 more At the end of the years, a total profit was Tk. 32800. Find the share of C.

Solution:
Ratio of capital of A, B and C.
= (10000 × 4 + 7000 × 8) : (10000 × 4 + 6000 × 8) : (10000 × 4 + 13000 × 8)
= 96000 : 88000 : 144000
= 12 : 11: 18

Distributing the final profit of Tk. 32800 in the given ratio, the share of C becomes = (32800 × 18)/41 = 14400.

৩,৫২৭.

If x/2 = y/3 = z/4 = (2x - 3y - + 5z)/k, then the value of k is -

ক
ক) 12
খ
খ) 15
গ
গ) 16
ঘ
ঘ) 18

ব্যাখ্যা

Let,
x/2 = y/3 = z/4 = m
Then, x = 2m, y = 3m, z = 4m
∴ x/2 = (2x - 3y + 5z)/k = 2m/2
⇒ (2 × 2m - 3 × 3m + 5 × 4m)/k = m
⇒ k = 4 - 9 + 20
= 15.

৩,৫২৮.

ক
132
খ
177
গ
185
ঘ
225
ঙ
None of these

ব্যাখ্যা

Question:

Solution:

৩,৫২৯.

Two-fifths of one-fourth of three-seventh of a number is 18. What is half of the number?

ক
ক) 175
খ
খ) 420
গ
গ) 350
ঘ
ঘ) 210

ব্যাখ্যা

প্রশ্ন : Two-fifths of one-fourth of three-seventh of a number is 15. What is half of the number?

সমাধান :

ধরি, সংখ্যাটি = x
ATQ,
2/5 × 1/4 × 3/7 × x = 18
Or, 6x / 140 = 18
Or, x = 420

∴ 1/2 of 420 = 210

৩,৫৩০.

By what percentage must 40 be increased to become 70?

ক
75%
খ
5%
গ
55%
ঘ
65%

ব্যাখ্যা

Question: By what percentage must 40 be increased to become 70?

Solution:
Let,
x% should be added.

Therefore,
40 + x% of 40 = 70
⇒ 40 + 40x/100 = 70
⇒ 40x/100 = 30
⇒ 2x/5 = 30
⇒ 2x = 150
⇒ x = 75

Therefore, 75% should be added to 40 to make it 50.

৩,৫৩১.

G is twice as fast as S in doing work. If G can do a work in 30 days less than S, how many days will they take to complete the work together?

ক
25
খ
20
গ
22
ঘ
15

ব্যাখ্যা

Question: G is twice as fast as S in doing work. If G can do a work in 30 days less than S, how many days will they take to complete the work together?

Solution:
G, S এর চেয়ে দ্বিগুণ গতিতে কাজ করে।
ধরি,
S একটি কাজ করে x দিনে
G সেই কাজ করে x/2 দিনে

প্রশ্নমতে,
x - x/2 = 30
⇒ 2x - x = 60
∴ x = 60

S কাজটি করে 60 দিনে
∴ S কাজটি 1 দিনে করে 1/60 অংশ

G কাজটি করে 60/2 দিনে = 30 দিনে
∴ G কাজটি 1 দিনে করে 1/30 অংশ

S ও G একত্রে 1 দিনে করে 1/60 + 1/30 অংশ
= (1 + 2)/60 অংশ
= 3/60 অংশ
= 1/20 অংশ

∴ S ও G একত্রে কাজটি 20 দিনে করতে পারবে।

৩,৫৩২.

A train moves with a speed of 108 km/hr. Its speed in metres per second is-

ক
10.8
খ
18
গ
30
ঘ
30.8
ঙ
None of these

ব্যাখ্যা

Question: A train moves with a speed of 108 km/hr. Its speed in metres per second is-

Solution:
Speed = 108 km/hr
To convert km/hr into m/s multiply the number by 5/18.
speed = 108 × (5/18) m/s = 30 m/s.

৩,৫৩৩.

One diagonal of a rhombus is three times the other diagonal. If its area is 54 sq. cm, find the sum of the diagonals.

ক
16√2 cm
খ
24 cm
গ
12√6 cm
ঘ
30 cm

ব্যাখ্যা

Question: One diagonal of a rhombus is three times the other diagonal. If its area is 54 sq. cm, find the sum of the diagonals.

Solution:
ধরি,
রম্বসের একটি কর্ণ = x সেমি
রম্বসের অপর কর্ণ = 3x সেমি

আমরা জানি,
রম্বসের ক্ষেত্রফল = (1/2) × কর্ণদ্বয়ের গুণফল

প্রশ্নমতে,
(1/2) . x . 3x = 54
⇒ 3x² = 54 × 2
⇒ 3x² = 108
⇒ x² = 108/3
⇒ x² = 36
⇒ x = √36
∴ x = 6

এখন,
একটি কর্ণ = 6 সেমি
∴ অপর কর্ণ = 3 × 6 = 18 সেমি

∴ কর্ণদ্বয়ের সমষ্টি = 6 + 18 = 24 cm

৩,৫৩৪.

A boat went to a place in 7km/h and came back in 8km/h. What is average speed of the boat?

ক
ক) 8 km/h
খ
খ) 7.47 km/h
গ
গ) 8.5 km/h
ঘ
ঘ) 7.37 km/h

ব্যাখ্যা

Question: A boat went to a place in 7km/h and came back in 8km/h. What is average speed of the boat?

Solution:
ধরি,
দূরত্ব = x

তাহলে,
যেতে সময় লাগে x/7 hour
আসতে সময় লাগে x/8 hour

আমরা জানি,
গড় বেগ = (মোট দুরত্ব)/মোট সময়
= 2x/(x/7 + x/8)
= 2x/ (15x/56)
= 112/15
= 7.47km/h

৩,৫৩৫.

An exam paper has two parts, A and B. Part A contains 12 questions and Part B contains 8 questions. If a student has to choose 7 questions from part A and 5 questions from part B, in how many ways can they choose the questions?

ক
48,764
খ
52,214
গ
56,468
ঘ
44,352

ব্যাখ্যা

Question: An exam paper has two parts, A and B. Part A contains 12 questions and Part B contains 8 questions. If a student has to choose 7 questions from part A and 5 questions from part B, in how many ways can they choose the questions?

Solution:
ways to choose 7 from part A = ¹²C₇
ways to choose 5 from part B = ⁸C₅
choose 7 from part A and 5 from part B = ¹²C₇ × ⁸C₅
= {12!/(7! 5!)} × {8!/(5! 3!)}
= 792 × 56
= 44,352

৩,৫৩৬.

In a class, there are 10 boys and 8 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

ক
13/21
খ
15/34
গ
17/45
ঘ
None of the above

ব্যাখ্যা

Question: In a class, there are 10 boys and 8 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected is:

Solution:
Total students = 10 + 8 = 18
Let S be the sample space, and E be the event of selecting 1 girl and 2 boys.

Then, n(S) = Number of ways of selecting 3 students out of 18 = ¹⁸C₃
= (18 × 17 × 16)/(3 × 2 × 1)
= 816

And, n(E) = Number of events of selecting 1 girl and 2 boys = ⁸C₁ × ¹⁰C₂
= 8 × [(10 × 9)/2]
= 8 × 45
= 360

∴ Probability = n(E)/n(S)
= 360/816
= 15/34

৩,৫৩৭.

How many triangles are there in the figure below?

ক
12
খ
18
গ
22
ঘ
26

ব্যাখ্যা

Question: How many triangles are there in the figure below?

Solution:

উপরের চিত্রে,
সাধারণ ত্রিভুজ আছে AGF, FDH, GEI, BDJ, DHJ, HIJ, IEJ, EJC অর্থাৎ 8 টি ।

এক বা একাধিক বাহু ছেদ করে ঐ রকম ত্রিভুজ আছে - ABC, ADE, DEJ, FGJ, BJF, CJG, FDJ, GEJ, DJI, JEH অর্থাৎ 10 টি।

অর্থাৎ মোট ত্রিভুজ আছে = 10 + 8 = 18 টি

৩,৫৩৮.

If x⁸ - 1442x⁴ + 1 = 0, then a possible value of x - (1/x) is:

ক
4
খ
6
গ
8
ঘ
None of the above

ব্যাখ্যা

Question: If x⁸ - 1442x⁴ + 1 = 0, then a possible value of x - (1/x) is:

Solution:
Given,
x⁸ - 1442x⁴ + 1 = 0
⇒ (x⁸/x⁴) - (1442x⁴/x⁴) + (1/x⁴) = 0
⇒ x⁴ - 1442 + (1/x⁴) = 0
⇒ x⁴ + (1/x⁴) = 1442
⇒ x⁴ + (1/x⁴) + 2 = 1444
⇒ {x² + (1/x²)}² = (38)²
⇒ {x²+ (1/x²)} = 38
⇒ {x² + (1/x²)} - 2 = 36
⇒ {x - (1/x)}²= 36
∴ x - (1/x) = 6

৩,৫৩৯.

A company makes a profit of 6% on its first Tk. 1,000 of sales each day and Tk. 55 per thousand on all sales in excess of Tk. 1,000 for that day. How much profit will the company make in a day when sales are Tk. 6,000?

ক
250
খ
300
গ
320
ঘ
335
ঙ
None of these

ব্যাখ্যা

Question: A company makes a profit of 6% on its first Tk. 1,000 of sales each day and Tk. 55 per thousand on all sales in excess of Tk. 1,000 for that day. How much profit will the company make in a day when sales are Tk. 6,000?

Solution:
Company makes profit for 1st Tk. 1000 of sales = 6% of 1000 = Tk. 60

Profit for Next Tk. (6000 - 1000) = Tk. 5000 of sales = 55 × 5 = Tk. 275

∴ Total profit = 60 + 275 = Tk. 335

৩,৫৪০.

If a regular tetrahedron has edges of length 8 centimeters, what is the tetrahedron's volume?

ক
60 cubic centimeters (approx.)
খ
70 cubic centimeters (approx.)
গ
80 cubic centimeters (approx.)
ঘ
90 cubic centimeters (approx.)
ঙ
50 cubic centimeters (approx.)

ব্যাখ্যা

A regular tetrahedron is made up of four congruent equilateral triangles.
It can be thought as a pyramid with a base that is an equilateral triangle.
The volume of a pyramid is 1/3 × A × h, where A is the area of the base
and h is the height of the pyramid perpendicular to the base.

The area of an equilateral triangle is √3/4 × 8², where 8 is the length of a side or edge.

The height of a regular tetrahedron is √(2/3) × 8

Therefore, the volume of the regular tetrahedron is:
V= 1/3 × √3/4 × 8² × √(2/3) × 8
= 128√2/3 cm³
= 60.34 cm^{3
-----------------------------------------------------------------------------------------------------
Shortly,}V= a³/(6√2) unit³
= 8³/(6√2) cm³
= 60.34 cm³
------------------------------------------------------------------------------------
Important note:

With a side length of 6, Pythagoras gives a slant height AM of 3sqrt(3).
The apex A will be above the centroid of the base BCD which divided MD in a 1 : 2 ratio, so MG = sqrt(3).
Now a second application of Pythagoras gives a height GA of 2sqrt(6).
The center of the tetrahedron, which is the center of the sphere, divides the height in a 1 : 3 ratio so r = GS = sqrt(6)/2.

৩,৫৪১.

A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical small bottles of diameter 3 cm and height 8 cm. How many bottles will be needed to empty the bowl?

ক
22
খ
25
গ
27
ঘ
29

ব্যাখ্যা

Question: A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical small bottles of diameter 3 cm and height 8 cm. How many bottles will be needed to empty the bowl?

Solution:
অর্ধগোলকের আয়তন = (1/2)× 4πr³/3
= (2/3) π9³ ঘনসেমি

প্রতি সিলিন্ডার আকৃতির বোতলের আয়তন = π (3/2)² × 8
= 18π ঘনসেমি
ধরি, n সংখ্যক বোতল লাগবে।

n × 18π = (2/3) π9³
⇒ n = (2/3) π9³/18π
∴ n = 27

৩,৫৪২.

Which number replaces the question mark?

ক
ক) 373
খ
খ) 439
গ
গ) 555
ঘ
ঘ) 849

ব্যাখ্যা

Question: Which number replaces the question mark?

Solution:
(2 + 1) × 3 = 9
(9 + 1) × 3 = 30
(30 + 1) × 3 = 93
(93 + 1) × 3 = 282
(282 + 1) × 3 =849

অতএব,ত্রিভুজের সংখ্যাটির সাথে ১ যোগ করে ৩ গুণ করলে পরের ত্রিভুজের সংখ্যা পাওয়া যায়।
∴ প্রশ্নবোধক স্থানে ৮৪৯ বসবে।

৩,৫৪৩.

If (8.97)²× ( 15.05)² ÷ √624.89 = 9ⁿ then the value of n is

ক
ক) 3
খ
খ) 4
গ
গ) 2
ঘ
ঘ) 5

ব্যাখ্যা

(8.97)² × (15.05)² ÷ √624.89 = 9ⁿ
⇒ 9² × 15² ÷ √625 = 9ⁿ
⇒ 81 × 225 ÷ 25 = 9ⁿ
⇒ 81 × 9 = 9ⁿ
⇒ 9³ = 9ⁿ
⇒ n = 3

৩,৫৪৪.

In order to obtain an income of Tk. 650 from 10% stock at Tk. 97, one must make an investment of-

ক
Tk. 3110
খ
Tk. 6305
গ
Tk. 6500
ঘ
Tk. 9700

ব্যাখ্যা

Question: In order to obtain an income of Tk. 650 from 10% stock at Tk. 97, one must make an investment of-

Solution:
To obtain Tk. 10, investment = Tk. 97.
To obtain Tk. 650

investment = Tk. (97/10) × 650
= Tk. 6305

৩,৫৪৫.

There are 8 more men than women on board of directors of a company. If there are 20 members on the board, how many are men?

ক
ক) 6
খ
খ) 8
গ
গ) 12
ঘ
ঘ) 14
ঙ
ঙ) 16

ব্যাখ্যা

Question: There are 8 more men than women on board of directors of a company. If there are 20 members on the board, how many are men?

Solution:
Let,
Number of men = x
∴ Number of women = x - 8

ATQ,
x + x - 8 = 20
⇒ 2x = 28
∴ x = 14

∴ There are 14 men on the board.

৩,৫৪৬.

If cot (x - 30°) = 1/√3, then sin² x = ?

ক
ক) √3/2
খ
খ) 1
গ
গ) 0
ঘ
ঘ) 1/2

ব্যাখ্যা

প্রশ্ন : If cot (x - 30°) = 1/√3, then sin²x = ?

সমাধান :

দেওয়া আছে
cot (x - 30°) =1/√3
cot (x - 30°) = cot 60°
x - 30° = 60°
x = 60° + 30°
x = 90°

এখন
sin x = sin90° = 1

বা, sin²x = 1

৩,৫৪৭.

An investor purchased 100 shares of stock X at tk per share and sold them all a year later at 24 tk per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

ক
92%
খ
240%
গ
280%
ঘ
300%

ব্যাখ্যা

Question: An investor purchased 100 shares of stock X at tk per share and sold them all a year later at 24 tk per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?

Solution:
buying price = price os total shares + brokerage charges on buy price
=100 × (49/8) + 2% of {100 × (49/8)}
= 624.75 tk

similarly selling price = (24 × 100) - 2% of 2400
= 2352 tk

So, Profit = SP - CP
= 2352 - 624.75
= 1727.25 tk

% = (1727.25/624.75) × 100%
= 276 ~ 280%

৩,৫৪৮.

The least number by which 294 must be multiplied to make it a perfect square is :

ক
2
খ
3
গ
6
ঘ
24

ব্যাখ্যা

Question: The least number by which 294 must be multiplied to make it a perfect square is :

Solution:
294 = 7 × 7 × 2 × 3

এখানে
2 এবং 3 জোড়াবিহীন
2 × 3 = 6 দ্বারা গুণ করলে 294 সংখ্যাটি পূর্ণবর্গ সংখ্যা হবে।

৩,৫৪৯.

A bus covers a certain distance at 16 h. It covers half the distance at 40 km/h and the rest at 60 km/h. Find the length of the journey.

ক
ক) 520 km
খ
খ) 448 km
গ
গ) 384 km
ঘ
ঘ) 768 km
ঙ
ঙ) 786 km

ব্যাখ্যা

Let the total distance covered = x
= Length of journey
According to the question,
x/2 × 1/40 + x/2 × 1/60 = 16
x/80 + x/120 = 160
(3x + 2x)/240 = 16
5x = 16 × 240
x = (16 × 240)/5
x = 16 × 48
x = 768 km

৩,৫৫০.

If cosA sinA = 0,then (cosA + sinA)² =?

ক
0
খ
2
গ
3
ঘ
1

ব্যাখ্যা

Question: If cosA sinA = 0,then (cosA + sinA)² =?

Solution:
(cosA + sinA)²
= cos²A + 2 cosA sinA + sin²A
= 1 + 2.0 [sin²A + cos²A = 1]
= 1 + 0
= 1

৩,৫৫১.

If x = 2y = 4z and xyz = 64, find the value of x.

ক
6
খ
12
গ
8
ঘ
11

ব্যাখ্যা

Question: If x = 2y = 4z and xyz = 64, find the value of x.

Solution:
Given,
x = 2y = 4z
So, y = x / 2 and z = x / 4

Now,
xyz = 64
⇒ x × (x/2) × (x/4) = 64
⇒ x³/8 = 64
⇒ x³ = 64 × 8
⇒ x³ = 512
⇒ x = ∛512
∴ x = 8

৩,৫৫২.

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

ক
ক) 1/2
খ
খ) 2/5
গ
গ) 8/15
ঘ
ঘ) 9/20

ব্যাখ্যা

Question: Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Solution:
Total number of tickets = 20

The numbers which are multiple of 3 or 5 are {3, 5, 6, 9, 10, 12, 15, 18, 20}
∴ Total expected events = 9

∴ The probability = 9/20

৩,৫৫৩.

Find the value of 'x' if the mean of the set of the numbers 8, 5, x, 10, 15, 21 is given as 11.

ক
3
খ
7
গ
9
ঘ
14

ব্যাখ্যা

প্রশ্ন: Find the value of 'x' if the mean of the set of the numbers 8, 5, x, 10, 15, 21 is given as 11.

সমাধান:
ATQ,
(8 + 5 + x + 10 + 15 + 21)/6 = 11
⇒ (59 + x)/6 = 11
⇒ 59 + x = 66
⇒ x = 66 - 59
∴ x = 7

৩,৫৫৪.

A shop offers a discount of 12% on a refrigerator that originally costs Tk. 50000. What is the selling price after the discount?

ক
Tk. 44000
খ
Tk. 42500
গ
Tk. 48000
ঘ
Tk. 45500
ঙ
Tk. 40800

ব্যাখ্যা

Question: A shop offers a discount of 12% on a refrigerator that originally costs Tk. 50000. What is the selling price after the discount?

Solution:
The original price of the refrigerator = Tk. 50000
And the discount percentage = 12%

We know,
Discount Amount = (Discount Percentage/100) × Original Price
= (12/100) × 50000
= 6000

∴ Selling Price = 50000 - 6000 = 44000
The selling price after the discount is Tk. 44000.

৩,৫৫৫.

A merchant marks his goods 40% above the cost price and sell them at a discount of 15%. Find his gain % = ?

ক
ক) 25%
খ
খ) 22%
গ
গ) 19%
ঘ
ঘ) 20%

ব্যাখ্যা

Let the cost price = 100 units
Marked price = 140 units
Selling price = 140 × 85/100 = 119
Profit % = 19/100×100 = 19%

৩,৫৫৬.

The average earnings of Rohan for the first three months of the calendar year 2023 is Tk. 1200. If his average earnings for the second and third months is Tk. 1300 then find his earnings in the first month.

ক
Tk. 900
খ
Tk. 1000
গ
Tk. 1200
ঘ
Tk. 1500

ব্যাখ্যা

Question: The average earnings of Rohan for the first three months of the calendar year 2023 is Tk. 1200. If his average earnings for the second and third months is Tk. 1300 then find his earnings in the first month.

Solution:
earnings of Rohan for the first three months = 3 × 1200 = 3600
earnings of Rohan for the second and third months = 2 × 1300 = 2600

his earnings in the first month = 3600 - 2600
= Tk. 1000

৩,৫৫৭.

Rana walked from A to B in the East 10 feet. Then she turned to the right and walked 3 feet. Again, she turned to the right and walked 14 feet. How far is she from A?

ক
3 ft
খ
5 ft
গ
4 ft
ঘ
7 ft

ব্যাখ্যা

Question: Rana walked from A to B in the East 10 feet. Then she turned to the right and walked 3 feet. Again, she turned to the right and walked 14 feet. How far is she from A?

Solution:

∴ Required Distance = AD
= √{3² + (14 - 10)²}
= √(3² + 4²)
= √(9 + 16)
= √25
= 5 ft

৩,৫৫৮.

The value of (0.125 + 0.027)/(0.5 × 0.5 + 0.09 - 0.15) is-

ক
ক) 0.02
খ
খ) 0.2
গ
গ) 0.08
ঘ
ঘ) 0.8

ব্যাখ্যা

let
0.5 = a
0.3 = b

(0.125 + 0.027)/(0.5 × 0.5 + 0.09 - 0.15)
= {(0.5)³ + (0.3)³}/(0.5 × 0.5 + 0.3 × 0.3 - 0.5 × 0.3)
= (a³ + b³)/(a² + b² - ab)
= (a + b)(a² + b² - ab)/(a² + b² - ab)
= a + b
= 0.5 + 0.3
= 0.8

৩,৫৫৯.

An ambulance moving at 33 km/h is 45 m behind a school bus. After 15 s, it is 30 m ahead of the bus. Find the speed of the school bus.

ক
4 km/h
খ
8 km/h
গ
10 km/h
ঘ
15 km/h
ঙ
18 km/h

ব্যাখ্যা

Question: An ambulance moving at 33 km/h is 45 m behind a school bus. After 15 s, it is 30 m ahead of the bus. Find the speed of the school bus.

Solution:
Relative Speed = Total distance/Total time
= (30 + 45)/15
= 75/15
= 5 m/s
= 5 × (18/5)
= 18 km/h

Now,
Relative Speed = Speed of ambulance - Speed of school bus
∴ Speed of school bus = Speed of ambulance - Relative speed
= 33 - 18
= 15 km/h

৩,৫৬০.

The traffic lights at three different road crossings change after every 24 sec, 36 sec, and 72 sec respectively. If they all change simultaneously at 8 : 20 : 00 hrs, then they will again change simultaneously at:

ক
8 : 20 : 48 hrs
খ
8 : 23 : 12 hrs
গ
8 : 32 : 10 hrs
ঘ
8 : 27 : 16 hrs
ঙ
8 : 21 : 12 hrs

ব্যাখ্যা

Question: The traffic lights at three different road crossings change after every 24 sec, 36 sec, and 72 sec respectively. If they all change simultaneously at 8 : 20 : 00 hrs, then they will again change simultaneously at:

Solution:

Time interval for simultaneous change = L.C.M. of 24, 36, 72 = 72 sec

72 seconds = 1 min 12 sec

Next simultaneous change = 8 : 20 : 00 + 1 min 12 sec = 8 : 21 : 12 hrs

৩,৫৬১.

The sum of five consecutive multiples of 6 is 150. What is the second largest number?

ক
46
খ
35
গ
36
ঘ
30

ব্যাখ্যা

Question: The sum of five consecutive multiples of 6 is 150. What is the second largest number?

Solution:
ধরি, ৬ এর পাঁচটি ক্রমিক গুণিতক হলো যথাক্রমে (x - 12), (x - 6), x, (x + 6) এবং (x + 12)

প্রশ্নমতে,
(x - 12) + (x - 6) + x + (x + 6) + (x + 12) = 150
⇒ 5x = 150
⇒ x = 150/5
⇒ x = 30

সুতরাং, সংখ্যাগুলো হলো 18, 24, 30, 36, 42।
এদের মধ্যে দ্বিতীয় বৃহত্তম সংখ্যাটি হলো 36।

৩,৫৬২.

A student's marks were wrongly entered as 89 instead of 62. Due to that the average marks for the class got increased by 3/2. The number of students in the class is-

ক
20
খ
10
গ
18
ঘ
24

ব্যাখ্যা

Question: A student's marks were wrongly entered as 89 instead of 62. Due to that the average marks for the class got increased by 3/2. The number of students in the class is-

Solution:
Let the number of students in the class be x.
Total increase in marks = x × 3/2 = 3x/2

ATQ,
3x/2 = (89 - 62)
⇒ 3x/2 = 27
⇒ 3x = 54
∴ x = 18

∴ The total number of students in the class is 18.

৩,৫৬৩.

The average of 25 results is 18. The average of the first 12 of those is 14 and the average of the last 12 is 17. What is the 13th result?

ক
68
খ
72
গ
76
ঘ
78

ব্যাখ্যা

Question: The average of 25 results is 18. The average of the first 12 of those is 14 and the average of the last 12 is 17. What is the 13th result?

Solution:
Sum of 1st 12 results = 12 × 14 = 168
Sum of last 12 results = 12 × 17 = 204
Let,
13th result = x

ATQ,
168 + 204 + x = (25 × 18)
⇒ 372 + x = 450
⇒ x = 450 - 372
∴ x = 78

৩,৫৬৪.

If p and n are integers such that p > n > 0 and p² - n²= 16, which of the following value of p - n?

ক
ক) 4
খ
খ) 2
গ
গ) 3
ঘ
ঘ) 1

ব্যাখ্যা

Question: If p and n are integers such that p > n > 0 and p² - n²= 16, which of the following value of p - n?

Solution:

p > n > 0 এবং p² - n² = 12

ধরি
p = 5 , n = 3

p² - n²= 16
5² - 3² = 16

সুতরাং,
p - n = 5 - 3 = 2

৩,৫৬৫.

A square and an equilateral triangle have equal perimeter. if the diagonal of the square is 12√2 cm then area of triangle is -

ক
ক) 56√3 cm²
খ
খ) 64√3 cm²
গ
গ) 47√5 cm²
ঘ
ঘ) 43√5 cm²
ঙ
ঙ) 37√7 cm²

ব্যাখ্যা

Let the side of the square be a cm.
Then, its diagonal = √2 a cm.
Now, √2 a = 12√2
⇒ a = 12 cm.
Perimeter of square = 4a = 48 cm.
Perimeter of equilateral triangle = 48 cm.
Each side of the triangle = 16 cm.
Area of the triangle = ((√3/4)×16×16) cm²
= 64√3 cm²

৩,৫৬৬.

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

ক
ক) 1/20
খ
খ) 3/5
গ
গ) 7/20
ঘ
ঘ) 2/5

ব্যাখ্যা

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

Let E = event that the ball drawn is neither red nor green
= event that the ball drawn is blue.
n(E) = 8
P(E) =n(E)/n(S) = 8/20 = 2/5

৩,৫৬৭.

A is two years older than B who is twice as old as C. If the total of the ages of A, B and C are 27, then how old is B?

ক
ক) 7 years
খ
খ) 8 years
গ
গ) 9 years
ঘ
ঘ) 10 years

ব্যাখ্যা

Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.

According to the question,
(2x + 2) + 2x + x = 27
5x = 25
⇒ x = 5
Hence, B's age = 2x = 10 years.

৩,৫৬৮.

A number is as much greater than 31 as less than 61. Which of the follwing is that numbers?

ক
ক) 15
খ
খ) 46
গ
গ) 26
ঘ
ঘ) 30

ব্যাখ্যা

Question: A number is as much greater than 31 as less than 61. Which of the follwing is that numbers?

Solution:
let
the number be a
Now
a - 31 = 61 - a
a + a = 61 + 31
2a = 92
a = 46

৩,৫৬৯.

A train travels 50% faster than a car. Both vehicles start from station P and reach station Q, 180 km away, at the same time. During the journey, the train stopped for 15 minutes at various stations. What is the speed of the car?

ক
120 km/h
খ
180 km/h
গ
200 km/h
ঘ
240 km/h
ঙ
260 km/h

ব্যাখ্যা

Question: A train travels 50% faster than a car. Both vehicles start from station P and reach station Q, 180 km away, at the same time. During the journey, the train stopped for 15 minutes at various stations. What is the speed of the car?

Solution:
Let speed of the car be x kmph.
Then, speed of the train = x + (50x)/100 = x + x/2
= (3x)/2

Now,
(180/x) - [180/{(3x)/2)}] = 15/60
⇒ (180/x) - (360/3x) = 1/4
⇒ (180/x) - (120/x) = 1/4
⇒ 60/x = 1/4
⇒ x = 240 km/h

৩,৫৭০.

A team of 5 players is to be selected from 7 forwards and 4 defenders. How many ways can this be done if exactly 3 forwards must be selected?

ক
140
খ
105
গ
84
ঘ
None above

ব্যাখ্যা

Question: A team of 5 players is to be selected from 7 forwards and 4 defenders. How many ways can this be done if exactly 3 forwards must be selected?

Solution:
Ways to choose 3 forwards from 7 = ⁷C₃ = 35
Ways to choose 2 defenders from 4 = ⁴C₂ = 6

Total combinations = 35 × 6 = 210

৩,৫৭১.

ক
1
খ
1/2
গ
- 3/2
ঘ
- 1

ব্যাখ্যা

Question:

Solution:

৩,৫৭২.

The H.C.F. of two numbers, each having three digits , is 17 and their L.C.M. is 714. The sum of the numbers will be:

ক
219
খ
221
গ
233
ঘ
239

ব্যাখ্যা

Question: The H.C.F. of two numbers, each having three digits , is 17 and their L.C.M. is 714. The sum of the numbers will be:

Solution:
Let, the numbers be 17x and 17y
where x and y are co-prime.

∴ LCM of 17x and 17y = 17 xy

ATQ,
17xy = 714
⇒ xy = 714/17
⇒ xy = 42
⇒ xy = 6 × 7

⇒ x = 6 and y = 7
∴ x = 7 and y =6

First number = 17x = 17 × 6 = 102
Second number = 17y = 17 × 7 = 119

∴ Sum of the numbers = (102 + 119) = 221

৩,৫৭৩.

A 10% monthly salary increase resulted in a Tk. 9,000 per year increase in salary for an employee. What was has monthly salary before the increase?

ক
ক) 5000
খ
খ) 7500
গ
গ) 9000
ঘ
ঘ) 12000

ব্যাখ্যা

12 মাসে বেতন বাড়ে = 9000 টাকা
1 মাসে বেতন বাড়ে = 9000/12
= 750 টাকা

প্রশ্নমতে
10% = 750 টাকা
1% = 750/10
100% = (750 × 100)/10
= 7500 টাকা

৩,৫৭৪.

What is the sum of the first 20 terms of the series 6, 11, 16, 21, ...?

ক
1010
খ
1190
গ
1260
ঘ
1070

ব্যাখ্যা

Question: What is the sum of the first 20 terms of the series 6, 11, 16, 21, ...?

Solution:
এটি একটি সমান্তর ধারা (arithmetic series)।
এখানে,
প্রথম পদ, a = 6
সাধারণ অন্তর, d = 11 - 6 = 5
পদের সংখ্যা, n = 20

সমান্তর ধারার n-সংখ্যক পদের সমষ্টি সূত্র:
S_n = (n/2) [2a + (n - 1)d]

∴ প্রথম 20টি পদের সমষ্টি:
S₂₀ = (20/2) [2 × 6 + (20 - 1) × 5]
= 10 [12 + 19 × 5]
= 10 [12 + 95]
= 10 × 107
= 1070

∴ প্রথম 20টি পদের সমষ্টি = 1070

৩,৫৭৫.

A runs twice as fast as B and B runs thrice as fast as C. The distance covered by C in 72 minutes, will be covered by A in:

ক
8 minutes
খ
10 minutes
গ
15 minutes
ঘ
12 minutes
ঙ
7 minutes

ব্যাখ্যা

Ratio of the speed of A, B and C = 6 : 3 : 1
Then, ratio of time taken= 1/6 : 1/3 : 1 = 1 : 2 : 6
Hence, time taken by A = 72/6 = 12 minutes.

৩,৫৭৬.

A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

ক
18 seconds
খ
12 seconds
গ
15 seconds
ঘ
24 seconds

ব্যাখ্যা

Question: A train is 100 meter long and is running at the speed of 30 km per hour. Find the time it will take to pass a man standing at a crossing.

Solution:
Given that,
Length of train, L = 100 meters
Speed of train, v = 30 km/h
= 30 × (1000/3600) m/s
= 30 × (5/18) m/s
= 150/18 m/s
= 25/3 m/s

We know,
Time taken = Distance/Speed
= 100/(25/3) m/s
= 100 × (3/25)
= 300/25
= 12 seconds

So the train takes 12 seconds to pass the man standing at the crossing.

৩,৫৭৭.

If P and Q together can complete a piece of work in 16 days and P alone in 24 days, in how many days can Q alone complete the work?

ক
72 days
খ
48 days
গ
42 days
ঘ
36 days

ব্যাখ্যা

Question: If P and Q together can complete a piece of work in 16 days and P alone in 24 days, in how many days can Q alone complete the work?

Solution:
P and Q complete a work in = 16 days
One day's work of (P + Q) = 1/16

P complete the work in = 24 days;
One day's work of P = 1/24

Then, Q's one day's work = (1/16) - (1/24)
= (3 - 2)/48
= 1/48

So, Q alone can complete the work in = 48 days.

৩,৫৭৮.

4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

ক
Tk. 5028
খ
Tk. 6068
গ
Tk. 2520
ঘ
Tk. 5082

ব্যাখ্যা

Question: 4200 Taka is lent at compound interest of 10% per annum for 2 years. Find the amount after two years.

Solution:
Compound amount = P (1 + r)ⁿ
= 4200 {1 + (10/100)}²
= 4200 × (110/100) × (110/100)
= 42 × 11 × 11
= 5082

৩,৫৭৯.

What is the angle between the hour and minute hands of a clock when it is 15 minutes past 3?

ক
5°
খ
6.5°
গ
7.5°
ঘ
9°

ব্যাখ্যা

Question: What is the angle between the hour and minute hands of a clock when it is 15 minutes past 3?

Solution:
15 minutes past 3 অর্থাৎ, ৩ টা 15 মিনিট।
= 3 + (15/60) ঘন্টা
= 3 + (1/4)
= 13/4 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/4 ঘন্টায় ঘোরে = (30° × 13)/4 = 390°/4 = 97.5°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 15 মিনিটে ঘোরে = 15 × 6° = 90°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = | 97.5° - 90° |
= 7.5°

৩,৫৮০.

In a group of cows and hens, the number of legs are 12 more than twice the number of heads. What is the number of cows?

ক
5
খ
6
গ
7
ঘ
8

ব্যাখ্যা

Question: In a group of cows and hens, the number of legs are 12 more than twice the number of heads. What is the number of cows?

Solution:
Let, Number of Cows = x
Number of Hens= y

Then, Total number of heads = x + y
Number of legs of cows = 4x
Number of legs of hens = 2y
∴ Total number of legs of cows and hens = 4x + 2y

ATQ,
4x + 2y = 2(x + y) + 12
⇒ 4x + 2y = 2x + 2y + 12
⇒ 4x - 2x = 2y + 12 - 2y
⇒ 2x = 12
∴ x = 6
So, the number of cows is 6.

৩,৫৮১.

What is the area of the region enclosed by the figure above?

ক
116
খ
144
গ
176
ঘ
179

ব্যাখ্যা

Question:

What is the area of the region enclosed by the figure above?

Solution:
Focus on the rectangle
12 × 10 = 120
and then the smaller one i.e.
7 × 8 = 56
thus area is 120 + 56 = 176

৩,৫৮২.

If (2p + 1/p) = 4, the value of (p³ + 1/8p³) is -

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 5/2

ব্যাখ্যা

Question: If (2p + 1/p) = 4, the value of (p³ + 1/8p³) is -

Solution:
Given,
(2p + 1/p) = 4
Or, (1/2) (2p + 1/p) = 4 × 1/2
Or, p + 1/2p = 2

Now, (p³ + 1/8p³) = (p)³ + (1/2p)³
= (p + 1/2p)³ - 3 . p . 1/2p . (p + 1/2p)
= (2)³ - 3 . (1/2) . 2
= 8 - 3
= 5

৩,৫৮৩.

A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

ক
12 years
খ
14 years
গ
18 years
ঘ
20 years
ঙ
22 years

ব্যাখ্যা

Let the son's present age be x years.
Then,
man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.

৩,৫৮৪.

If 3 less than twice the number is equal to 2 more than 3 times the number, then 5 less than 5 times the number is:

ক
- 25
খ
- 30
গ
46
ঘ
25

ব্যাখ্যা

Question: If 3 less than twice the number is equal to 2 more than 3 times the number, then 5 less than 5 times the number is:

Solution:
Let the number be x

ATQ,
2x - 3 = 3x + 2
∴ x = - 5

∴ Five times the number = 5 × (- 5)
= - 25
∴ Five less than this = - 25 - 5
= - 30

৩,৫৮৫.

In a class of 65 students and 4 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 40% of the total number of students. How many sweets are there?

ক
104
খ
845
গ
949
ঘ
897

ব্যাখ্যা

Question: In a class of 65 students and 4 teachers, each student got sweets that are 20% of the total number of students and each teacher got sweets that are 40% of the total number of students. How many sweets are there?

Solution:
There are 65 students and 4 teachers
Each student got sweets that are 20% of the total number of students.
So each student got sweets = 65 × 20%
= 13 sweets.

∴ Total sweets for students is = 65 × 13 = 845

Each teacher got sweets that are 40% of the total number of students.
So each teacher got sweets = 65 × 40% = 26 sweets.

There are 4 teachers, so total sweets for teachers = 4 × 26 = 104

∴ Total sweets = sweets for students + sweets for teachers
= 845 + 104
= 949

Therefore, the total number of sweets is 949.

৩,৫৮৬.

Mr. Rafin can complete a job in 15 days. while Mr. Shafin takes twice as long to do the same job. If they work together, how many days will they require to complete the job?

ক
ক) 12
খ
খ) 15
গ
গ) 10
ঘ
ঘ) 6

ব্যাখ্যা

Question: Mr. Rafin can complete a job in 15 days. while Mr. Shafin takes twice as long to do the same job. If they work together, how many days will they require to complete the job?

Solution:
রাফিন সাহেব সময় নেয় ১৫ দিন
∴ শাফিন সাহেব সময় নেয় ৩০ দিন

তারা ১ দিনে মোট করতে পারে = (১/১৫ + ১/৩০)
= ৩/৩০
= ১/১০

∴ সম্পূর্ণ অংশ শেষ করতে তাদের সময় লাগবে = ১০ দিন

৩,৫৮৭.

Doubling the selling price results in tripling the profit. Calculate the profit percentage.

ক
100%
খ
50%
গ
70%
ঘ
110%

ব্যাখ্যা

Question: Doubling the selling price results in tripling the profit. Calculate the profit percentage.

Solution:
Let the first selling price Tk. 100
then, the 2nd selling price Tk. 200
Suppose, the first profit is Tk x

ATQ,
100 - x = 200 - 3x
⇒ 2x = 100
⇒ x = 50

So, the profit is Tk 50
Then, the cost price is = 100 - 50 = 50

∴ Profit = (50/50) × 100 = 100%

৩,৫৮৮.

The ratio of X : Y is 3 : 4, and the ratio of Y : Z is 8 : 9. If X = 18, what is the value of Z?

ক
24
খ
27
গ
30
ঘ
36

ব্যাখ্যা

Question: The ratio of X : Y is 3 : 4, and the ratio of Y : Z is 8 : 9. If X = 18, what is the value of Z?

Solution:
দেওয়া আছে,
X : Y = 3 : 4
Y : Z = 8 : 9
এবং X = 18

এখন,
X : Y = 3 : 4
⇒ X/Y = 3/4
⇒ 3Y = 4X
⇒ Y = (4 × 18) / 3 ; [X = 18]
∴ Y = 24

আবার,
Y : Z = 8 : 9
⇒ Y/Z = 8/9
⇒ 8Z = 9Y
⇒ Z = (9 × 24) / 8
∴ Z = 27

সুতরাং, Z এর মান হলো 27

৩,৫৮৯.

If a right-angled isosceles triangle has base 4 cm, then height is:

ক
2 cm
খ
4 cm
গ
6 cm
ঘ
8 cm

ব্যাখ্যা

Question: If a right-angled isosceles triangle has base 4 cm, then height is:

5 Combine Banks (২০২২ সাল ভিত্তিক) Post Name: Officer Cash/Officer Teller (১০ম গ্রেড) Exam Date: 11.07.2025 Faculty of Business Studies (FBS), DU

Solution:
(Right-angled isosceles triangle) সমকোণী সমদ্বিবাহু ত্রিভুজ এর ভূমি = 4 cm.
সমকোণী সমদ্বিবাহু ত্রিভুজ এর ভূমি ও উচ্চতা সমান।
ভূমি = উচ্চতা = 4 cm.
∴ উচ্চতা = 4 cm

৩,৫৯০.

In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the number of girls becomes-

ক
110
খ
128
গ
132
ঘ
144

ব্যাখ্যা

Question: In a school having roll strength 286, the ratio of boys and girls is 8 : 5. If 22 more girls get admitted into the school, the number of girls becomes-

Solution:
Boys : girls = 8 : 5
Let, the boys = 8x, girl = 5x

According to the 1st condition,
8x + 5x = 286
⇒ 13x = 286
⇒ x = 286/13
∴ x = 22
Boys = 8 × 22 = 176 and girls = 5 × 2 = 110

22 more girls get admitted then the number of girls become = (5x + 22)
= 110 + 22
= 132

৩,৫৯১.

Rakesh had to do a multiplication instead of taking 25 as one of the multipliers, she took 52. As a result, the product went up by 540. What is the new product?

ক
ক) 1050
খ
খ) 1060
গ
গ) 1040
ঘ
ঘ) 1080

ব্যাখ্যা

Question: Rakesh had to do a multiplication instead of taking 25 as one of the multipliers, she took 52. As a result, the product went up by 540. What is the new product?

Solution:
ধরি, সংখ্যাটি = x

প্রশ্নমতে
52x - 25x = 540
⇒27x = 540
⇒x = 540/27
⇒ x = 20

নতুন গুণফল = 52 × 20 = 1040

৩,৫৯২.

A can finish a work in 15 days, and B can do it in 25 days. They work together for 5 days. What fraction of the work remains unfinished?

ক
3/5
খ
7/15
গ
2/3
ঘ
None of the above

ব্যাখ্যা

Question: A can finish a work in 15 days, and B can do it in 25 days. They work together for 5 days. What fraction of the work remains unfinished?

Solution:
Work done by A in 1 day = 1/15
Work done by B in 1 day = 1/25

Combined work in 1 day = 1/15 + 1/25
= (5 + 3) / 75
= 8/75

Work done in 5 days = 5 × (8/75) = 40/75 = 8/15

Fraction of work left = 1 - 8/15 = 7/15

৩,৫৯৩.

Find out the wrong number in the series:
3, 8, 15, 24, 34, 48, 63

ক
24
খ
34
গ
48
ঘ
63

ব্যাখ্যা

Question: Find out the wrong number in the series:
3, 8, 15, 24, 34, 48, 63

Solution:
8 - 3 = 5
15 - 8 = 7
24 - 15 = 9
35 - 24 = 11 [34* - 24 = 10]
48 - 35 = 13
63 - 48 = 15

The differences between consecutive terms are respectively 5, 7, 9, 11, 13 and 15.
So, 34 is the wrong number.

৩,৫৯৪.

A group of 10 boxes has their average weight increased by 4 kg after replacing a 60 kg box with a new one. What is the weight of the new box?

ক
75
খ
85
গ
92
ঘ
100

ব্যাখ্যা

Question: A group of 10 boxes has their average weight increased by 4 kg after replacing a 60 kg box with a new one. What is the weight of the new box?

Solution:
Let the weight of the new box be x kg.
Let the total weight of the original 10 boxes = W
Original average = W/10

After replacing the 60 kg box with x,
The total weight becomes: W - 60 + x
The new average = (W - 60 + x) / 10

Accordingly:
New average = Old average + 4
(W - 60 + x) / 10 = W/10 + 4
⇒ W - 60 + x = W + 40
⇒ x = 40 + 60
⇒ x = 100

৩,৫৯৫.

Alam sold two vehicles for Tk. 46,000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

ক
ক) 2% loss
খ
খ) 1% profit
গ
গ) 1% loss
ঘ
ঘ) None of these

ব্যাখ্যা

Question: Alam sold two vehicles for Tk. 46,000 each. If he gained 10% on the first and lost 10% on another, then what is his percentage profit or loss in this transaction?

Solution:
In the first case he gains 10%
∴ C. P. of the first car = (100 × 46000)/110 = 41,818.18

In the second case he loses 10%
∴ C. P. of the second car = (100 × 46000)/90 = 51,111.11

∴ Total cost of both cars = 41818.18 + 51111.11 = Tk 92,929.29
∴ Total S. P. of both cars = 2 × 46000 = Tk.92,000

Total loss = 92,929.29 - 92,000 = Tk. 929.29

%loss = (929.29/92,929.29) ×100 = 0.99% ≈ 1%

৩,৫৯৬.

What would be the compound interest accrued on an amount of Tk. 5000 at the rate of 20% per annum in 2 years?

ক
ক) Tk. 2200
খ
খ) Tk. 2400
গ
গ) Tk. 2600
ঘ
ঘ) Tk. 2800

ব্যাখ্যা

Question: What would be the compound interest accrued on an amount of Tk. 5000 at the rate of 20% per annum in 2 years?

Solution:
Here,
Principal = Tk. 5000
Rate = 20%
Time = 2 years

Amount = 5000 × {1 + (20/100)}²
= 5000 × (120/100) × (120/100)
= 7200

∴ Compound interest = Tk. (7200 - 5000) = Tk. 2200

৩,৫৯৭.

If 9a² - 9a - 4 is divided by 3a - 4, the result is:

ক
3a + 1
খ
2a + 1
গ
3a - 2
ঘ
3a - 1

ব্যাখ্যা

Question: If 9a² - 9a - 4 is divided by 3a - 4, the result is:

Solution:
9a² - 9a - 4
= 9a² - 12a + 3a - 4
= 3a(3a - 4) + 1(3a - 4)
= (3a - 4)(3a + 1)

Now,
(9a² - 9a - 4)/(3a - 4) = {(3a - 4)(3a + 1)}/(3a + 1) = (3a + 1)

৩,৫৯৮.

In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk?

ক
ক) 1
খ
খ) 1/40
গ
গ) 40
ঘ
ঘ) 80

ব্যাখ্যা

Let,
The required number of days be x.
Less Cows, More days[Indirect proportion]
Less Bags, Less days [Direct proportion]
Cows(1 : 40), bags(40 : 1)}::40 : x
∴ 1 × 40 × x = 40 × 1 × 40
= 40.

৩,৫৯৯.

If the first and sixth term of a geometric series are respectively 1/2 and 1/64, then the common ratio is____

ক
ক) 1/4
খ
খ) 1/2
গ
গ) 1
ঘ
ঘ) 2

ব্যাখ্যা

Given, ar⁰ = 1/2
Or, a = 1/2
And, ar⁵ = 1/64
Or, r⁵ = 1/32
Or, r⁵ = (1/2)⁵
∴ Ratio, r = 1/2

৩,৬০০.

If, a - (1/a) = 2, then the value of a³ - (1/a³) is -

ক
15
খ
2
গ
14
ঘ
11

ব্যাখ্যা

Given,
a - (1/a) = 2
On cubing both of the sides,
a³ - (1/a³) - 3 × a × (1/a) (a - 1/a) = 2³
⇒ a³ - (1/a³) - 3(a - 1/a) = 8
⇒ a³ - (1/a³) - 3 × 2 = 8
⇒ a³ - (1/a³) = 8 + 6
∴ a³ - (1/a³) = 14.