Bank Math

PrepBank · পাতা ৯১ / ১৬১ · ৯,০০১–৯,১০০ / ১৬,১২৪

৯,০০১.

In a lottery, there are 16 prizes and 32 blanks. A lottery is drawn at random. What is the probability of getting a prize?

ক
ক) 1/16
খ
খ) 1/32
গ
গ) 1/3
ঘ
ঘ) None of the above

সঠিক উত্তর: গ

গ) 1/3

উত্তর

সঠিক উত্তর: গ

গ) 1/3

গ

ব্যাখ্যা

Question: In a lottery, there are 16 prizes and 32 blanks. A lottery is drawn at random. What is the probability of getting a prize?

Solution:
Total outcome = 16 + 32 = 48
Favorable outcome = 16
P (getting a prize) =16/48
= 1/3

৯,০০২.

A and B together can complete a work in 12 days, B and C together can complete the same work in 8 days and A and C together can complete it in 16 days. In total, how many days do A, B and C together take to complete the same work?

ক
ক) 73/7 days
খ
খ) 97/11 days
গ
গ) 75/13 days
ঘ
ঘ) 96/13 days

সঠিক উত্তর: ঘ

ঘ) 96/13 days

উত্তর

সঠিক উত্তর: ঘ

ঘ) 96/13 days

ঘ

ব্যাখ্যা

(A + B)'s 1 day work = 1/12
(B + C)'s 1 day work =1/8
(A + C)'s 1 day work =1/16

2( A+B +C ) one day work =(1/12) + (1/8) + (1/16)
= (4 + 6 + 3)/48
= 13/48

( A+B +C ) one day work =13/96

So (A+B+C) done work = 96/13 days

৯,০০৩.

The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than him. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?

ক
ক) 23
খ
খ) 24
গ
গ) 25
ঘ
ঘ) None

সঠিক উত্তর: ক

ক) 23

উত্তর

সঠিক উত্তর: ক

ক) 23

ক

ব্যাখ্যা

Given, Captain's age 26 years and Wicketkeeper's age 29 years.
Let, Average age be X years

ATQ,
9(x - 1) + 26 + 29 = 11x
⇒ 9x - 9 + 26 + 29 = 11x
⇒ 2x = 46
⇒ x = 23

৯,০০৪.

If tan (x − 30°) = 1/√3, cosx = ?

ক
ক) 1/2
খ
খ) 0
গ
গ) 1/√2
ঘ
ঘ) 1

সঠিক উত্তর: ক

ক) 1/2

উত্তর

সঠিক উত্তর: ক

ক) 1/2

ক

ব্যাখ্যা

tan (x - 30°) = 1/√3 = tan 30°
Or, x - 30° = 30°
Or, x = 60°

∴ cos 60° = 1/2

৯,০০৫.

An outlet pipe can empty a cistern in 4 hours. In what time will it empty 3/4 part of the cistern?

ক
2 hours
খ
3 hours
গ
4 hours
ঘ
5 hours

সঠিক উত্তর: খ

3 hours

উত্তর

সঠিক উত্তর: খ

3 hours

খ

ব্যাখ্যা

Question: An outlet pipe can empty a cistern in 4 hours. In what time will it empty 3/4 part of the cistern?

Solution:
The outlet pipe empties one complete cistern in 4 hours
Time taken to empty 3/4 Part of the cistern = (3/4) × 4 = 3 hours.

৯,০০৬.

Mr. Kamal purchased brand P pen for Taka 200 each and brand R pen for Taka 100 each. If he purchased a total of 8 of these pens for Taka 1,200 how many pens of brand P did he purchased?

ক
4
খ
5
গ
8
ঘ
12

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

ধরি, P brand এর কলম সংখ্যা x টি
R brand এর কলম সংখ্যা (8 - x) টি

200x + (8 - x) × 100 = 1200
⇒ 200x + 800 - 100x = 1200
⇒ 100x = 1200 - 800
⇒ x = 400/100
⇒ x = 4

৯,০০৭.

How many different registration numbers can be formed using two distinct letters followed by two distinct digits?

ক
42,500
খ
50,500
গ
58,500
ঘ
72,500
ঙ
None of the above

সঠিক উত্তর: গ

58,500

উত্তর

সঠিক উত্তর: গ

58,500

গ

ব্যাখ্যা

Question: How many different registration numbers can be formed using two distinct letters followed by two distinct digits?

Solution:
Here,
Number of ways to choose and arrange two distinct letters out of 26 alphabets = ²⁶P₂
= 26 × 25
= 650

Number of ways to choose and arrange two distinct digits out of 10 digits (0 - 9) = ¹⁰P₂
= 10 × 9
= 90

Total number of registration numbers = 650 × 90
= 58,500

৯,০০৮.

Two ingoing pipes are used to fill a cistern of capacity 2000 liters. The first pipe can fill the cistern twice as fast as the second one. Together, both pipes can fill the cistern in just 16/3 hours. What is the fill-up capacity of the first pipe per hour?

ক
200 liters
খ
220 liters
গ
250 liters
ঘ
500 liters
ঙ
None of the above

সঠিক উত্তর: গ

250 liters

উত্তর

সঠিক উত্তর: গ

250 liters

গ

ব্যাখ্যা

Question: Two ingoing pipes are used to fill a cistern of capacity 2000 liters. The first pipe can fill the cistern twice as fast as the second one. Together, both pipes can fill the cistern in just 16/3 hours. What is the fill-up capacity of the first pipe per hour?

Solution:
Let the first pipe fill the cistern in X hour,
so, the second pipe can fill the cistern in 2X hours.

both pipes can fill in one hour = (1/X) + (1/2X)
= 3/2X
ATQ,
2X/3 = 16/3
∴ X = 8 hours.

∴ the fill-up capacity of the first pipe per hour is = 2000/8 = 250 liters.

৯,০০৯.

Find the cost of a cylinder of radius 14 m and height 3.5 m when the cost of its metal is Tk. 50 per cubic meter-

ক
Tk. 107800
খ
Tk. 10800
গ
Tk. 109800
ঘ
Tk. 108700

সঠিক উত্তর: ক

Tk. 107800

উত্তর

সঠিক উত্তর: ক

Tk. 107800

ক

ব্যাখ্যা

Question: Find the cost of a cylinder of radius 14 m and height 3.5 m when the cost of its metal is Tk. 50 per cubic meter-

Solution:
We know,
The volume of the cylinder = πr²h
= (22/7) × 14 × 14 × 3.5
= 2156 m³

Cost of the cylinder = 2156 × 50
= Tk. 107800

৯,০১০.

Bird : Nest :: Dog : ?

ক
Cage
খ
Chain
গ
Bone
ঘ
Kennel

সঠিক উত্তর: ঘ

Kennel

উত্তর

সঠিক উত্তর: ঘ

Kennel

ঘ

ব্যাখ্যা

Question: Bird : Nest :: Dog : ?

Solution:
A nest is the home of a bird, just as a kennel is the home of a dog.

৯,০১১.

A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70. Then how many horses are there?

ক
16
খ
14
গ
12
ঘ
10

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A certain number of horses and an equal number of men are going somewhere. Half of the owners are on their horses back while the remaining ones are walking along leading their horses. If the number of legs walking on the ground is 70. Then how many horses are there?

Solution:
Let, the number of horses be x.
Then, the number of men = x
Number of man walking = x/2

ATQ,
4x + (x/2) . 2 = 70
⇒ 5x = 70
∴ x = 14

৯,০১২.

A bag contains 6 red balls, 9 black balls, and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is neither red nor white?

ক
3/7
খ
9/20
গ
11/20
ঘ
4/9

সঠিক উত্তর: খ

9/20

উত্তর

সঠিক উত্তর: খ

9/20

খ

ব্যাখ্যা

Question: A bag contains 6 red balls, 9 black balls, and 5 white balls. One ball is drawn at random. What is the probability that the ball drawn is neither red nor white?

Solution:

Total balls = 6 + 9 + 5 = 20

Favorable outcomes = balls that are neither red nor white, that is, black balls = 9

∴ P(black) = Favorable outcomes/Total outcomes
= 9/20

Therefore, the probability is 9/20.

৯,০১৩.

A cube of dimension a fits perfectly in a hollow spherical ball. What is the total surface area of that ball?

ক
4πa²
খ
3πa²
গ
5πa²
ঘ
6πa²

সঠিক উত্তর: খ

3πa²

উত্তর

সঠিক উত্তর: খ

3πa²

খ

ব্যাখ্যা

Question: A cube of dimension a fits perfectly in a hollow spherical ball. What is the total surface area of that ball?

Solution:
here,
the lenght of the cube is = a
∴ Diagonal of the cube is = √3a

as the diagonal of the cube is equal to the diameter of the ball,
2r = √3a
r = √3a/2

∴ the total surface area of the ball is = 4πr²
= 4π(√3a/2)²
= 3πa²

৯,০১৪.

Q. (56-65) Choose the correct answer
৫৬)In this world nothing is low, nothing mean. The rock we have frequented may hide a rich mine, the water we have fished may have pearl beds beneath, the man we have neglected may have high soul. So all the things we see around us have their______.

ক
ক) uses
খ
খ) price
গ
গ) existence
ঘ
ঘ) power

সঠিক উত্তর: খ

খ) price

উত্তর

সঠিক উত্তর: খ

খ) price

খ

ব্যাখ্যা

Question: In this world nothing is low, nothing mean. The rock we have frequented may hide a rich mine, the water we have fished may have pearl beds beneath, the man we have neglected may have high soul. So all the things we see around us have their______.

Solution:
এই পৃথিবীতে কিছু অমূল্য নয়। আমরা যে শিলা বারবার দেখেছি তা হয়তো একটি সমৃদ্ধ খনি লুকিয়ে রাখতে পারে, আমরা যে জলে মাছ ধরেছি তার নীচে মুক্তার বিছানা থাকতে পারে, যে মানুষটিকে আমরা অবহেলা করেছি তার উচ্চ আত্মা থাকতে পারে।

অতএব, প্রত্যেক জিনিসের একটি মূল্য আছে।

৯,০১৫.

Three mechanics A, B, and C can manufacture 120 units in 12, 20, and 30 hours respectively. What is the ratio of the time taken by A alone to complete the work to the time taken by all three working together to complete the same work?

ক
5 : 2
খ
4 : 3
গ
3 : 1
ঘ
2 : 1

সঠিক উত্তর: ঘ

2 : 1

উত্তর

সঠিক উত্তর: ঘ

2 : 1

ঘ

ব্যাখ্যা

Question: Three mechanics A, B, and C can manufacture 120 units in 12, 20, and 30 hours respectively. What is the ratio of the time taken by A alone to complete the work to the time taken by all three working together to complete the same work?

Solution:
(A + B + C) together can do in 1 hour = (1/12) + (1/20) + (1/30)
= (5 + 3 + 2)/60
= 10/60
= 1/6
So, working together they complete the work in 6 hours.

And A alone takes 12 hours.

∴ Ratio of the time taken by A and (A + B + C) =12 : 6 = 2 : 1

৯,০১৬.

A trader purchases an item for Tk. 540 and sets it marked price at 30% above the cost price. He then sells it at a discount of 20% on the marked price. What is his profit percentage?

ক
8%
খ
16%
গ
4%
ঘ
12%

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A trader purchases an item for Tk. 540 and sets it marked price at 30% above the cost price. He then sells it at a discount of 20% on the marked price. What is his profit percentage?

Solution:
Let
the cost price be Tk. 100
Therefore the marked price is Tk. 130 (30% above CP)
Discount is Tk. 26 (20% of marked price)
Selling price is = (Tk. 130 - Tk. 26) = Tk. 104

Therefore, profit percentage is 4%.

The given cost price of Tk. 540 is unnecessary and is only for creating confusion.

৯,০১৭.

A mother can do a job as fast as her two daughters working together. If one daughter does the job alone in 3 hours and the other does it alone in 6 hours, how many hours does it take the mother to do the job alone?

ক
2
খ
3
গ
4
ঘ
6
ঙ
None of these

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

First daughter, in 1 hour, did 1/3 part
Second daughter, in 1 hour, did 1/6 part
Mother, in 1 hour, did (1/3 + 1/6) part
= 3/6 part
= 1/2 part
so, mother did it in 2 days.

৯,০১৮.

The product P of two prime numbers is between 9 and 55. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then P =

ক
ক) 15
খ
খ) 33
গ
গ) 34
ঘ
ঘ) 51

সঠিক উত্তর: ঘ

ঘ) 51

উত্তর

সঠিক উত্তর: ঘ

ঘ) 51

ঘ

ব্যাখ্যা

one of the prime numbers is greater than 2 but less than 6 = 3 or 5
the other is greater than 13 but less than 25 = 17, 19 or 23
17 × 3, 19 × 3 or 23 × 3 ⇒ 51, 57 or 69
17 × 5, 19 × 5 or 23 × 5 ⇒ 85, 95 or 115
Option 51 is among 51, 57, 69, 85, 95 or 115

৯,০১৯.

একজন শিক্ষার্থী বিদ্যালয়ের তিনটি পরীক্ষায় ইংরেজিতে গড়ে ৬২ নম্বর পেয়েছে। বার্ষিক পরীক্ষায় কত নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে?

ক
৭০ নম্বর
খ
৭৪ নম্বর
গ
৮১ নম্বর
ঘ
৮৫ নম্বর
ঙ
কোনোটিই নয়

সঠিক উত্তর: খ

৭৪ নম্বর

উত্তর

সঠিক উত্তর: খ

৭৪ নম্বর

খ

ব্যাখ্যা

প্রশ্ন: একজন শিক্ষার্থী বিদ্যালয়ের তিনটি পরীক্ষায় ইংরেজিতে গড়ে ৬২ নম্বর পেয়েছে। বার্ষিক পরীক্ষায় কত নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে?

সমাধান:
তিনটি পরীক্ষায় গড় নম্বর = ৬২
∴ তিনটি পরীক্ষায় মোট নম্বর = (৬২ × ৩)
= ১৮৬

ধরি,
বার্ষিক পরীক্ষায় ক নম্বর পেলে তাঁর নম্বরের গড় ৬৫ হবে।

প্রশ্নমতে,
(১৮৬ + ক)/৪ = ৬৫
⇒ ১৮৬ + ক = ২৬০
⇒ ক = ২৬০ - ১৮৬
∴ ক = ৭৪

৯,০২০.

If the average of 'p' numbers is 3q² and the average of 'q' numbers is 3p², what is the average of the combined (p + q) numbers?

ক
p²q²
খ
3pq
গ
3(p + q)
ঘ
2pq/(p + q)

সঠিক উত্তর: খ

3pq

উত্তর

সঠিক উত্তর: খ

3pq

খ

ব্যাখ্যা

Question: If the average of 'p' numbers is 3q² and the average of 'q' numbers is 3p², what is the average of the combined (p + q) numbers?

Solution:
দেওয়া আছে,
'p' সংখ্যার গড় = 3q²∴ p সংখ্যার সমষ্টি = p × 3q²

'q' সংখ্যার গড় = 3p²∴ 'q' সংখ্যার সমষ্টি = q × 3p²

∴ মোট সমষ্টি = (p × 3q²) + (q × 3p²)
= 3pq² + 3qp²
= 3pq(q + p)

∴ তাদের গড় = মোট সমষ্টি/(p + q)
= 3pq(p + q)/(p + q)
= 3pq

৯,০২১.

A rope can make 70 rounds of the circumference of a cylinder whose radius of the base is 14cm. How many times can it go round a cylinder having radius 20 cm?

ক
ক) 54 rounds
খ
খ) 42 rounds
গ
গ) 49 rounds
ঘ
ঘ) 52 rounds

সঠিক উত্তর: গ

গ) 49 rounds

উত্তর

সঠিক উত্তর: গ

গ) 49 rounds

গ

ব্যাখ্যা

Let the required number of rounds be x

More radius, less rounds(Indirect proportion)

Hence we can write as
(radius) 14 : 20 :: x : 70
⇒ 14 × 70 = 20x
⇒ 14 × 7 = 2x
⇒ x = 7 × 7
= 49 days.

৯,০২২.

A number when divided by the sum of 55 and 45 gives two times their difference as quotient and 11 as the remainder. The number is -

ক
20011
খ
2111
গ
2011
ঘ
3011

সঠিক উত্তর: গ

2011

উত্তর

সঠিক উত্তর: গ

2011

গ

ব্যাখ্যা

Question: A number when divided by the sum of 55 and 45 gives two times their difference as quotient and 11 as the remainder. The number is -

Solution:
the sum of 55 and 45 is = (55 + 45) = 100
the difference of 55 and 45 is = (55 - 45) = 10

so, the number is = {(2 × 10) × 100} + 11
= 2000 + 11
= 2011

৯,০২৩.

A wheel of an engine of 450 cm in circumference makes 20 revolutions in 6 seconds. What is the speed of the wheel in km/h?

ক
46 km/h
খ
48 km/h
গ
50 km/h
ঘ
54 km/h
ঙ
56 km/h

সঠিক উত্তর: ঘ

54 km/h

উত্তর

সঠিক উত্তর: ঘ

54 km/h

ঘ

ব্যাখ্যা

Question: A wheel of an engine of 450 cm in circumference makes 20 revolutions in 6 seconds. What is the speed of the wheel in km/h?

Solution:
Total distance = (450 × 20) cm
= 9000 cm
= 9000/100 m
= 90 m

We know,
Speed = (Total distance ÷ Time)
= (90 ÷ 6) m/sec
= 15 m/sec
= (15 × 18/5) km/h
= 54 km/h

৯,০২৪.

A truck can carry 24 motorcycles or 36 scooters at a time. If there are 10 motorcycles on the truck, how many scooters can be loaded onto it?

ক
10 scooters
খ
11 scooters
গ
21 scooters
ঘ
30 scooters
ঙ
31 scooters

সঠিক উত্তর: গ

21 scooters

উত্তর

সঠিক উত্তর: গ

21 scooters

গ

ব্যাখ্যা

Question: A truck can carry 24 motorcycles or 36 scooters at a time. If there are 10 motorcycles on the truck, how many scooters can be loaded onto it?

Solution:
Here,
24 motorcycles = 36 scooters
∴ 1 motorcycle = 36/24 scooters = 3/2 scooters
∴ 10 motorcycles = (36 × 10)/24 scooters = 15 scooters

∴ Maximum number of scooters that can still be loaded = 36 - 15 = 21 scooters

৯,০২৫.

In a 500-meter race, Q starts 50 meters ahead of P, yet P defeats Q by a margin of 25 meters. What distance did Q cover when P reached the finish line?

ক
425 meters
খ
475 meters
গ
400 meters
ঘ
450 meters

সঠিক উত্তর: ক

425 meters

উত্তর

সঠিক উত্তর: ক

425 meters

ক

ব্যাখ্যা

Question: In a 500-meter race, Q starts 50 meters ahead of P, yet P defeats Q by a margin of 25 meters. What distance did Q cover when P reached the finish line?

Solution:
Total distance Q needed to cover = 500 - 50 = 450 meters
Distance covered by P = 500 meters
But P defeats Q by 25 meters

∴ Distance covered by Q when P reaches the finish line = 450 - 25 = 425 meters

∴ Q covered a distance of 425 meters when P reached the finish line.

৯,০২৬.

Kiron invests Tk. 500 in a Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

ক
Tk. 650
খ
Tk. 660
গ
Tk. 750
ঘ
Tk. 700

সঠিক উত্তর: ঘ

Tk. 700

উত্তর

সঠিক উত্তর: ঘ

Tk. 700

ঘ

ব্যাখ্যা

Question: Kiron invests Tk. 500 in a Bank of Bangladesh at a simple interest rate of 8%. How much will be in his account after 5 years?

Solution:
Let,
P = Tk. 500
r = 8% = 8/100
n = 5 years

∴ I = Pnr
= 500 × 5 × (8/100)
= 200

∴ total amount after 5 years will be = (500 + 200)
= Tk. 700

৯,০২৭.

S.I. on Tk. 1500 at 7% per annum for a certain time is Tk. 210. Find the time.

ক
3 years
খ
1.5 years
গ
2 years
ঘ
2.8 years

সঠিক উত্তর: গ

2 years

উত্তর

সঠিক উত্তর: গ

2 years

গ

ব্যাখ্যা

Question: S.I. on Tk. 1500 at 7% per annum for a certain time is Tk. 210. Find the time.

Solution:
P = 1500
r = 7%
I = 210
n = ?

n = I/(Pr)
= (210 × 100)/(1500 × 7)
= 2 years

৯,০২৮.

Calculate sin(- 585°).

ক
1/3
খ
√2/3
গ
1/2
ঘ
1/√2

সঠিক উত্তর: ঘ

1/√2

উত্তর

সঠিক উত্তর: ঘ

1/√2

ঘ

ব্যাখ্যা

Question: Calculate sin(- 585°).

Solution:
sin(- 585°)
= - sin(585°)
= - sin(360° + 225°)
= - sin(2π + 225°)
= - sin225°
= - sin(180° + 45°)
= - sin(π + 45°)
= sin45°
= 1/√2

৯,০২৯.

A shop offers a ‘Buy 2, Get 1 Free’ deal. What is the equivalent percentage discount?

ক
30.33%
খ
33.33%
গ
25%
ঘ
20%

সঠিক উত্তর: খ

33.33%

উত্তর

সঠিক উত্তর: খ

33.33%

খ

ব্যাখ্যা

Question: A shop offers a ‘Buy 2, Get 1 Free’ deal. What is the equivalent percentage discount?

Solution:
Assume the price of each item = 1 Taka.
Then,
Cost of 2 items = 2 Taka
Since 1 item is received for free, total items = 2 + 1 = 3

After the discount,
Cost of 3 items = 2 Taka
∴ Cost per item = 2/3 Taka

Actual price per item = 1 Taka
∴ Discount per item = 1 − (2/3) = 1/3 Taka

So, discount on 1 Taka = 1/3 Taka
∴ Discount on 100 Taka = 100 × (1/3) = 33.33 Taka

Therefore, in a “Buy 2, Get 1 Free” offer, the equivalent discount is 33.33%.

৯,০৩০.

The mean weight of a class of 20 students is 48 kg. Two more students weighing 60 kg and 58 kg respectively join the class. What is the mean weight of the class now?

ক
32 kg
খ
36 kg
গ
48 kg
ঘ
49 kg

সঠিক উত্তর: ঘ

49 kg

উত্তর

সঠিক উত্তর: ঘ

49 kg

ঘ

ব্যাখ্যা

Question: The mean weight of a class of 20 students is 48 kg. Two more students weighing 60 kg and 58 kg respectively join the class. What is the mean weight of the class now?

Solution:
The mean Weight of 20 students = 48
∴ Total weight = 20 × 48 = 960

Add two students weighing 60, 58 to 960 = 960 + 60 + 58 = 1078

Therefore, Mean = 1078/22
= 49 kg

So the new mean weight of the class is 49 kg.

৯,০৩১.

A committee of 3 men and 2 women is to be formed from 6 men and 4 women. How many ways can this be done?

ক
60
খ
120
গ
240
ঘ
360

সঠিক উত্তর: খ

120

উত্তর

সঠিক উত্তর: খ

120

খ

ব্যাখ্যা

Question: A committee of 3 men and 2 women is to be formed from 6 men and 4 women. How many ways can this be done?

Solution:
Ways to choose 3 men out of 6 = ⁶C₃ = 20
Ways to choose 2 women out of 4 = ⁴C₂ = 6

Total number of ways = 20 × 6 = 120

৯,০৩২.

A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

ক
ক) 4%
খ
খ) 5%
গ
গ) 6%
ঘ
ঘ) 7%

সঠিক উত্তর: খ

খ) 5%

উত্তর

সঠিক উত্তর: খ

খ) 5%

খ

ব্যাখ্যা

Question: A sum of Tk. 10,000 amounts to Tk. 12,000 in 4 years at the rate of simple interest. What is the rate of interest?

Solution:
সুদ = ১২০০০ - ১০০০০ টাকা
= ২০০০ টাকা

ধরি, সুদের হার r%

I = pnr
⇒ 2000 = 10000 × 4 × r/100
⇒ r = 5

সুদের হার ৫%

৯,০৩৩.

The angle of elevation of the top of a tower at a point on the ground 37 m away from the foot of the tower is 45°. What is the height of the tower?

ক
42 m
খ
36 m
গ
38 m
ঘ
37 m

সঠিক উত্তর: ঘ

37 m

উত্তর

সঠিক উত্তর: ঘ

37 m

ঘ

ব্যাখ্যা

Question: The angle of elevation of the top of a tower at a point on the ground 37 m away from the foot of the tower is 45°. What is the height of the tower?

Solution:

Let AB be tower and C is a point on the ground 37 m away
From the foot of tower B
The angle of elevation is 45°

Let h be the height of the tower.
∴ tanθ = AB/BC
⇒ tan45^∘= AB/37
⇒ 1 = AB/37
∴ AB = 37 m

৯,০৩৪.

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 4 cm. How many bottles will be needed to empty the bowl?

ক
40
খ
48
গ
54
ঘ
60

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

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 4 cm. How many bottles will be needed to empty the bowl?

Solution:
Volume of hemisphere = (1/2) (4/3) πr3
= (1/2) (4/3) π9³
= (2/3) 729π

Volume of cylinder = π(3/2)² 4
= 9π

bottles will be needed to empty the bowl = (2 × 729π)/(3 × 9π)
= 54

৯,০৩৫.

Two trains 105 meters and 90 meters long, run at the speeds of 45 km/h and 72 km/h respectively, in opposite directions on parallel tracks. The time which they take to cross each other is:

ক
ক) 8 seconds
খ
খ) 7 seconds
গ
গ) 5 seconds
ঘ
ঘ) 6 seconds

সঠিক উত্তর: ঘ

ঘ) 6 seconds

উত্তর

সঠিক উত্তর: ঘ

ঘ) 6 seconds

ঘ

ব্যাখ্যা

অতিক্রান্ত সময়, t = (d₁ + d₂)/(v₁ + v₂)
= (105 + 90)/{(45 + 72) × 5}/18
= 195/(117 × 5)/18
= 195 × 18/(117 × 5)
= 6 seconds

৯,০৩৬.

Find the value of (3log2+2log3) / (2log6+log2)

ক
ক) 2
খ
খ) 6
গ
গ) 1
ঘ
ঘ) 4

সঠিক উত্তর: গ

গ) 1

উত্তর

সঠিক উত্তর: গ

গ) 1

গ

ব্যাখ্যা

3log2+2log3
=log2³+log3²=log8+log9
=log(8×9)
=log72

2log6+log2
=log6²+log2
=log36+log2
=log72

3log2+2log3 / 2log6+log2
=log72 / log72
= 1

৯,০৩৭.

Find the value of n, if 9^{n - 1} = 243.

ক
2
খ
3.5
গ
4
ঘ
5
ঙ
6.5

সঠিক উত্তর: খ

3.5

উত্তর

সঠিক উত্তর: খ

3.5

খ

ব্যাখ্যা

Question: Find the value of n, if 9^{n - 1} = 243.

Solution:
9^{n - 1} = 243
⇒ (3²)^{n - 1} = 3⁵
⇒ 3^{2(n - 1)} = 3⁵
⇒ 3^{2n - 2} = 3⁵
⇒ 2n - 2 = 5
⇒ 2n = 5 + 2
⇒ 2n = 7
⇒ n = 7/2
⇒ n = 3.5

৯,০৩৮.

A jar contains only marbles of three colour: red, green and yellow. The red and green marbles are in the ratio of 2 : 5 and the yellow and red marbles are in ration of 5 : 6. Which of the following could be the total number of marbles?

ক
52
খ
64
গ
100
ঘ
None of these

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: A jar contains only marbles of three colour: red, green and yellow. The red and green marbles are in the ratio of 2 : 5 and the yellow and red marbles are in ration of 5 : 6. Which of the following could be the total number of marbles?

Solution:
Red : Green = 2 : 5 = 6 : 15
Yellow : Red = 5 : 6 = 5 : 6
Red : Green : Yellow = 6 : 15 : 5

অনুপাতের রাশিগুলোর সমষ্টি = 6 + 15 + 5 = 26
মার্বেল সংখ্যা হবে 26 এর গুণিতক।
মার্বেল সংখ্যা হতে পারে 26, 52, 78, 104,..............

৯,০৩৯.

The ages of Ram and Mohan are in the ratio of 5 : 7 and the difference between them is 12 years. The ages (in years) of Ram and Mohan are respectively:

ক
ক) 25 and 35 years
খ
খ) 20 and 28 years
গ
গ) 30 and 42 years
ঘ
ঘ) 28 and 40 years

সঠিক উত্তর: গ

গ) 30 and 42 years

উত্তর

সঠিক উত্তর: গ

গ) 30 and 42 years

গ

ব্যাখ্যা

Let
the age of Ram and Mohan be 5x and 7x respectively
According to the question
⇒ 7x - 5x = 12
⇒ 2x = 12
⇒ x = 6

The age of Ram = 5 × 6 = 30 years
The age of Mohan = 7 × 6 = 42 years

∴ The required result will be "30 years and 42 years" respectively.

৯,০৪০.

A prime number N, in the range of 10 to 40, remains unchanged when its digits are reversed. The square of such a number is:

ক
1089
খ
484
গ
225
ঘ
121

সঠিক উত্তর: ঘ

121

উত্তর

সঠিক উত্তর: ঘ

121

ঘ

ব্যাখ্যা

Question: A prime number N, in the range of 10 to 40, remains unchanged when its digits are reversed. The square of such a number is:

Solution:
মৌলিক সংখ্যা ১১ এর একক ও দশক স্থানীয় অঙ্ক একই।

১১^২
= ১২১

৯,০৪১.

A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

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

সঠিক উত্তর: খ

18 years

উত্তর

সঠিক উত্তর: খ

18 years

খ

ব্যাখ্যা

Question: A sum of money triples itself in 6 years at compound interest. In how many years will it amount to 27 times itself at the same rate of interest?

Solution:
let,
the sum = P

ATQ,
3P = P(1 + r)⁶
⇒ (1 + r)⁶ = 3

Again,
let, sum will 27 times in n years

Then,
27P = P(1 + r)ⁿ
⇒ 27 = (1 + r)ⁿ
⇒ 3³ = (1 + r)ⁿ
⇒ {(1 + r)⁶}³ = (1 + r)ⁿ
⇒ (1 + r)¹⁸ = (1 + r)ⁿ
∴ n = 18

৯,০৪২.

What is the H.C.F. of the following fractions? 6/7, 12/21, 18/35.

ক
1/12
খ
2/35
গ
4/75
ঘ
3/70

সঠিক উত্তর: খ

2/35

উত্তর

সঠিক উত্তর: খ

2/35

খ

ব্যাখ্যা

Question: What is the H.C.F. of the following fractions? 6/7, 12/21, 18/35.

Solution:
আমরা জানি,
ভগ্নাংশের গসাগু = (লবের গসাগু)/(হরের লসাগু)

এখানে লবসমূহ = 6, 12 এবং 18
6 = 2 × 3
12 = 2² × 3
18 = 2 × 3²
∴ লবসমূহের গসাগু (H.C.F.) = 2 × 3 = 6

এখানে হরসমূহ = 7, 21 এবং 35
7 = 7 × 1
21 = 3 × 7
35 = 5 × 7
∴ হরসমূহের লসাগু (L.C.M.) = 3 × 5 × 7 = 105

ভগ্নাংশের গসাগু = লবের গসাগু/হরের লসাগু
= 6/105
= 2/35

৯,০৪৩.

If 2 jackets and 3 sweaters cost Tk. 4,400, and 3 jackets and 2 sweaters cost Tk. 4,700, find the cost of a single jacket.

ক
Tk. 1300
খ
Tk. 1000
গ
Tk. 1060
ঘ
Tk. 2400

সঠিক উত্তর: গ

Tk. 1060

উত্তর

সঠিক উত্তর: গ

Tk. 1060

গ

ব্যাখ্যা

Question: If 2 jackets and 3 sweaters cost Tk. 4,400, and 3 jackets and 2 sweaters cost Tk. 4,700, find the cost of a single jacket.

Solution:
ধরি, একটি জ্যাকেটের মূল্য x টাকা এবং একটি সোয়েটারের মূল্য y টাকা।

প্রশ্নমতে,
2x + 3y = 4400 ............... (i)
3x + 2y = 4700 .............. (ii)

(ii) × 3 - (i) × 2 ⇒
(9x + 6y) - (4x + 6y) = 14100 - 8800
⇒ 9x - 4x = 5300
⇒ 5x = 5300
⇒ x = 5300/5
⇒ x = 1060

সুতরাং, একটি জ্যাকেটের মূল্য 1060 টাকা।

৯,০৪৪.

If an article was sold at 18% profit on cost price then the selling price of the article was Tk. 9,381. What would have been the selling price of the article if it was sold at 25% profit?

ক
ক) Tk. 9,984.5
খ
খ) Tk. 9,927.5
গ
গ) Tk. 9,937.5
ঘ
ঘ) None of these

সঠিক উত্তর: গ

গ) Tk. 9,937.5

উত্তর

সঠিক উত্তর: গ

গ) Tk. 9,937.5

গ

ব্যাখ্যা

ধরি,
পণ্যটির ক্রয়মূল্য x টাকা
প্রশ্নমতে,
18 % of x = 9,381 - x
⇒ 18x/100 + x = 9,381
⇒118x/100 = 9,381
⇒ x = (9,381×100)/118
∴ x = 7,950
পণ্যটির ক্রয়মূল্য 7,950 টাকা

25% লাভে,
পণ্যটির বিক্রয়মূল্য= 25% of 7,950
= (125 × 7,950)/100
= 9,937.5

৯,০৪৫.

A number is decreased by 10% and then increased by 10%. The number of obtained is 10 less than the original number. What was the original number?

ক
ক) 4,000
খ
খ) 3,000
গ
গ) 2,000
ঘ
ঘ) 1,000

সঠিক উত্তর: ঘ

ঘ) 1,000

উত্তর

সঠিক উত্তর: ঘ

ঘ) 1,000

ঘ

ব্যাখ্যা

ধরি,
মূল সংখ্যা = 100x
10% কমলে দাঁড়ায় = 100x - 100x এর 10%
= 90x
90x সংখ্যাটি 10% বাড়ালে নতুন সংখ্যা = 90x + 90x এর 10%
= 99x
প্রশ্নমতে,
100x - 99x = 10
x = 10

নির্ণেয় সংখ্যা = 100x
=100 × 10 = 1000

৯,০৪৬.

A rectangle and a square have the same area. The square has a perimeter of 32 meters and the length of the rectangle is 4 meters. What is the width of the rectangle (in meters)?

ক
24
খ
16
গ
12
ঘ
8

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A rectangle and a square have the same area. The square has a perimeter of 32 meters and the length of the rectangle is 4 meters. What is the width of the rectangle (in meters)?

Solution:
Given that,
Perimeter of square = 32 m
Area of rectangle = Area of square
And length of rectangle = 4 m

Now,
Perimeter of square,
4s = 32
⇒ s = 32/4 = 8
∴ s = 8 m
∴ Area of square = s² = 8² = 64 m²

According to the Question,
Area of rectangle = Area of square
∴ Area of rectangle = 64 m²

∴ Area of rectangle = length × width
64 = 4 × w
⇒ w = 64/4
∴ w = 16 m

So the width of the rectangle = 16 meters

৯,০৪৭.

1 - [2 - {3 - (4 - 5) + 6} + 7] =?

ক
- 2
খ
0
গ
1
ঘ
2

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: 1 - [2 - {3 - (4 - 5) + 6} + 7] =?

Solution:
1 - [2 - {3 - (4 - 5) + 6} + 7]
= 1 - [2 - {3 - (-1) + 6} + 7]
= 1 - [2 - {3 + 1 + 6} + 7]
= 1 - [2 - {10} + 7]
= 1 - [2 - 10 + 7]
= 1- [-1]
= 1 + 1
= 2

৯,০৪৮.

ক
25
খ
59
গ
100
ঘ
116
ঙ
170

সঠিক উত্তর: গ

100

উত্তর

সঠিক উত্তর: গ

100

গ

ব্যাখ্যা

Question:

Solution:

৯,০৪৯.

A rectangular plot of land has a fence along three of its four sides, the unfenced side and the side opposite the unfenced side have a length that is three times the length of the other two sides. If the area of the plot is 675 square feet, what is the total length of the fence in feet?

ক
50 feet
খ
62 feet
গ
70 feet
ঘ
75 feet
ঙ
None

সঠিক উত্তর: ঘ

75 feet

উত্তর

সঠিক উত্তর: ঘ

75 feet

ঘ

ব্যাখ্যা

Question: A rectangular plot of land has a fence along three of its four sides, the unfenced side and the side opposite the unfenced side have a length that is three times the length of the other two sides. If the area of the plot is 675 square feet, what is the total length of the fence in feet?

Solution:
Let,
Width of the rectangular land = x
∴ Length of the rectangular land = 3x

ATQ,
3x × x = 675
⇒ 3x² = 675
⇒ x² = 225
∴ x = 15

Total length of the fence = (x + 3x + x) feet
= 5x feet
= 5 × 15 feet
= 75 feet

৯,০৫০.

Solution A is made up of alcohol and water mixed in the ratio of 21 : 4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2 : 3 by volume. If Solution A and Solution B are mixed in the ratio of 5 : 6 by volume, what percent of the resultant mixture is alcohol?

ক
32.5%
খ
60%
গ
40%
ঘ
52.5%

সঠিক উত্তর: খ

60%

উত্তর

সঠিক উত্তর: খ

60%

খ

ব্যাখ্যা

Question: Solution A is made up of alcohol and water mixed in the ratio of 21 : 4 by volume; Solution B is made up of alcohol and water mixed in the ratio of 2 : 3 by volume. If Solution A and Solution B are mixed in the ratio of 5 : 6 by volume, what percent of the resultant mixture is alcohol?

Solution:
25 units of A contain 21 units of alcohol and 4 units of water.
So, 5 units of A contain (21/5) units of alcohol and (4/5) units of water
5 units of B contain 2 units of alcohol and 3 units of water

If we mix 5 × 5 = 25 units of A with 5 × 6 = 30 units of B (so that A and B are mixed in the ratio of 5 : 6), the resultant 55 units solution will contain:
Alcohol: (21/5) × 5 + (2 × 6) = 33 units
Water: (4/5) × 5 + (3 × 6) = 22 units

% of alcohol in the resultant solution = (33/55) × 100 = 60

৯,০৫১.

The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is

ক
ক) 180
খ
খ) 120
গ
গ) 75
ঘ
ঘ) 63

সঠিক উত্তর: গ

গ) 75

উত্তর

সঠিক উত্তর: গ

গ) 75

গ

ব্যাখ্যা

Question : The number of degrees that the hour hand of a clock moves through between noon and 2.30 in the afternoon of the same day is-

Solution:
12 টা থেকে 2.30 পর্যন্ত সময়ের ব্যবধান 2 ঘণ্টা 30 মিনিট = 5/2 ঘণ্টা

ঘড়ির ঘণ্টার কাঁটা 12 ঘণ্টায় অতিক্রম করে 360°
ঘড়ির ঘণ্টার কাঁটা 1 ঘণ্টায় অতিক্রম করে 360° /12
ঘড়ির ঘণ্টার কাঁটা 5/2 ঘণ্টায় অতিক্রম করে (360° × 5)/(12 × 2) = 75°

৯,০৫২.

If n is negative, all but which of the following must also be negative?

ক
ক) n³
খ
খ) n⁵
গ
গ) 1/n²
ঘ
ঘ) 1/n
ঙ
ঙ) None of the above

সঠিক উত্তর: গ

গ) 1/n²

উত্তর

সঠিক উত্তর: গ

গ) 1/n²

গ

ব্যাখ্যা

Since option C has a positive power so that it will be positive.

৯,০৫৩.

Find the ratio of purchase price to sell price if there is loss of 19%?

ক
81 : 19
খ
19 : 81
গ
100 : 81
ঘ
19 : 100

সঠিক উত্তর: গ

100 : 81

উত্তর

সঠিক উত্তর: গ

100 : 81

গ

ব্যাখ্যা

ধরি, ক্রয়মূল্য 100 টাকা
19% ক্ষতিতে বিক্রয়মূল্য (100 - 19) = 81 টাকা
ক্রয়মূল্য : বিক্রয়মূল্য = 100 : 81

৯,০৫৪.

A boat goes 10 km upstream in 50 minutes, and the speed of the stream is 3 kmph. Find the speed of the boat in still water (in km/h).

ক
10 km/h
খ
12 km/h
গ
15 km/h
ঘ
18 km/h

সঠিক উত্তর: গ

15 km/h

উত্তর

সঠিক উত্তর: গ

15 km/h

গ

ব্যাখ্যা

Question: A boat goes 10 km upstream in 50 minutes, and the speed of the stream is 3 kmph. Find the speed of the boat in still water (in km/h).

Solution:
Let the speed of the boat in still water = x km/h
Speed of the stream = 3 km/h (given)
Upstream speed = x - 3 km/h
Distance upstream = 10 km
Time upstream = 50 minutes = 50/60 hours = 5/6 hours

We know,
Speed = Distance/Time
Upstream speed = 10 /(5/6) = 10 × (6/5) = 12 km/h
So,
⇒ x - 3 = 12
⇒ x = 12 + 3
∴ x = 15 km/h

The speed of the boat in still water is 15 km/h.

৯,০৫৫.

How many ways can five different rings be worn on four fingers of one hand?

ক
2056
খ
625
গ
512
ঘ
1024

সঠিক উত্তর: ঘ

1024

উত্তর

সঠিক উত্তর: ঘ

1024

ঘ

ব্যাখ্যা

Question: How many ways can five different rings be worn on four fingers of one hand?

Solution:
Each ring may be worn on any of the 4 fingers.
So, each ring may be worn in 4 different ways.
∴ 5 rings may be worm in (4×4×4×4×4) = 4⁵ = 1024 ways.

৯,০৫৬.

If (3/5)^x = 81/625, then what is the value of x^x?

ক
0
খ
16
গ
256
ঘ
32
ঙ
None of these

সঠিক উত্তর: গ

256

উত্তর

সঠিক উত্তর: গ

256

গ

ব্যাখ্যা

Question: If (3/5)^x = 81/625, then what is the value of x^x?

Solution:
(3/5)^x = 81/625
We know,
3⁴ = 81 and
5⁴ = 625
∴ (3/5)⁴ = 81/625

∴ On comparing both the equation,
we get x = 4
Now, x^x = 4⁴ = 256

৯,০৫৭.

If a + 1/a = √3, then what is the value of a³⁰ + a²⁴ + a⁶ + 1?

ক
0
খ
1
গ
√3
ঘ
3

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If a + 1/a = √3, then what is the value of a³⁰ + a²⁴ + a⁶ + 1?

Solution:
Given, a + 1/a = √3
Now,
a³ + 1/a³ = (a + 1/a)³ - 3 . a . (1/a)(a + 1/a)
⇒ a³ + 1/a³ = (√3)³ - 3(√3) [∵ a + 1/a = √3]
⇒ a³ + 1/a³ = 3(√3) - 3(√3)
⇒ a³ + 1/a³ = 0
⇒ a⁶ + 1 = 0 [Multiplying both sides by a³]

Then,
a³⁰ + a²⁴ + a⁶ + 1
= a²⁴(a⁶ + 1) + (a⁶ + 1)
= (a²⁴ × 0) + 0
= 0

৯,০৫৮.

Question:

ক
225
খ
194
গ
324
ঘ
234
ঙ
None of these

সঠিক উত্তর: ঘ

234

উত্তর

সঠিক উত্তর: ঘ

234

ঘ

ব্যাখ্যা

Question:

Solution:

৯,০৫৯.

A number when divided by 195 leaves a remainder 47. If the same number is divided by 15, the remainder will be?

ক
ক) 0
খ
খ) 1
গ
গ) 2
ঘ
ঘ) 3

সঠিক উত্তর: গ

গ) 2

উত্তর

সঠিক উত্তর: গ

গ) 2

গ

ব্যাখ্যা

Question: A number when divided by 195 leaves a remainder 47. If the same number is divided by 15, the remainder will be?

Solution:
Let the number be x and the quotient is q.

Then,
x = 195q + 47
= (15 × 13q) + (15 × 3) + 2
= 15 (13q + 3) + 2

So, the given number when divided by 15 gives 2 as remainder.

৯,০৬০.

Praveen and Sunny enter into a partnership. Praveen puts in Tk. 50 and Sunny put in Tk. 45. At the end of 4 months Praveen withdraws half of his capital, and at the end of 6 months, Sunny withdraws half of his capital. Ashik then enters with a capital of Tk. 70. At the end of 12 months, in what ratio will the profit be divided?

ক
65 : 32 : 56
খ
54 : 60 : 66
গ
84 : 82 : 80
ঘ
80 : 81 : 84

সঠিক উত্তর: ঘ

80 : 81 : 84

উত্তর

সঠিক উত্তর: ঘ

80 : 81 : 84

ঘ

ব্যাখ্যা

Question: Praveen and Sunny enter into a partnership. Praveen puts in Tk. 50 and Sunny put in Tk. 45. At the end of 4 months Praveen withdraws half of his capital, and at the end of 6 months, Sunny withdraws half of his capital. Ashik then enters with a capital of Tk. 70. At the end of 12 months, in what ratio will the profit be divided?

Solution:
Let Praveen's capital is C1 = 50 for period T1= 4 months, and C11= 25 for period T11= 8
Sunny's capital is C2 = 45 for period T2 = 6 months, and C22 = 45/2 for period T22= 6 months.
Ashik's capital is C3 = 70 for period T3 = 6 months.

Now, apply the profit ratio formula:

(C1 × T1): (C2 × T2): (C3 × T3) = p1: p2: p3
But here we have 2 different values for Praveen and Sunny.
So, (C1 × T1 + C11 × T11) : (C2 × T2 + C22 × T22) : (C3 × T3) = p1: p2 : p3
Now, (50 × 4 + 25 × 8) : (45 × 6 + (45 × 6)/2) : (70 × 6) = p1: p2 : p3
The ratio of their profit is p1: p2 : p3 = 400 : 405 : 420
Divide all ratios by 5.
Hence, the ratio will be 80 : 81 : 84

৯,০৬১.

Three workers X, Y and Z are paid a total of Tk.5, 500 for particular jobs. X paid 133.33% of the amount paid to Y and Y is paid 75% amount paid to Z. How much is paid to Z?

ক
ক) 1780
খ
খ) 1890
গ
গ) 1975
ঘ
ঘ) 2000

সঠিক উত্তর: ঘ

ঘ) 2000

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2000

ঘ

ব্যাখ্যা

ধরি, y বেতন পায় 100 টাকা
x পায় (133.33% of 100) টাকা = 133.33 টাকা
এবং, z পায় (100 × 100 /75) = 400/3 = 133.33 টাকা
x : y : z = 133.33 : 100 : 133.33 = 400 : 300 : 400 = 4 : 3 : 4
∴ z পায় = 5500 এর 4/(4 + 3 + 4) টাকা = 2000 টাকা

৯,০৬২.

The volume of a sphere is 36π cm³ . What is the radius of the sphere?

ক
ক) 6 cm
খ
খ) 5 cm
গ
গ) 3 cm
ঘ
ঘ) 2 cm

সঠিক উত্তর: গ

গ) 3 cm

উত্তর

সঠিক উত্তর: গ

গ) 3 cm

গ

ব্যাখ্যা

Volume of sphere = 36π cm³
Volume of sphere = (4/3) × πr³
⇒ (4/3) × πr³ = 36π
⇒ 36π = (4/3) × π × r³
⇒ 9 = (1/3) × r³
⇒ 27 = r³
⇒ r = 3

∴ The radius of sphere is 3 cm.

৯,০৬৩.

There are two numbers such that the sum of twice the first and thrice the second is 39, while the sum of thrice the first, and twice the second is 36. The larger of the two is -

ক
ক) 3
খ
খ) 6
গ
গ) 9
ঘ
ঘ) 12

সঠিক উত্তর: গ

গ) 9

উত্তর

সঠিক উত্তর: গ

গ) 9

গ

ব্যাখ্যা

Let the numbers be x and y.
Then, 2x + 3y = 39 .......(i) and
3x + 2y = 30 .........(ii)
On solving (i) and (ii), we get : x = 6 and y = 9.
larger number = 9

৯,০৬৪.

If RESEARCH is $#!#%$&@ then SCARE is-

ক
!&%$#
খ
!@%$#
গ
!$%#&
ঘ
!@%#$

সঠিক উত্তর: ক

!&%$#

উত্তর

সঠিক উত্তর: ক

!&%$#

ক

ব্যাখ্যা

Question: If RESEARCH is $#!#%$&@ then SCARE is-

Solution:
RESEARCH ⇔ $#!#%$&@
R ⇔ $
E ⇔ #
S ⇔ !
A ⇔ %
C ⇔ &
H ⇔ @

∴ SCARE ⇔ !&%$#

৯,০৬৫.

Three numbers are in the ratio of 3 : 4 : 5 and their H.C.F. is 20. Their L.C.M. is -

ক
ক) 1000
খ
খ) 1200
গ
গ) 1500
ঘ
ঘ) 1600

সঠিক উত্তর: খ

খ) 1200

উত্তর

সঠিক উত্তর: খ

খ) 1200

খ

ব্যাখ্যা

Question: Three numbers are in the ratio of 3 : 4 : 5 and their H.C.F. is 20. Their L.C.M. is -

Solution:
সংখ্যা তিনটির গ. সা. গু ২০

সংখ্যা তিনটি হচ্ছে (৩ × ২০) বা ৬০, (৪ × ২০) বা ৮০, (৫ × ২০) বা ১০০

৬০ = ৩ × ২ × ২ × ৫
৮০ = ২ × ২ × ২ × ২ × ৫
১০০ = ২ × ২ × ৫ ×৫

ল. সা. গু = ২ × ২ × ২ × ২ × ৩ × ৫ × ৫
= ১২০০

৯,০৬৬.

The quadratic equation whose one rational root is 3 + √2 is-

ক
x² - 7x + 5 = 0
খ
x² + 7x + 6 = 0
গ
x² - 7x + 6 = 0
ঘ
x² - 6x + 7 = 0

সঠিক উত্তর: ঘ

x² - 6x + 7 = 0

উত্তর

সঠিক উত্তর: ঘ

x² - 6x + 7 = 0

ঘ

ব্যাখ্যা

Question: The quadratic equation whose one rational root is 3 + √2 is-

Solution:
one root is 3 + √2
∴ other root is 3 - √2

Sum of roots = 3 + √2 + 3 - √2 = 6
Product of roots = (3 + √2)(3 - √2) = (3)² - (√2)² = 9 - 2 = 7

∴ Required quadratic equation is x² - 6x + 7 = 0

৯,০৬৭.

There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket?

ক
120
খ
240
গ
180
ঘ
210

সঠিক উত্তর: ক

120

উত্তর

সঠিক উত্তর: ক

120

ক

ব্যাখ্যা

Question: There are 10 oranges in a basket. Find the no. of ways in which 3 oranges are chosen from the basket?

Solution:
Required number of ways = ¹⁰C₃
= 10!/{3! (10 - 3)!}
= 10!/(3! 7!)
= (10 × 9 × 8)/(3 × 2)
= 120

৯,০৬৮.

A solid cylindrical block has a radius of 7 meters and a height of 10 meters. If the material of the cylinder costs Tk. 20 per cubic meter, find the total cost of the material required.

ক
Tk. 32,800
খ
Tk. 20,800
গ
Tk. 30,800
ঘ
Tk. 30,200
ঙ
None

সঠিক উত্তর: গ

Tk. 30,800

উত্তর

সঠিক উত্তর: গ

Tk. 30,800

গ

ব্যাখ্যা

Question: A solid cylindrical block has a radius of 7 meters and a height of 10 meters. If the material of the cylinder costs Tk. 20 per cubic meter, find the total cost of the material required.

Solution:
Given,
Radius of the cylinder, r = 7 m
Height of the cylinder, h = 10 m
Cost per cubic meter = Tk. 20

The volume of the cylinder:
V = πr²h
= (22/7) × (7)² × 10
= (22/7) × 49 × 10
= 22 × 7 × 10
= 1540 cubic metres

Total cost = Volume × Cost per cubic metre
= 1540 × 20
= Tk. 30,800

∴ The total cost of the material is Tk. 30,800.

৯,০৬৯.

If a² + b² + c² + 3 = 2(a - b - c), then the value of 2a - b + c is?

ক
ক) 0
খ
খ) 2
গ
গ) 4
ঘ
ঘ) None of these

সঠিক উত্তর: খ

খ) 2

উত্তর

সঠিক উত্তর: খ

খ) 2

খ

ব্যাখ্যা

Question: If a² + b² + c² + 3 = 2(a - b - c), then the value of 2a - b + c is?

Solution:
a² + b² + c² + 3 = 2(a - b - c)
⇒ a² + b² + c² + 3 = 2a - 2b - 2c
⇒ a² + b² + c² + 3 - 2a + 2b + 2c = 0
⇒ (a² - 2a + 1) + (b² + 2b + 1) + (c² + 2c + 1) = 0
∴ (a - 1)² + (b + 1)² + (c + 1)² = 0

∴ a = 1
∴ b = -1
∴ c = -1

2a - b + c
= 2 - (- 1) + (- 1)
= 2 + 1 - 1
= 2

৯,০৭০.

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

ক
4 km/h.
খ
5 km/h.
গ
6 km/h.
ঘ
7 km/h.

সঠিক উত্তর: গ

6 km/h.

উত্তর

সঠিক উত্তর: গ

6 km/h.

গ

ব্যাখ্যা

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

Solution:
Let, the speed of jashim = a kmph and the speed of Rubayet = b kmph

ATQ,
a × 6 + b × 6 = 60
⇒ a + b = 10 ......... (1)
And,
{(2a/3) × 5} + (2b × 5) = 60
⇒ 10a + 30b = 180
⇒ a + 3b = 18 .......... (2)

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

৯,০৭১.

In how many ways can 3 boys and 3 girls be selected from 12 boys and 9 girls?

ক
ক) 304
খ
খ) 9240
গ
গ) 14880
ঘ
ঘ) 18480

সঠিক উত্তর: ঘ

ঘ) 18480

উত্তর

সঠিক উত্তর: ঘ

ঘ) 18480

ঘ

ব্যাখ্যা

Question: In how many ways can 3 boys and 3 girls be selected from 12 boys and 9 girls?

Solution:
12 জন বালক হতে প্রতিবার 3 জন বালক বেছে নেয়া যায় = ¹²C₃ = 220 উপায়ে
9 জন বালিকা হতে প্রতিবার 3 জন বালিকা বেছে নেয়া যায় = ⁹C₃ = 84 উপায়ে

∴ মোট বেছে নেয়া যায় = 220 × 84 = 18480 উপায়ে

৯,০৭২.

The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

ক
13000
খ
13500
গ
12500
ঘ
14500

সঠিক উত্তর: খ

13500

উত্তর

সঠিক উত্তর: খ

13500

খ

ব্যাখ্যা

Question: The population of a village decreases at the rate of 25% per annum. If its population 2 years ago was 24000, the present population is =?

Solution:
Given that,
The population of a village 2 years ago = 24000
Rate of growth = 25% p.a.
Time period = 2 years

Present population = P{(1 - (r/100)}ⁿ
= 24000 × {1 - (25/100)}²
= 24000 × {1 - (1/4)}²
= 24000 × (3/4)²
= 24000 × (9/16)
= 13500

৯,০৭৩.

Find the probability of selecting a prime number from a set of numbers 1 to 15 (both inclusive).

ক
ক) 3/5
খ
খ) 1/15
গ
গ) 7/15
ঘ
ঘ) 2/5

সঠিক উত্তর: ঘ

ঘ) 2/5

উত্তর

সঠিক উত্তর: ঘ

ঘ) 2/5

ঘ

ব্যাখ্যা

Question: Find the probability of selecting a prime number from a set of numbers 1 to 15 (both inclusive).

Solution:
1 থেকে 15 পর্যন্ত মোট সংখ্যা = 15
1 থেকে 15 পর্যন্ত মৌলিক সংখ্যা 6টি যথাক্রমে 2, 3, 5, 7, 11, 13.

∴ নির্ণেয় সম্ভাব্যতা = 6/15 = 2/5

৯,০৭৪.

What is 200% of 0.010?

ক
0.0002
খ
0.002
গ
0.2
ঘ
0.02

সঠিক উত্তর: ঘ

0.02

উত্তর

সঠিক উত্তর: ঘ

0.02

ঘ

ব্যাখ্যা

Question: What is 200% of 0.010?

Solution:
200% of 0.010
= (200/100) × 10/1000
= 2/100
= 1/50
= 0.02

৯,০৭৫.

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 pay of 7th day?

ক
ক) Tk. 150
খ
খ) Tk. 140
গ
গ) Tk. 90
ঘ
ঘ) Tk. 160

সঠিক উত্তর: ক

ক) Tk. 150

উত্তর

সঠিক উত্তর: ক

ক) Tk. 150

ক

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 pay of 7th day?

Solution:
Let,
The pays of seven days respectively : x, x + 10, x + 20, x + 30, x + 40, x + 50, x + 60

ATQ,
x + x + 10 + x + 20 + x + 30 = x + 40 + x + 50 + x + 60
⇒ 4x + 60 = 3x + 150
∴ x = 90

∴ His pay of 7th day is Tk. (90 + 60)
= Tk. 150

৯,০৭৬.

The ratio of milk and water in a solution is 7 : 4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2. Find the final amount of water in the solution.

ক
48 liters
খ
54 liters
গ
56 liters
ঘ
60 liters

সঠিক উত্তর: গ

56 liters

উত্তর

সঠিক উত্তর: গ

56 liters

গ

ব্যাখ্যা

Question: The ratio of milk and water in a solution is 7 : 4. After adding 8 liters of water, the ratio of milk and water becomes 3 : 2. Find the final amount of water in the solution.

Solution:
Let the initial amount of milk = 7x liters
Let the initial amount of water = 4x liters

According to the question,
7x/(4x + 8) = 3/2
⇒ 2 × 7x = 3 × (4x + 8)
⇒ 14x = 12x + 24
⇒ 14x - 12x = 24
⇒ 2x = 24
⇒ x = 12

∴ Final amount of water = 4x + 8
= 4 × 12 + 8
= 48 + 8 = 56 liters

৯,০৭৭.

if log_x 1/216 = - 3, then x = ?

ক
6
খ
1/6
গ
- 1/6
ঘ
- 6

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If log_x 1/216 = - 3, then x = ?

Solution:
Given that,
log_x 1/216 = - 3
⇒ x^{- 3} = 1/216
⇒ 1/x³ = 1/216
⇒ x³ = 216
⇒ x³ = 6³
∴ x = 6

৯,০৭৮.

A train 220m long passed a pole in 22 seconds. How long will it take to pass a platform 530m long?

ক
ক) 60s
খ
খ) 65s
গ
গ) 75s
ঘ
ঘ) 82s

সঠিক উত্তর: গ

গ) 75s

উত্তর

সঠিক উত্তর: গ

গ) 75s

গ

ব্যাখ্যা

Question: A train 220m long passed a pole in 22 seconds. How long will it take to pass a platform 530m long?

Solution:
ট্রেনটির মোট দূরত্ব অতিক্রম করতে হবে = (220 + 530) মিটার = 750 মিটার

ট্রেনটি 220 মিটার অতিক্রম করতে সময় নেয় = 22 সেকেন্ড
ট্রেনটি1 মিটার অতিক্রম করতে সময় নেয় = 22/220 সেকেন্ড
ট্রেনটি 890 মিটার অতিক্রম করতে সময় নেয় = (22 × 750)/220 সেকেন্ড
= 75 সেকেন্ড

৯,০৭৯.

The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

ক
30
খ
32
গ
36
ঘ
50
ঙ
None of these

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The cost price of 40 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is-

Solution:
Let,
Cost price of each article be Tk. 1
Cost price of x articles = Tk. x
Selling price of x articles = Tk. 40

∴ Profit = Tk. (40 - x)

ATQ,
(40 - x)/x = 25%
Or, 100(40 - x)/x = 25
Or, 4000 - 100x = 25x
Or, 125x = 4000
∴ x = 32

৯,০৮০.

The sum of seventh and eleventh term of an arithmetic progression is 18. What is the sum of the first seventeen terms of that progression?

ক
153
খ
120
গ
127
ঘ
143

সঠিক উত্তর: ক

153

উত্তর

সঠিক উত্তর: ক

153

ক

ব্যাখ্যা

Question: The sum of seventh and eleventh term of an arithmetic progression is 18. What is the sum of the first seventeen terms of that progression?

Solution:
In an arithmetic progression.
Let first term = a
Common difference = d

We know,
a = a + (n - 1)d
∴ a₇ = a + 6d and a₁₁ = a + 10d

Given that,
Seventh term + eleventh term = 18
⇒ a₇ + a₁₁ = 18
⇒ a + 6d + a + 10d = 18
⇒ 2a + 16d = 18
⇒ 2(a + 8d) = 18
∴ a + 8d = 9 ........(1)

We need the sum of the first 17 terms.
S₁₇ = (n/2) × [2a + (n - 1)d]
= (17/2) × [2a + 16d]
= 17/2 × 2(a + 8d)
= 17 × (a + 8d)
= 17 × 9
= 153

So the sum of the first seventeen terms is 153.

৯,০৮১.

200 litres of a mixture contains milk and water in the ratio 17 : 3. After the addition of some more milk to it, the ratio of milk to water in the resulting mixture becomes 7 : 1. The quantity of milk added to it was?

ক
ক) 20 Litres
খ
খ) 40 Litres
গ
গ) 60 Litres
ঘ
ঘ) 80 Litres

সঠিক উত্তর: খ

খ) 40 Litres

উত্তর

সঠিক উত্তর: খ

খ) 40 Litres

খ

ব্যাখ্যা

Milk : water = 17:3 = 17x : 3x
∴ 17x + 3x = 200
⇒ x =10litre
so, Milk = 170 litre and water = 30 litre in initial mixture.
Let 'y' litre of milk added in mixture
i.e. (170+y) : 30 = 7:1
⇒ (170 + y)/ 30= 7/1
∴ y = 210 - 170 = 40 litres

৯,০৮২.

A box contains 6 bottles of variety 1 drink, 3 bottles of variety 2 drink, and 4 bottles of variety 3 drink. Three bottles of them are drawn at random, what is the probability that the three are not of the same variety?

ক
ক) 833/858
খ
খ) 752/833
গ
গ) 632/713
ঘ
ঘ) none of these

সঠিক উত্তর: ক

ক) 833/858

উত্তর

সঠিক উত্তর: ক

ক) 833/858

ক

ব্যাখ্যা

Total number of drink bottles = 6 + 3 + 4 = 13.
Let S be the sample space
Then, n(S) = number of ways of taking 3 drink bottles out of 13.
Therefore, n(S) = ¹³C₃
= (13 x 12 x 11)/(1 x 2 x 3)
= 66 x 13
= 858.
Let E be the event of taking 3 bottles of the same variety
Then, E = event of taking (3 bottles out of 6) or (3 bottles out of 3) or (3 bottles out of 4)
n(E) = ⁶C₃ + ³C₃ + ⁴C₃
= (6 x 5 x 4 )/ (1 x 2 x 3) + 1 + (4 x 3 x 2) / (1 x 2 x 3)
= 20 + 1 + 4
= 25
The probability of taking 3 bottles of the same variety = n(E)/n(S)
= 25/858.
Then, the probability of taking 3 bottles are not of the same variety = 1 - 25/858
= 833/858.

৯,০৮৩.

A man completes a journey in 8 hours. He travels the first half of the journey at the rate of 40 km/hr and the second half at the rate of 60 km/hr. Find the total journey in km.

ক
360 km
খ
384 km
গ
400 km
ঘ
320 km
ঙ
420 km

সঠিক উত্তর: খ

384 km

উত্তর

সঠিক উত্তর: খ

384 km

খ

ব্যাখ্যা

Question: A man completes a journey in 8 hours. He travels the first half of the journey at the rate of 40 km/hr and the second half at the rate of 60 km/hr. Find the total journey in km.

Solution:
ধরা যাক, মোট যাত্রার দূরত্ব হলো D কিমি।
তাহলে, যাত্রার প্রথম অর্ধেকের দূরত্ব হবে D/2 কিমি
এবং দ্বিতীয় অর্ধেকের দূরত্বও হবে D/2 কিমি।

প্রথম অর্ধেক যাত্রায়, সময় = দূরত্ব/গতিবেগ
= (D/2)/40 ঘন্টা
= D/80 ঘন্টা

দ্বিতীয় অর্ধেক যাত্রায়, সময় = দূরত্ব/গতিবেগ
= (D/2)/60 ঘন্টা
= D/120 ঘন্টা

প্রশ্নমতে,
D/80 + D/120 = 8
⇒ (3D + 2D)/240 = 8
⇒ 5D/240 = 8
⇒ 5D = 8 × 240
⇒ 5D = 1920
⇒ D = 1920/5
⇒ D = 384 কিমি

∴ মোট যাত্রার দূরত্ব 384 কিলোমিটার।

৯,০৮৪.

How many diagonals can be drawn in a pentagon?

ক
4
খ
5
গ
6
ঘ
3

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: How many diagonals can be drawn in a pentagon?

Solution:
A pentagon has 5 sides. We obtain the diagonals by joining the vertices in pairs.
Total number of sides and diagonals,
= ⁵C₂
= 10
This includes its 5 sides also.

∴ Diagonals = 10 – 5 = 5

৯,০৮৫.

If 382A is divisible by 9, find the value of the smallest natural number A?

ক
ক) 3
খ
খ) 4
গ
গ) 5
ঘ
ঘ) 6

সঠিক উত্তর: গ

গ) 5

উত্তর

সঠিক উত্তর: গ

গ) 5

গ

ব্যাখ্যা

Question: If 382A is divisible by 9, find the value of the smallest natural number A?

Solution:
একটি সংখ্যা ৯ দ্বারা বিভাজ্য হবে, যদি সংখ্যাটির অংকগুলোর যোগফল ৯ দ্বারা বিভাজ্য হয়।

৩ + ৮ + ২ = ১৩। ১৩ এর সাথে ৫ যোগ করলে ১৮ হয় যা ৯ দ্বারা বিভাজ্য।
অতএব, A অঙ্কটি হবে ৫।

৯,০৮৬.

(33-41) Choose the correct answer.
(33) Find the missing number.

ক
100
খ
25
গ
24
ঘ
10

সঠিক উত্তর: ক

100

উত্তর

সঠিক উত্তর: ক

100

ক

ব্যাখ্যা

Question:

Solution:
In 1st figure:
26 - 16 = 10 ⇒ 10 × 5 = 50

In 2nd figure:
13 - 8 = 5 ⇒ 5 × 5 = 25

In 3rd figure:
52 - 32 = 20 ⇒ 20 × 5 = 100

৯,০৮৭.

Q. 33 – 56: Read the following questions carefully and choose the right answer.
৩৩) A driver of an auto rickshaw sees a lorry 60m ahead of him. After 30 seconds the lorry is 90m behind. If the speed of the auto rickshaw is 38km/hr, then what is the speed of the lorry?

ক
ক) 23km/hr
খ
খ) 25km/hr
গ
গ) 20km/hr
ঘ
ঘ) 18km/hr

সঠিক উত্তর: গ

গ) 20km/hr

উত্তর

সঠিক উত্তর: গ

গ) 20km/hr

গ

ব্যাখ্যা

Total distance is 60+90= 150 meters.
Time taken is 30 seconds.
Speed of the lorry = 150/30
= 5 m/s
= (5×18)/5
= 18 kmph

Now
relative speed = speed of auto rickshaw – speed of lorry
or, 18 = 38 – speed of lorry
∴ Speed of lorry = 38 – 18 = 20 km/h

৯,০৮৮.

Sonar Bangla express, normally reaches its destination at 72 km/h in 6 hours. Find the speed at which it must travel to reduce the travel time by 2 hours?

ক
78 km/h
খ
66 km/h
গ
58 km/h
ঘ
108 km/h

সঠিক উত্তর: ঘ

108 km/h

উত্তর

সঠিক উত্তর: ঘ

108 km/h

ঘ

ব্যাখ্যা

Question: Sonar Bangla express, normally reaches its destination at 72 km/h in 6 hours. Find the speed at which it must travel to reduce the travel time by 2 hours?

Solution:
Distance to be covered = Speed × Time
= 72 × 6
= 432 km

Reduced time = 6 - 2 = 4 hours

∴ Required speed = 432/4
= 108 km/h

∴ The train must travel at 108 km/h to reduce the time by 2 hours.

৯,০৮৯.

a, b, c, d, e, f are five consecutive odd numbers, their average is-

ক
ক) 5(a+4)
খ
খ) abcde/5
গ
গ) 5(a+b+c+d+e)
ঘ
ঘ) a+b+c+f
ঙ
ঙ) None of these

সঠিক উত্তর: ঙ

ঙ) None of these

উত্তর

সঠিক উত্তর: ঙ

ঙ) None of these

ঙ

ব্যাখ্যা

পাঁচটি ধারাবাহিক বেজোর সংখ্যার প্রথমটি a হলে পরের চারটি হবে a+2, a+4, a+6, a+8। এদের যোগফলঃ a + a+2 + a+4 + a+6 + a+8 = 5a + 20 = 5(a+4)। সুতরাং এদের গড় = 5(a+4)/5 = (a+4)

৯,০৯০.

What is the area of the hexagonal region shown in the figure?

ক
216
খ
108√3
গ
54√3
ঘ
216√3

সঠিক উত্তর: গ

54√3

উত্তর

সঠিক উত্তর: গ

54√3

গ

ব্যাখ্যা

Question: What is the area of the hexagonal region shown in the figure?

Solution:
দেওয়া আছে,
সুষম ষড়ভুজের বাহুর দৈর্ঘ্য, a = 6 একক
বাহুর সংখ্যা, n = 6

আমরা জানি,
সুষম বহুভুজের ক্ষেত্রফল = {(n × a²)/4} × cot(180°/n) বর্গ একক
∴ সুষম ষড়ভুজের ক্ষেত্রফল = {(6 × 6²)/4} × cot(180°/6) বর্গ একক
= 54 × cot30° বর্গ একক
= 54√3 বর্গ একক

∴ নির্ণেয় ক্ষেত্রফল 54√3 বর্গ একক

৯,০৯১.

A collection of books went on sale and 2/3 of them was sold for Tk 3.20 each. If none of the 41 remaining books were sold, what was the total amount received for the books that were sold?

ক
ক) 162.6 Tk
খ
খ) 198.4 Tk
গ
গ) 200 Tk
ঘ
ঘ) 262.4 Tk

সঠিক উত্তর: ঘ

ঘ) 262.4 Tk

উত্তর

সঠিক উত্তর: ঘ

ঘ) 262.4 Tk

ঘ

ব্যাখ্যা

Remaining books = 1 - 2/3 = 1/3
1/3 of the books = 41 books
So, 2/3 of the books = 41×(2/3) / (1/3) = 82

∴ Total amount received for the sold books = 82 × 3.20 = 262.4 TK

৯,০৯২.

12 people at a party shake hands once with everyone else in the room. How many handshakes took place?

ক
72
খ
66
গ
76
ঘ
64
ঙ
None of these

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

There are 12 people, so this is our n value.
So, ¹²C₂= 66

৯,০৯৩.

On simplification √{(0.65)² - (0.16)²} reduces to-

ক
0.63
খ
0.54
গ
0.65
ঘ
None of these

সঠিক উত্তর: ক

0.63

উত্তর

সঠিক উত্তর: ক

0.63

ক

ব্যাখ্যা

Question: On simplification √{(0.65)² - (0.16)²} reduces to-

Solution:
Given that,
√{(0.65)² - (0.16)²}
Since, a² - b² = (a - b)( a + b)
= √{(0.65 + 0.16)(0.65 - 0.16)}
= √{(0.81)(0.49)}
= √{(0.9)(0.9)×(0.7)(0.7)}
= 0.9 × 0.7
= 0.63

৯,০৯৪.

Jamal has 160 chocolates. He gave 5% chocolates to Rana, 15% to Amit and one - fourth of the chocolates to Galib. How many chocolates are left with Jamal after distribution?

ক
56
খ
72
গ
88
ঘ
None of these

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Jamal has 160 chocolates. He gave 5% chocolates to Rana, 15% to Amit and one - fourth of the chocolates to Galib. How many chocolates are left with Jamal after distribution?

Solution:
Rana gets = 160 × 5/100 = 8 chocolates
Amit gets = 160 × 15/100 = 24 chocolates
Galib gets = 160/4 = 40 chocolates

chocolates are left with Jamal after distribution = 160 - 8 - 24 - 40 = 88 chocolates

৯,০৯৫.

A batsman scored 45, 68, 52, 71, and 59 runs in five innings. How many runs must he score in the sixth innings to have an average of exactly 60 runs?

ক
58
খ
61
গ
65
ঘ
73

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: A batsman scored 45, 68, 52, 71, and 59 runs in five innings. How many runs must he score in the sixth innings to have an average of exactly 60 runs?

Solution:
ধরি, 6-তম ইনিংসে রান = x
প্রথম 5টি ইনিংসে মোট রান = (45 + 68 + 52 + 71 + 59) = 295

প্রশ্নমতে,
(295 + x)/6 = 60
⇒ 295 + x = 60 × 6
⇒ 295 + x = 360
⇒ x = 360 - 295
⇒ x = 65

∴ 6-তম ইনিংসে 65 রান করতে হবে।

৯,০৯৬.

{2/(a - b)} - {5/(b - a)} =

ক
ক) - 10/(2ab - a² - b²)
খ
খ) - 3/(a - b)
গ
গ) - 7/(a - b)
ঘ
ঘ) -7/(b - a)
ঙ
ঙ) - 3/(b - a)

সঠিক উত্তর: ঘ

ঘ) -7/(b - a)

উত্তর

সঠিক উত্তর: ঘ

ঘ) -7/(b - a)

ঘ

ব্যাখ্যা

Question: {2/(a - b)} - {5/(b - a)} =

Solution:
2/(a - b) - 5/(b - a)
= - 2/(b - a) - 5/(b - a)
= (- 2 - 5)/(b - a)
= - 7/(b - a)

৯,০৯৭.

56 men complete a piece of work in 24 days. In how many days can 42 men complete the same piece of work?

ক
ক) 118
খ
খ) 32
গ
গ) 48
ঘ
ঘ) 98

সঠিক উত্তর: খ

খ) 32

উত্তর

সঠিক উত্তর: খ

খ) 32

খ

ব্যাখ্যা

Let,
The required number of days be x.
Less Man, More Days [Indirect proportion]
∴ 42 : 56 :: 24 : x
⇒ 42x = 56 × 24
⇒ x = (56 × 24)/42
⇒ x = 32.

৯,০৯৮.

While selling a jug online, the seller offered a discount of 23% but managed to make a profit of 10% which translates into Tk. 77/-. What was the list price of the jug?

ক
ক) Tk. 770
খ
খ) Tk. 847
গ
গ) Tk. 1100
ঘ
ঘ) Tk. 1120

সঠিক উত্তর: গ

গ) Tk. 1100

উত্তর

সঠিক উত্তর: গ

গ) Tk. 1100

গ

ব্যাখ্যা

The seller manages to make a 10% profit.
Value of this 10% profit = Tk. 77
% Profit = Profit/Cost price × 100
∴ 10 = 77/C.P. × 100
∴ CP = Tk. 770
And S.P. = 770+77 = Tk. 847

Price after Commission = Selling Price
= (100-23)% of L.P.
= 77% of L.P.
∴ 847 = 77/100 × L.P.
∴ L.P. = List Price = Tk. 1100

৯,০৯৯.

What is the greatest prime factor of (4²)² - 1?

ক
ক) 3
খ
খ) 5
গ
গ) 13
ঘ
ঘ) 17

সঠিক উত্তর: ঘ

ঘ) 17

উত্তর

সঠিক উত্তর: ঘ

ঘ) 17

ঘ

ব্যাখ্যা

এখানে
(4²)² - 1 = (4²)² - 1²
= (4² + 1)(4²- 1)
= (16 + 1)(16 - 1)
= 17 × 15
= 17 × 3 × 5

সুতরাং, বৃহত্তম মৌলিক উৎপাদক হলো 17

৯,১০০.

If {(5x/6) + 3} and {(x/3) + 10} are equal, then what is the value of x?

ক
ক) 6
খ
খ) 7
গ
গ) 12
ঘ
ঘ) 14

সঠিক উত্তর: ঘ

ঘ) 14

উত্তর

সঠিক উত্তর: ঘ

ঘ) 14

ঘ

ব্যাখ্যা

Question: If {(5x/6) + 3} and {(x/3) + 10} are equal, then what is the value of x?

Solution:
ATQ,
{(5x/6) + 3} = {(x/3) + 10}
⇒ (5x/6) - (x/3) = 10 - 3
⇒ (5x - 2x)/6 = 7
⇒ 3x/6 = 7
⇒ x = 42/3
∴ x = 14