Bank Math

PrepBank · পাতা ১০৬ / ১৬১ · ১০,৫০১–১০,৬০০ / ১৬,১২৪

১০,৫০১.

Find the odd man out.
2, 5, 10, 17, 26, 37, 50, 64

ক
50
খ
37
গ
26
ঘ
64

ব্যাখ্যা

Question: Find the odd man out.
2, 5, 10, 17, 26, 37, 50, 64

Solution:

2, 5, 10, 17, 26, 37, 50, 64
(1 × 1) + 1, (2 × 2) + 1, (3 × 3) + 1, (4 × 4) + 1, (5 × 5) + 1, (6 × 6) + 1, (7 × 7) + 1, (8 × 8) + 1

∴ 64 is out of pattern.

১০,৫০২.

A 60 litre mixture of sugar and water contains sugar and water in the ratio 2 : 3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1 : 1?

ক
6
খ
10
গ
15
ঘ
None

ব্যাখ্যা

Question: A 60 litre mixture of sugar and water contains sugar and water in the ratio 2 : 3. How many litres of the mixture should be replaced by sugar so that the ratio of sugar and water becomes 1 : 1?

Solution:
ধরি, mixture এর x পরিমাণকে sugar দ্বারা replace করতে হবে ।
অর্থাৎ , sugar/water = {2/5 × (60 - x) + x}/{(3/5) × (60 - x)} = 1/1
Or, (120 - 2x + 5x)/5 = (180 - 3x)/5
Or, 120 + 3x = 180 - 3x
Or, 6x = 60
Or, x = 10.

১০,৫০৩.

A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

ক
Tk. 698
খ
Tk. 789
গ
Tk. 608
ঘ
Tk. 628

ব্যাখ্যা

Question: A sum of money at simple interest amounts to Tk. 815 in 3 years and to Tk. 854 in 4 years. The sum is-

Solution:
Simple interest for 1 year = Tk. (854 - 815)
= Tk. 39

∴ Simple interest for 3 years = Tk.(39 × 3)
= Tk. 117

∴ Sum = (815 - 117)
= Tk. 698

১০,৫০৪.

A quadratic equation ax² + bx + c = 0 has no real roots, if-

ক
ক) b² – 4ac > 0
খ
খ) b² – 4ac = 0
গ
গ) b² – 4ac < 0
ঘ
ঘ) b² – ac > 0
ঙ
ঙ) b² – 2ac > 0

ব্যাখ্যা

A quadratic equation ax² + bx + c = 0 has no real roots, if b² – 4ac < 0.
That means, the quadratic equation contains imaginary roots.

১০,৫০৫.

What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?

ক
20
খ
20.5
গ
24
ঘ
24.5

ব্যাখ্যা

Question: What is the measure of the radius of the circle that circumscribes a triangle whose sides measure 9, 40 and 41?

Solution:

First of all we can notice that a triangle whose sides measure 9, 40 and 41 is a right triangle because 9² + 40² = 41²

A right triangle inscribed in a circle always has its hypotenuse as the diameter of the circle. Conversely, if the diameter of a circle forms one side of a triangle inscribed in the circle, that triangle is a right triangle.

Thus, the diameter of the circle is equal to the hypotenuse of the triangle, which is 41. Therefore, the radius of the circle is = Diameter/2
= 41/2
= 20.5

১০,৫০৬.

The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their age after 6 years will be -

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

ব্যাখ্যা

Question: The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their age after 6 years will be -

Solution:
Let, man's age be = 7x years
Then, son's age = 3x years

ATQ,
7x × 3x = 756
⇒ 21x² = 756
⇒ x² = 36
⇒x = 6

The ratio of their ages after 6 years = (7 × 6 + 6) : (3 × 6 + 6)
= 48 : 24
= 2 : 1

১০,৫০৭.

If area of circle is equal to volume of sphere with equal radii, find the radius.

ক
√3
খ
√3/2
গ
1/2
ঘ
3/4
ঙ
1

ব্যাখ্যা

Question: If area of circle is equal to volume of sphere with equal radii, find the radius.

Solution:
Let r be the radius, We have
πr² = (4/3)πr³
⇒ r = 3/4

১০,৫০৮.

A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

ক
ক) 18 km/hr
খ
খ) 16 km/hr
গ
গ) 15 km/hr
ঘ
ঘ) 12 km/hr

ব্যাখ্যা

Question: A man travels 50 km at speed 25 km/hr and next 40 km at 20 km/hr and there after travel 90 km at 15 km/hr. His average speed is:

Solution:
We know,
Average speed = Total distance/Total time
= (50 + 40 + 90)/(2 + 2 + 6) km/hr
= 180/10 km/hr
= 18 km/hr.

১০,৫০৯.

When a mobile is sold for Tk. 4250, the owner loses 15%. At what price must the mobile be sold to gain 15%?

ক
Tk. 6255
খ
Tk. 5750
গ
Tk. 5490
ঘ
Tk. 5060

ব্যাখ্যা

Question: When a mobile is sold for Tk. 4250, the owner loses 15%. At what price must the mobile be sold to gain 15%?

Solution:
Let,
the new S.P be Tk. x

ATQ,
85 : 4250 = 115 : x
⇒ 85/4250 = 115/x
⇒ 85x = 115 × 4250
⇒ x = (115 × 4250)/85
∴ x = 5750

১০,৫১০.

If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?

ক
200 hectares
খ
220 hectares
গ
250 hectares
ঘ
280 hectares

ব্যাখ্যা

Question: If 8 men can reap 40 hectares in 12 days, then how many hectares can 30 men reap in 20 days?

Solution:
8 men can reap in 12 days 40 hectares
1 men can reap in 1 days 40/(12 × 8) hectares
30 men reap in 20 days = (40 × 600)/96
= 250 hectares

১০,৫১১.

sin²12° + sin²78° = ?

ক
0
খ
1
গ
1/2
ঘ
1/√2

ব্যাখ্যা

Question: sin²12° + sin²78° = ?

Solution:
Given that,
sin²12° + sin²78°
= sin²12° + sin²(90° - 12°)
= sin²12° + cos²12°
= 1

১০,৫১২.

If the Price of 6 toys is Tk. 264.37. What will be the approximate price of 5 toys?

ক
ক) Tk. 120
খ
খ) Tk. 100
গ
গ) Tk..200
ঘ
ঘ) Tk. 220
ঙ
ঙ) None of these

ব্যাখ্যা

Let the required Price be Tk. X .
Then, Lest toys , Less cost (Direct Proportion)
Therefore 6 : 5 :: 264.37 : x
=> 6 × x = 5 × 264.37
=> x = 220.308
Therefore, Approximate price of 5 toys = Tk. 220

১০,৫১৩.

The average price of three items of furniture is Tk. 25000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?

ক
ক) 5000 Tk.
খ
খ) 15000 Tk.
গ
গ) 20000 Tk.
ঘ
ঘ) 25000 Tk.

ব্যাখ্যা

Question: The average price of three items of furniture is Tk. 25000. If their prices are in the ratio 3 : 5 : 7, what is the price of the cheapest item?

Solution:
The average price of three items of furniture is Rs. 25000.
total price = (25000 × 3) = 75000
their prices are in the ratio 3 : 5 : 7

∴ the price of the cheapest item is = 75000 × 3/15
= 15000 tk

১০,৫১৪.

Samir borrows 2500 taka from a leasing company at 5% compound interest per year. Calculate the total that must be paid after 24 months.

ক
ক) 2,025.89
খ
খ) 2,756.25
গ
গ) 2,852.92
ঘ
ঘ) 2,758.78

ব্যাখ্যা

Here, n = 24 months = 2 years

Compound interest rate = 5% = 5/100

We know, C = P ( 1 + r%)² = 2500 (1 + 5/100)²= tk. 2,756.25

১০,৫১৫.

If 4(P’s Capital) = 6(Q’s Capital) = 10(R’s Capital), then out of the total profit of Tk. 4650, Q will receive-

ক
ক) Tk. 2250
খ
খ) Tk. 1500
গ
গ) Tk. 1400
ঘ
ঘ) Tk. 900

ব্যাখ্যা

প্রশ্ন: If 4(P’s Capital) = 6(Q’s Capital) = 10(R’s Capital), then out of the total profit of Tk. 4650, Q will receive-

সমাধান:
Let,
P’s capital = p
Q’s capital = q
R’s capital = r
Then
4p = 6q = 10r
⇒ 2p = 3q = 5r
Here,
q = (2p)/3
r = (2p)/5

∴ P : Q : R = p : (2p)/3 : (2p)/5
= 15p : 10p : 6p
= 15 : 10 : 6

∴ Q will receive = 4650 × (10/31) = 150 × 10 = 1500

১০,৫১৬.

If tanθ + cotθ = 5, then tan²θ + cot²θ is?

ক
23
খ
33
গ
43
ঘ
53

ব্যাখ্যা

Question: If tanθ + cotθ = 5, then tan²θ + cot²θ is?

Solution:
Given,
tanθ + cotθ = 5
⇒ (tanθ + cotθ)² = 5²( Squaring both sides)
⇒ tan²θ + cot²θ + 2tanθcotθ = 25
⇒ tan²θ + cot²θ = 25 - 2 [∵ tanθ . cotθ = 1]
∴ tan²θ + cot²θ = 23

১০,৫১৭.

দুইটি সংখ্যার অনুপাত ৫ : ৮ এবং লসাগু ২০০। সংখ্যা দুইটি কত?

ক
২৫, ৪০
খ
১৫, ২৪
গ
১০, ১৫
ঘ
২০, ৪৫
ঙ
কোনোটিই নয়

ব্যাখ্যা

প্রশ্ন: দুইটি সংখ্যার অনুপাত ৫ : ৮ এবং লসাগু ২০০। সংখ্যা দুইটি কত?

সমাধান:
ধরি,
সংখ্যা দুইটি যথাক্রমে = ৫ক এবং ৮ক
∴ ৫x এবং ৮x এর লসাগু = ৪০ক

প্রশ্নানুসারে,
৪০ক = ২০০
⇒ ক = ২০০/৪০
∴ ক = ৫

∴ সংখ্যা দুইটি হলো ৫ক = ৫ × ৫ = ২৫
এবং ৮ক = ৮ × ৫ = ৪০

১০,৫১৮.

A school has a total of 90 students. There are 30 students taking Physics, 25 taking English, and 13 taking both. How many students are taking either Physics or English?

ক
40
খ
42
গ
44
ঘ
48

ব্যাখ্যা

Question: A school has a total of 90 students. There are 30 students taking Physics, 25 taking English, and 13 taking both. How many students are taking either Physics or English?

Solution:
Students taking physics n(P) = 30 (these 30 include those 13 that take both)
Students taking english n(E) = 25 (these 25 also include those 13)
Students taking both n(P ∩ E) = 13
Students taking either Physics or English n(P ∪ E) = ?

We know
n(P ∪ E) = n(P) + n(E) - n(P ∩ E)
= 30 + 25 - 13 = 42

১০,৫১৯.

A cubical container with a side of 8 meters is to be painted on the entire outer surface area. If the cost of painting is Tk. 25 per square meter, what will be the total cost of painting?

ক
Tk. 7200
খ
Tk. 9600
গ
Tk. 12000
ঘ
Tk. 10600

ব্যাখ্যা

Question: A cubical container with a side of 8 meters is to be painted on the entire outer surface area. If the cost of painting is Tk. 25 per square meter, what will be the total cost of painting?

Solution:
দেওয়া আছে,
ঘনকাকৃতির পাত্রের বাহুর দৈর্ঘ্য, a = 8 m
যেহেতু সম্পূর্ণ বাইরের পৃষ্ঠতলে রং করতে হবে, তাই রং করার ক্ষেত্রফল ঘনকটির সমগ্র পৃষ্ঠতলের ক্ষেত্রফলের সমান হবে।

ঘনকের সমগ্র পৃষ্ঠতলের ক্ষেত্রফল = 6a²
∴ রং করার ক্ষেত্রফল = 6 × 8²
⇒ রং করার ক্ষেত্রফল = 6 × 64
⇒ রং করার ক্ষেত্রফল = 384 বর্গমিটার।

এখন, প্রতি বর্গমিটারে রং করার খরচ = 25 টাকা
সুতরাং, মোট খরচ = (রং করার ক্ষেত্রফল) × (প্রতি বর্গমিটারে খরচ)
⇒ মোট খরচ = 384 × 25
⇒ মোট খরচ = 9600 টাকা।

অতএব, রং করতে মোট খরচ হবে 9600 টাকা।

১০,৫২০.

What is the value of 7 log₁₀ (10/9) - 2 log₁₀ (25/24) + 3 log₁₀ (81/80) ?

ক
log₁₀ 4
খ
log₁₀ 2
গ
2 log₁₀ 5
ঘ
log₁₀ 3

ব্যাখ্যা

Question: What is the value of 7 log₁₀ (10/9) - 2 log₁₀ (25/24) + 3 log₁₀ (81/80) ?

Solution:
7 log₁₀ (10/9) - 2 log₁₀ (25/24) + 3 log₁₀ (81/80)
= log₁₀ (10/9)⁷ - log₁₀(25/24)² + log₁₀ (81/80)³
= log₁₀ {(10/9)⁷/(25/24)²} + log₁₀ (81/80)³
= log₁₀ {(10/9)⁷ × (24/25)² × (81/80)³}
= log₁₀ {10⁷ × (2 × 2 × 2 × 3)² × (9²)³}/{(9⁷ × (5²)² × (10 × 8)³}
= log₁₀ {10⁷ × 2⁶ × 3² × 9⁶}/{9⁷ × 5⁴ × 10³ × (2³)³}
= log₁₀ {(10⁷ × 2⁶ × 9 × 9⁶)/(9⁷ × 5⁴ × 10³ × 2⁹)}
= log₁₀ {(10⁷ × 2⁶ × 9⁷)/(9⁷ × 5⁴ × 10³ × 2⁹)}
= log₁₀ {10⁴ /(5⁴ × 2³⁾}
= log₁₀ {(2 × 5)⁴/(5⁴ × 2³)}
= log₁₀ (2⁴ × 5⁴)/(5⁴ × 2³)}
= log₁₀ 2

১০,৫২১.

The expression x³ - 2x² + 4x - 8 is divided by x - 2. What is the remainder?

ক
0
খ
2
গ
- 8
ঘ
8

ব্যাখ্যা

Question: The expression x³ - 2x² + 4x - 8 is divided by x - 2. What is the remainder?

Solution:
Let,
f(x) = x³ - 2x² + 4x - 8
f(2) = (2)³ - 2(2)² + 4(2) - 8
= 8 - 8 + 8 - 8
= 0

So, the remainder when x³ - 2x² + 4x - 8 is divided by x - 2 is 0.

১০,৫২২.

A wire can be bent in the form of a circle of radius 49 cm. If it is bent in the form of a square, then its area will be -

ক
5929 cm²
খ
4355 cm²
গ
4186 cm²
ঘ
3690 cm²
ঙ
None

ব্যাখ্যা

Question: A wire can be bent in the form of a circle of radius 49 cm. If it is bent in the form of a square, then its area will be -

Solution:
Given,
radius of the circle r = 49 cm

Circumference of the circle = 2πr
= 2 × (22/7) × 49
= 2 × 22 × 7
= 308 cm

The length of one side of the square = 308/4 = 77 cm

Area of the square = (77)² cm²
= 5929 cm²

১০,৫২৩.

A kite is flown with a thread of length 200 meter. The thread is fully stretched and makes an angle of 60° with the horizontal, find the approximate height of the kite above the ground.

ক
346 m
খ
173 m
গ
100 m
ঘ
141 m

ব্যাখ্যা

Question: A kite is flown with a thread of length 200 meter. The thread is fully stretched and makes an angle of 60° with the horizontal, find the approximate height of the kite above the ground.

Solution:

Let height of the kite above the ground be AC = h.
Length of thread, BC = 200 m

From ΔABC,
sin60° = AC/BC
⇒ √3/2 = h/200
⇒ h = (200 × √3)/2
∴ h = 173.20

∴ Height of the kite above the ground be 173 m (approximately)

১০,৫২৪.

The difference between the present ages of Abir and Deepak is 14 years. Eight years ago, the ratio of their ages was 5 : 7 respectively. What is Deepak's present age?

ক
ক) 55 years
খ
খ) 56 years
গ
গ) 57 years
ঘ
ঘ) 58 years

ব্যাখ্যা

Let the age of Abir eight years ago be 5x
Let the age of Deepak eight years ago be 7x
Present age of Abir would be 5x + 8
Present age of Deepak would be 7x + 8

According to question,
7x + 8 - (5x + 8) = 14
7x + 8 - 5x - 8 = 14
2x = 14
x = 7

Deepak's present age = 7 × 7 + 8 = 57 years

১০,৫২৫.

A boat can row 180 km upstream , with the speed of still water in 30 kmph and the difference between time taken upstream and downstream is 2.5 hours. Find the speed of the stream.

ক
5 kmph
খ
7 kmph
গ
6 kmph
ঘ
4 kmph

ব্যাখ্যা

Question: A boat can row 180 km upstream , with the speed of still water in 30 kmph and the difference between time taken upstream and downstream is 2.5 hours. Find the speed of the stream.

Solution:
Speed of boat in still water = 30 kmph.
Speed of stream = x kmph

ATQ,
180/(30 - x) - 180/(30 + x) = 2.5
⇒ {180(30 + x) - 180(30 - x)}/(900 - x²) = 2.5
⇒ 5400 + 180x - 5400 + 180x = 2.5 × (900 - x²)
⇒ 360x = 2250 - 2.5x²
⇒ 2.5x² + 360x - 2250 = 0
⇒ x² + 144x - 900 = 0
⇒ x² + 150x - 6x - 900 = 0
⇒ x(x + 150) - 6(x + 150)
⇒ (x + 150)(x - 6) = 0
∴ x = 6, - 150
Speed cannot be negative so the speed of the stream is 6 kmph.

১০,৫২৬.

A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

ক
18
খ
27
গ
30
ঘ
35

ব্যাখ্যা

Question: A contractor employs 45 persons to do a job in 40 days. After 10 days, it was found that only one-sixth of the work was finished. How many more persons are to be employed to finish the job as per schedule?

Solution:
দেওয়া আছে:
মোট লোক = 45 জন
নির্ধারিত সময় = 40 দিন
10 দিনে সম্পন্ন কাজ = 1/6 অংশ

ধরি, সম্পূর্ণ কাজ = 1 একক

45 জন লোক 10 দিনে করে = 1/6 অংশ কাজ
∴ 45 জন লোক 1 দিনে করে = (1/6) ÷ 10 = 1/60 অংশ
∴ 1 জন লোক 1 দিনে করে = (1/60) ÷ 45 = 1/2700 অংশ

অবশিষ্ট কাজ = 1 - 1/6 = 5/6 অংশ
অবশিষ্ট সময় = 40 - 10 = 30 দিন

∴ অবশিষ্ট 5/6 অংশ কাজ 30 দিনে করতে হবে

∴ প্রতিদিনের প্রয়োজনীয় কাজের হার = (5/6) ÷ 30 অংশ
= 5/180 = 1/36 অংশ

এখন,
প্রতিদিন 1/2700 অংশ কাজ করে 1 জন
∴ 1 অংশ কাজ করে = 1 ÷ (1/2700) জন
∴ 1/36 অংশ কাজ করে = (2700/36) জন
= 75 জন

∴ অতিরিক্ত লোকের প্রয়োজন = 75 - 45 = 30 জন

১০,৫২৭.

A man on tour travels 160 km by car at 64 km/hr and another 160 km by bus at 80 km/hr. The average speed for the whole journey is

ক
36.12 km/hr
খ
50 km/hr
গ
71.11 km/hr
ঘ
82.6 km/hr

ব্যাখ্যা

Question: A man on tour travels 160 km by car at 64 km/hr and another 160 km by bus at 80 km/hr. The average speed for the whole journey is

Solution:
The total distance traveled is the sum of distances traveled by car and bus, which is 160 km + 160 km = 320 km.

Time taken for the car journey = Distance ÷ Speed = 160 km ÷ 64 km/hr = 2.5 hours
Time taken for the bus journey = Distance ÷ Speed = 160 km ÷ 80 km/hr = 2 hours

The total time taken for the entire journey is 2.5 hours (car) + 2 hours (bus) = 4.5 hours.

Average speed = Total distance traveled ÷ Total time taken
⇒ 320 km ÷ 4.5 hours ≈ 71.11 km/hr

১০,৫২৮.

A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water from the tank in:

ক
ক) 10 hrs
খ
খ) 12 hrs
গ
গ) 14 hrs
ঘ
ঘ) 16 hrs

ব্যাখ্যা

Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 7/3 hours to fill the tank. The leak can drain all the water from the tank in:

Solution:
ধরি, ছিদ্র দিয়ে ট্যাঙ্ক খালি হয় x ঘণ্টায়
১ ঘণ্টায় খালি হয় ১/x ঘন্টায়

একটি পাম্প ২ ঘন্টায় পূর্ণ হয় ১ অংশ
১ ঘণ্টায় পূর্ণ হয় ১/২ অংশ

প্রশ্নমতে,
(১/২) - (১/x) = ৩/৭
⇒ ১/x = (১/২) - (৩/৭)
= ১/১৪
x = ১৪ ঘণ্টা

১০,৫২৯.

ক
27
খ
29
গ
24
ঘ
36

ব্যাখ্যা

Question:

Solution:
দেয়া আছে,

• ট্রেস (Trace): Matrix এর Trace হলো একটি বর্গাকার ম্যাট্রিক্সের প্রধান কর্ণের উপাদানগুলোর যোগফল।
• প্রধান কর্ণ হলো ম্যাট্রিক্সের উপরের বাম কোণ থেকে নিচের ডান কোণ পর্যন্ত বিস্তৃত উপাদানগুলো।
প্রদত্ত ম্যাট্রিক্স A এর প্রধান কর্ণের উপাদানগুলো হলো 5, 9 এবং 13
সুতরাং, প্রদত্ত ম্যাট্রিক্সের ট্রেস (Trace) B = 5 + 9 + 13 = 27

১০,৫৩০.

If a + (1/a) = 3, what is a³ + (1/a³)?

ক
24
খ
7
গ
30
ঘ
18

ব্যাখ্যা

Question: If a + (1/a) = 3, what is a³ + (1/a³)?

Solution:
দেওয়া আছে
a + (1/a) = 3

a³ + 1/a³ = (a + 1/a)³ - 3.a.1/a(a + 1/a)
= 3³ - 3 × 3
= 27 - 9
= 18

১০,৫৩১.

The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

ক
ক) 7:6
খ
খ) 8:7
গ
গ) 9:8
ঘ
ঘ) 3:4

ব্যাখ্যা

A's age = 44 × (6/11) years = 24 years and
B's age = (44 - 24) years = 20 years.
Ratio of their ages after 8 years = (24 + 8)/(20 + 8)
= 32/28
= 8/7
= 8:7

১০,৫৩২.

If LOSS = 1355 and GAIN = 2468 then 84615 =?

ক
ক) GAILS
খ
খ) LAINS
গ
গ) NAILS
ঘ
ঘ) SAINT

ব্যাখ্যা

Question: If LOSS = 1355 and GAIN = 2468 then 84615 =?

Solution:
LOSS = 1355, GAIN = 2468
∴ 84615 = NAILS

১০,৫৩৩.

If 6th March, 2010 is Saturday, what was the day of the week on 6th March, 2008?

ক
Wednesday
খ
Thursday
গ
Friday
ঘ
Saturday

ব্যাখ্যা

Question: If 6th March, 2010 is Saturday, what was the day of the week on 6th March, 2008?

Solution:
From 6 March 2008 to 6 March 2009
⋅Although 2008 is a leap year, 29 February 2008 is before 6th March, so that extra day does not fall in this interval.
So this interval has 365 days → 1 odd day.
From 6 March 2009 to 6 March 2010
⋅ 2009 is a normal year → 365 days → 1 odd day.

Total odd days between 6th March 2008 and 6th March 2010
= 1 + 1 odd days
= 2 odd days.

Given,
6th March 2010 is Saturday
∴ 2 days before Saturday is Thursday.

So, 6th March 2008 was Thursday.

১০,৫৩৪.

A shopkeeper blends two varieties of rice from two different regions, one variety costing tk 50 per kg and the other tk 30 per kg in the ratio 3 : 2. He sells the blended rice at tk 45 per kg. Find the profit or loss percent.

ক
7.14% loss
খ
9.21% loss
গ
7.14% profit
ঘ
9.21% profit

ব্যাখ্যা

Question: A shopkeeper blends two varieties of rice from two different regions, one variety costing tk 50 per kg and the other tk 30 per kg in the ratio 3 : 2. He sells the blended rice at tk 45 per kg. Find the profit or loss percent.

Solution:
Let 3 kg of the first variety be mixed with 2 kg of second variety.
Then total cost price of 5 kg of rice = (50 × 3) + (30 × 2) = tk 210
Selling price of 5 kg of rice = (45 × 5) = tk 225
∴ Profit = tk (225 - 210) = tk 15

∴ Percentage of profit = (15 × 100)/210 = 7.14%

১০,৫৩৫.

a, b and c are all positive integers such that a + b + c = 150 and none of these values are equal to each other. What is the smallest possible value for the median of a, b, & c?

ক
ক) 5
খ
খ) 4
গ
গ) 3
ঘ
ঘ) 2
ঙ
ঙ) None of the above

ব্যাখ্যা

a + b + c = 150.

Since, we have to find out the most possible smallest value,
We assume a = 1, b = 2 and c = 147.

So, the median is 2.

১০,৫৩৬.

Tk. 1400 is lent out at 5% per annum simple interest for 4 years. Find the amount after 4 years.

ক
Tk. 1580
খ
Tk. 1480
গ
Tk. 1680
ঘ
Tk. 1280

ব্যাখ্যা

Question: Tk. 1400 is lent out at 5% per annum simple interest for 4 years. Find the amount after 4 years.

Solution:
We know,
A = p(1 + nr)
= 1400 {1 + (4 × 5)/100}
= 1400 × (120/100)
= 1680

১০,৫৩৭.

The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

ক
23 years
খ
22 years
গ
21 years
ঘ
20 years

ব্যাখ্যা

Question: The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

Solution:
Let the present age of the son =x
Then, the present age of the mother =(60-x)
As per question:
Six years ago mother's age was 5 times the age of her son:
So, (60-x) -6=5(x-6)
54 - x = 5x -30
84=6x
x=84/6
x=14 Years

Age of son after 6 years
=x+6
=14+6
=20 Years

১০,৫৩৮.

A sum of money becomes 8/5 of itself in 5 years at a certain rate of interest. What is the rate of the interest?

ক
ক) 9%
খ
খ) 7%
গ
গ) 10%
ঘ
ঘ) 12%
ঙ
ঙ) 5%

ব্যাখ্যা

Let the sum of money be P(which is the principal value) and rate of interest be R.
According to the question,
Amount (principal +simple interest) = 8P/5
Time (T) = 5 years
Simple interest (SI) = PRT/100
SI = 5PR/100
Amount = P + SI
8P/5 = P + (5PR/100)
8P/5 = P(100 + 5R)/100
160 = 100 + 5R
5R = 60
R = 12
Therefore, rate of interest = 12% p.a.

Alternative Method:
Given A = 8/5p (8/5 of the sum) .
Time = 5years .
Let the sum be P = 100.
Then, the amount = 8/5p = (value of p is 100)
= 8/5 × 100
= 160 .
S. I. = A-P
= 160 - 100
= 60 .
Hence,
Rate = S.I. × 100/P × T
= 60 × 100/100 × 5
= 12% p.a.

১০,৫৩৯.

M is older than N but younger than O. If m, n and o are the ages of M, N and O respectively, then which of the following is true?

ক
n < m < o
খ
m < n < o
গ
o < m < n
ঘ
o < n < m

ব্যাখ্যা

Question: M is older than N but younger than O. If m, n and o are the ages of M, N and O respectively, then which of the following is true?

Solution:
M এর বয়স m বছর
N এর বয়স n বছর
O এর বয়স o বছর

M, N এর চেয়ে বড় এবং O এর চেয়ে ছোট।
অতএব, n < m < o

১০,৫৪০.

The acid and water in two vessels A and B are in the ratio 4 : 3 and 2 : 3. In what ratio should the liquid in both the vessels be mixed to obtain a new mixture in vessel C containing half acid and half water?

ক
ক) 7 : 5
খ
খ) 5 : 7
গ
গ) 7 : 3
ঘ
ঘ) 5 : 3
ঙ
ঙ) 3 : 7

ব্যাখ্যা

According to the question,
Acid : Water -
Vessel A - 4 : 3
Vessel B - 2 : 3
Now using alligation,

১০,৫৪১.

A number when divided by 729 given a remainder of 56. What will we get as remainder if the same number is divided by 27?

ক
ক) 1
খ
খ) 2
গ
গ) 3
ঘ
ঘ) 4

ব্যাখ্যা

Here let the number be A.
So, A=729 × y + 56 [ where y is quotient ]
It can be written as A = 27(27 × y + 2) + 2
When A is divided by 27, the remainder is 2.

১০,৫৪২.

The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Tk. 4000. The total price of 12 chairs and 3 tables is:

ক
Tk.3000
খ
Tk.3200
গ
Tk.3600
ঘ
Tk.3900

ব্যাখ্যা

Let the cost of a chair and that of table be Rs. x and Rs. y respectively.
Then,10x = 4y or y = 5x/2
∴15x + 2y = 4000
⇒15x + 2 × 5x/2 = 4000
⇒20x = 4000
∴ x = 200
So, y = 5 × 200/2 = 500
Hence, the cost of 12 chairs and 3 tables = 12x + 3y = Tk. (2400 + 1500) = Tk.3900

১০,৫৪৩.

Two numbers when divided by 17, leaves remainder 13 and 11 respectively. If the sum of those two numbers is divided by 17, the remainder will be?

ক
5
খ
7
গ
1
ঘ
9

ব্যাখ্যা

Question: Two numbers when divided by 17, leaves remainder 13 and 11 respectively. If the sum of those two numbers is divided by 17, the remainder will be?

Solution:
Let
The quotient = n
Dividend = divisor × quotient + remainder
First number = (17 × n) + 13
Second number = (17 × n) + 11

Let,
n = 1
∴ first number = 30
and, second number = 28

after adding these two the reminder is = (30 + 28)/17
= 58/17
∴ reminder = 7

১০,৫৪৪.

A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7?

ক
1/9
খ
11/90
গ
2/15
ঘ
13/90

ব্যাখ্যা

Question: A two-digit number is chosen at random. What is the probability that the chosen number is a multiple of 7?

Solution:
There are 90 two-digit numbers (all integers from 10 to 99).
Of those, there are 13 multiples of 7 ⇒ 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98.

∴ The probability that the chosen number is a multiple of 7 is 13/90

১০,৫৪৫.

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

ক
10°
খ
7.5°
গ
8°
ঘ
12.5°

ব্যাখ্যা

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

Solution:
20 minutes past 4 অর্থাৎ, 4 টা 20 মিনিট।
= 4 + (20/60) ঘন্টা
= 4 + (1/3) ঘন্টা
= 13/3 ঘন্টা

আমরা জানি,
ঘণ্টার কাঁটা 12 ঘণ্টায় 360° ঘোরে।
∴ 1 ঘণ্টায় ঘোরে = 360°/12 = 30°
∴ 13/3 ঘন্টায় ঘোরে = (30° × 13)/3
= 390°/3 = 130°

আবার,
মিনিটের কাঁটা 60 মিনিটে 360° ঘোরে।
∴ 1 মিনিটে ঘোরে = 360°/60 = 6°
∴ 20 মিনিটে ঘোরে = 20 × 6° = 120°

∴ ঘড়ির কাঁটা দুটির মধ্যবর্তী কোণ = | 130° - 120° | = 10°

১০,৫৪৬.

If a² + b² + c² - ab - bc - ca = 0 then a : b : c is -

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

ব্যাখ্যা

a² + b² + c² - ab - bc - ca = 0 .....(i)
Multiple equation (i) by 2 we get
⇒ 2a² + 2b² + 2c² - 2ab - 2bc - 2ca = 0
⇒ (a² + b² - 2ab) + (b² + c² - 2bc) + (c² + a² - 2ca) = 0 [ (a + b)² = a² + b² + 2ab]
⇒ (a - b)² + ((b - c)² + (c - a)² = 0 [if x² + y² + z² = 0 then x = 0, y = 0, z = 0]
∴ a - b = 0
⇒ a = b
b - c = 0
⇒ b = c
c - a = 0
⇒ c = a
∴ a : b : c = 1 : 1 : 1

১০,৫৪৭.

If rsinθ = 1, rcosθ = √3 then the value of √3tanθ + 3 = ?

ক
4
খ
√3 + 4
গ
4√3
ঘ
2

ব্যাখ্যা

Question: If rsinθ = 1, rcosθ = √3 then the value of √3tanθ + 3 = ?

Solution:
দেওয়া আছে,
rsinθ = 1 ......... (1)
rcosθ = √3 .............. (2)

(1) ÷ (2) হতে পাই
rsinθ/rcosθ =1/√3
⇒ tanθ = 1/√3
⇒ √3√tanθ = 1

এখন, √3tanθ + 3 = 1 + 3
∴ √3tanθ + 3 = 4

১০,৫৪৮.

২৪ সে.মি. উচ্চতা বিশিষ্ট একটি কোণকের ভূমির ব্যাস ১৪ সে.মি. হলে এর তীর্যক উচ্চতার দৈর্ঘ্য কত?

ক
২৩ সে.মি.
খ
২৫ সে.মি.
গ
২৮ সে.মি.
ঘ
২৯ সে.মি.
ঙ
৩১ সে.মি.

ব্যাখ্যা

প্রশ্ন: ২৪ সে.মি. উচ্চতা বিশিষ্ট একটি কোণকের ভূমির ব্যাস ১৪ সে.মি. হলে এর তীর্যক উচ্চতার দৈর্ঘ্য কত?

সমাধান:
দেওয়া আছে,
উচ্চতা, h = ২৪ সে.মি.
এবং ব্যাসার্ধ, r = ১৪/২ = ৭ সে.মি

অতএব, কোণকের তীর্যক উচ্চতা L = √(h^২ + r^২) সে.মি.
= √(২৪^২ + ৭^২) সে.মি.
= √(৫৭৬ + ৪৯) সে.মি.
= √৬২৫ সে.মি.
= ২৫ সে.মি.

১০,৫৪৯.

ক
5
খ
1/5
গ
0
ঘ
2
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন:

১০,৫৫০.

If tanθ = 3/4, then cosecθ = ?

ক
1/2
খ
5/3
গ
13/5
ঘ
2/3

ব্যাখ্যা

Question: If tanθ = 3/4, then cosecθ = ?

Solution:
এখানে,
tanθ = 3/4 = লম্ব/ভূমি

∴ লম্ব = 3, ভূমি = 4
∴ অতিভুজ = √(3²+ 4²)
= √25 = 5

∴ cosecθ = অতিভুজ/লম্ব
= 5/3

১০,৫৫১.

What is the interest for 2 years on Tk. 600 at a simple interest rate of 9.5%?

ক
114 Tk.
খ
118 Tk.
গ
125 Tk.
ঘ
140 Tk.

ব্যাখ্যা

Question: What is the interest for 2 years on Tk. 600 at a simple interest rate of 9.5%?

Solution:
Interest rate, R = 9.5%
Principal amount, P = 600 tk
Time, T = 2 years

We Know, SI = PRT/100
= (600 × 2 × 9.5)/100
= 114 Tk.

∴ The interest for 2 years is Tk. 114.

১০,৫৫২.

A book sells for Tk. 65. This price gives the seller a profit 30% on his cost. What will be the new selling price if he cuts his profit to 10% of the costs?

ক
ক) 55
খ
খ) 50
গ
গ) 45
ঘ
ঘ) None

ব্যাখ্যা

Question: A book sells for Tk. 65. This price gives the seller a profit 30% on his cost. What will be the new selling price if he cuts his profit to 10% of the costs?

Solution:
ধরি, ক্রয়মূল্য ১০০ টাকা
৩০% লাভে, বিক্রয়মূল্য = ১০০ + ৩০ টাকা
= ১৩০ টাকা

বিক্রয়মূল্য ১৩০ টাকা হলে ক্রয়মূল্য ১০০ টাকা
বিক্রয়মূল্য ৬৫ টাকা হলে ক্রয়মূল্য = (১০০ × ৬৫)/১৩০ টাকা
= ৫০ টাকা

১০% লাভে,
ক্রয়মূল্য ৫০ টাকা হলে বিক্রয়মূল্য = ৫০ + ৫০ এর ১০%
= ৫০ + ৫
= ৫৫ টাকা

১০,৫৫৩.

f(7) = 14 and g(x) = f(x + 4) - 5. Then g(3) = ?

ক
ক) 8
খ
খ) 9
গ
গ) 7
ঘ
ঘ) 6

ব্যাখ্যা

Question: f(7) = 14 and g(x) = f(x + 4) - 5. Then g(3) = ?

Solution:
দেয়া আছে,
f(7) = 14
g(x) = f(x + 4) - 5
g(3) = f(3 + 4) - 5
= f(7) - 5
= 14 - 5
= 9

১০,৫৫৪.

A mixture of 200 liters of wine and water contains 30% water. How much more water should be added so that water becomes 40% of the new mixture?

ক
35.25 liters.
খ
30.50 liters.
গ
33.33 liters.
ঘ
25 liters.

ব্যাখ্যা

Question: A mixture of 200 liters of wine and water contains 30% water. How much more water should be added so that water becomes 40% of the new mixture?

Solution:
Number of liters of water in 200 liters of the mixture = 30% of 200 = 30/100 × 200 = 60 liters.

Let P liters of water added to the mixture to make water 25% of the new mixture.

Total amount of water becomes (60 + P) and total volume of mixture is (200 + P).
(60 + P) = 40/100 × (200 + P)
300 + 5P = 400 + 2P
=> P = 33.33 liters.

১০,৫৫৫.

Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.

ক
33
খ
22
গ
16
ঘ
11

ব্যাখ্যা

Question: Find the average of the square of first 5 consecutive odd numbers starting from 1 to 9, where the last odd number is 9.

Solution:
The average of square of first n consecutive odd numbers starting from 1 to X, where the last odd number is X, is given by = X(X + 2)/3
Here,
X=9
So, average = 9(9 + 2)/3
= (9 × 11)/3
= 99/3
= 33

১০,৫৫৬.

An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

ক
ক) 720 km/hr
খ
খ) 620 km/hr
গ
গ) 360 km/hr
ঘ
ঘ) 420 km/hr

ব্যাখ্যা

Question: An aeroplane covers a certain distance at a speed of 240 kmph in 5 hours. To cover the same distance in 5/3 hours, it must travel at a speed of:

Solution:
Distance = (240 x 5) = 1200 km.

Speed = Distance/Time
Or, Speed = 1200/(5/3) km/hr.

∴ Required speed = 1200/(5/3) km/hr
= 720 km/hr.

১০,৫৫৭.

- 2 < (6 - 2x)/3 < 4, find the value of x.

ক
ক) - 3 < x < 6
খ
খ) 0 < x < 6
গ
গ) 3 < x or x < - 6
ঘ
ঘ) x < - 3 or x > 6

ব্যাখ্যা

Question: - 2 < (6 - 2x)/3 < 4, find the value of x.

Solution:
- 2 < (6 - 2x)/3 < 4
⇒ - 6 < 6 - 2x < 12
⇒ - 6 - 6 < - 2x < 12 - 6
⇒ - 12 < - 2x < 6
⇒ 6 > x > - 3
∴ - 3 < x < 6

১০,৫৫৮.

একজন কর্মচারির বেতন ২০% বৃদ্ধির পর সাপ্তাহিক ১৮০ টাকা পেল। তার আগের সাপ্তাহিক বেতন কত ছিল?

ক
ক) ১৪৪ টাকা
খ
খ) ১৫০ টাকা
গ
গ) ১৬০ টাকা
ঘ
ঘ) ১৬৪ টাকা

ব্যাখ্যা

প্রশ্ন: একজন কর্মচারির বেতন ২০% বৃদ্ধির পর সাপ্তাহিক ১৮০ টাকা পেল। তার আগের সাপ্তাহিক বেতন কত ছিল?

সমাধান:
২০% বৃদ্ধিতে,
বর্তমান বেতন ১২০ টাকা হলে আগের বেতন ১০০ টাকা
বর্তমান বেতন ১৮০ টাকা হলে আগের বেতন (১০০ × ১৮০)/১২০ টাকা
= ১৫০ টাকা

১০,৫৫৯.

2, 3, 6, 9, 18, ......, 54 What is the missing number in the series?

ক
36
খ
30
গ
27
ঘ
21

ব্যাখ্যা

Question: 2, 3, 6, 9, 18, ......, 54 What is the missing number in the series?

Solution:
There are two separate series

1st one for even number
2
2 × 3 = 6
6 × 3 = 18
18 × 3 = 54

2nd one for odd number
3
3 × 3 = 9
9 × 3 = 27

So the missing number = 27

১০,৫৬০.

In a lottery, there are 15 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize?

ক
ক) 3/8
খ
খ) 1/15
গ
গ) 1/25
ঘ
ঘ) 2/5

ব্যাখ্যা

Total outcome = 15 + 25 = 40
Favorable outcome = 15
P (getting a prize) =15/40
= 3/8

১০,৫৬১.

The present ages of Samba and Bambi are in the ratio of 6:4. Five years ago their ages were in the ratio of 5:3. How old is samba?

ক
ক) 30
খ
খ) 36
গ
গ) 42
ঘ
ঘ) 48
ঙ
ঙ) 46

ব্যাখ্যা

Bambi’s present age = 6x,
Samba’s present age = 4x
Therefore,
(6x - 5)/(4x - 5) = 5/3
Or, 20x - 25 = 18x - 15
So, x = 5
And samba’s age = 6 × 5 = 30

১০,৫৬২.

A mixture contains two liquids 'A' and 'B' in the ratio 5 : 3. If 8 litres of the mixture is withdrawn and replaced with 8 litres of 'A', the ratio becomes 2 : 1. What was the initial quantity of 'B'?

ক
45 litres
খ
24 litres
গ
27 litres
ঘ
32 litres

ব্যাখ্যা

Question: A mixture contains two liquids 'A' and 'B' in the ratio 5 : 3. If 8 litres of the mixture is withdrawn and replaced with 8 litres of 'A', the ratio becomes 2 : 1. What was the initial quantity of 'B'?

Solution:
ধরি, প্রাথমিক মিশ্রণের পরিমাণ ছিল 8x লিটার।
যেখানে A এর পরিমাণ = 5x লিটার এবং B এর পরিমাণ = 3x লিটার।

8 লিটার মিশ্রণ তুলে নেওয়ার পর,
মিশ্রণে A এর পরিমাণ = 5x - (5/8) × 8 = 5x - 5 লিটার।
মিশ্রণে B এর পরিমাণ = 3x - (3/8) × 8 = 3x - 3 লিটার।

নতুন 8 লিটার 'A' যোগ করার পর,
A এর নতুন পরিমাণ = (5x - 5) + 8 = 5x + 3 লিটার।

প্রশ্নানুযায়ী, নতুন অনুপাত,
⇒ (5x + 3) / (3x - 3) = 2/1
⇒ 1(5x + 3) = 2(3x - 3)
⇒ 5x + 3 = 6x - 6
⇒ 3 + 6 = 6x - 5x
⇒ 9 = x

সুতরাং, প্রাথমিকভাবে B এর পরিমাণ ছিল = 3x = 3 × 9 = 27 লিটার।

১০,৫৬৩.

If the difference between the circumference and diameter of a circle is 150 cm, then the diameter of the circle is-

ক
70 cm
খ
44 cm
গ
60 cm
ঘ
120 cm

ব্যাখ্যা

Question: If the difference between the circumference and diameter of a circle is 150 cm, then the diameter of the circle is-

Solution:
ধরি,
বৃত্তের ব্যাসার্ধ = r
বৃত্তের ব্যাস = 2r
বৃত্তের পরিধি = 2πr

প্রশ্নমতে,
2πr - 2r = 150
⇒ 2r(π - 1) = 150
⇒ r = (150/2){(22/7) - 1}
⇒ r = 75/(22 - 7)/7
⇒ r = (75 × 7)/15
∴ r = 35

∴ বৃত্তের ব্যাস = 2r = 2 × 35 = 70 সে.মি.

১০,৫৬৪.

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

ক
18 Years
খ
20 Years
গ
23 Years
ঘ
26 Years
ঙ
None of these

ব্যাখ্যা

Question: The captain of a cricket team of 11 members is 26 years old, and the wicket-keeper is three years older than the captain. If the ages of captain and wicketkeeper are excluded, the average age of the remaining players of the team is one year less than the average age of the whole team. What is the average age of the team?

Solution:
Let, the average age of the whole team by = x years.
Total age of the whole team = 11x years
Age of the captain = 26 years
Age of the wiket-keeper = (26 + 3) = 29 years

The average age of the remaining players after excluding the ages of captain and wicketkeeper = x - 1
∴ Total age of the players without the ages of captain and wicketkeeper = 9(x - 1)

Now,
11x - (26 + 29) = 9(x - 1)
⇒ 11x - 55 = 9x - 9
⇒ 11x - 9x = - 9 + 55
⇒ 2x = 46
∴ x = 23 Years.

১০,৫৬৫.

What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?

ক
-10
খ
-1/10
গ
10
ঘ
1/10

ব্যাখ্যা

Question: What is the slope of a line perpendicular to the line whose equation is 20x - 2y = 6?

Solution:
দেওয়া আছে,
20x - 2y = 6
⇒ - 2y = - 20x + 6
⇒ y = {(- 20)/(- 2)}x + 6/(- 2)
⇒ y = 10x - 3

এখানে, প্রদত্ত রেখার ঢাল, m₁= 10

আমরা জানি, দুটি রেখা পরস্পর লম্ব (Perpendicular) হলে তাদের ঢালদ্বয়ের গুণফল -1 হয়।

ধরি, লম্ব রেখার ঢাল m₂
অর্থাৎ, m₁× m₂ = -1

তাহলে,
10 × m₂ = -1
⇒ m₂= -1/10
∴m₂ = (-1/10)

∴ লম্ব রেখার ঢাল (-1/10)।

১০,৫৬৬.

One-half percent, written as a decimal, is-

ক
5
খ
0.05
গ
0.0005
ঘ
0.005

ব্যাখ্যা

Question: One-half percent, written as a decimal, is-

Solution:
As we know,1% =1/100
Hence,
(1/2)% = (1/2) × (1/100)
= 1/200
= 0.005

১০,৫৬৭.

Ι3x - 15Ι = 18 হলে x এর সম্ভাব্য মানগুলোর সমষ্টি কত?

ক
12
খ
- 11
গ
11
ঘ
10
ঙ
কোনটিই নয়

ব্যাখ্যা

প্রশ্ন: Ι3x - 15Ι = 18 হলে x এর সম্ভাব্য মানগুলোর সমষ্টি কত?

সমাধান:
দেওয়া আছে,
|3x - 15| = 18

(3x - 15) কে ধনাত্মক বিবেচনা করে পাই,
3x - 15 = 18
বা, 3x = 15 + 18
বা, 3x = 33
∴ x = 11

(3x - 15) কে ঋণাত্মক বিবেচনা করে পাই,
-(3x - 15) = 18
বা, - 3x + 15 = 18
বা, - 3x = 18 - 15
বা, - 3x = 3
∴ x = - 1

x এর সম্ভাব্য সকল মানের সমষ্টি = 11 + (- 1) = 11 - 1 = 10

১০,৫৬৮.

Jishan and Akash can complete a work in 15 days and 10 days respectively. They started doing the work together but after 2 days Akash had to leave and Jishan alone completed the remaining work. The whole work was completed in :

ক
ক) 10 days
খ
খ) 12 days
গ
গ) 14 days
ঘ
ঘ) 16 days

ব্যাখ্যা

(Jishan + Akash)'s 1 day's work =1/15 + 1/10
= (2 + 3)/30
= 5/30
= 1/6
(Jishan + Akash)'s 2 day's work = (1/6) ×2 = 1/3

Remaining work = 1 - 1/3 =(3 - 1)/3 = 2/3

1/15 work is done by Jishan in 1 day
2/3 work will be done by a in = 15 × (2/3) = 10 days

The total time taken = (10 + 2) = 12 days.

১০,৫৬৯.

A project has 3 test cases. Three teams are formed to study the 3 different test cases. Mr. X is assigned to all three teams. Except for Mr. X, each member is assigned to exactly one team. If each team has exactly 6 members, then what is the exact number of members required?

ক
ক) 16
খ
খ) 12
গ
গ) 14
ঘ
ঘ) 15

ব্যাখ্যা

Question: A project has 3 test cases. Three teams are formed to study the 3 different test cases. Mr. X is assigned to all three teams. Except for Mr. X, each member is assigned to exactly one team. If each team has exactly 6 members, then what is the exact number of members required?

Solution:
একটি প্রজেক্টে ৩ টি কেস আছে।
৩ টি কেস অধ্যয়ন করার জন্য ৩ টি টিম গঠন করা হয়েছে।

Mr.X প্রতিটি টিমেই আছে। বাকি প্রতি সদস্যের টিম আলাদা।
প্রতি টিমে ৬ জন সদস্য আছে।
অর্থাৎ, প্রতি টিমে Mr.X ছাড়া সদস্য আছে = ৬ - ১ জন
= ৫ জন

∴ মোট সদস্যের প্রয়োজন = (৫ × ৩) + ১ জন
= ১৫ + ১ জন
= ১৬ জন

১০,৫৭০.

Which of the following is true for x if 3(x - 4) > 2x + 5?

ক
x > 17
খ
x < 17
গ
x = 17
ঘ
None of the above

ব্যাখ্যা

Question: Which of the following is true for x if 3(x - 4) > 2x + 5?

Solution:
3(x - 4) > 2x + 5
⇒ 3x - 12 > 2x + 5
⇒ 3x - 2x > 5 + 12
⇒ x > 17

১০,৫৭১.

What is the measure of the angle formed by the hands of the clock at 2'o clock?

ক
30º
খ
60º
গ
45º
ঘ
90º

ব্যাখ্যা

Question: What is the measure of the angle formed by the hands of the clock at 2'o clock?

Solution:
Angle = |(11M - 60H)°/2|
= |(11 × 0 - 60 × 2)°/2|
= |(- 120)°/2|
= | - 60°|
= 60°

১০,৫৭২.

The slope of the line 4x + 8y = 16 is not the same as the slope of which one of the following lines?

ক
x + 2y = 8
খ
2x + 4y = 12
গ
y = 2x + 5
ঘ
y = (- x/2) + 3
ঙ
None of these

ব্যাখ্যা

Question: The slope of the line 4x + 8y = 16 is not the same as the slope of which one of the following lines?

Solution:
প্রথমে, প্রদত্ত রেখাটির ঢাল নির্ণয় করতে হবে। রেখাটির সমীকরণকে y = mx + c আকারে রূপান্তর করতে হবে। এখানে 'm' হলো ঢাল (Slope)।

প্রদত্ত রেখার সমীকরণ: 4x + 8y = 16
⇒ 8y = -4x + 16
⇒ y = (-4/8)x + (16/8)
⇒ y = (-1/2)x + 2
∴ এই রেখাটির ঢাল (m) হলো -1/2

এবার, প্রদত্ত অপশনগুলোর প্রত্যেকটির ঢাল নির্ণয় করি:

(ক) x + 2y = 8
⇒ 2y = -x + 8
⇒ y = (-1/2)x + 4
∴ ঢাল, m = -1/2

(খ) 2x + 4y = 12
⇒ 4y = -2x + 12
⇒ y = (-2/4)x + (12/4)
⇒ y = (-1/2)x + 3
∴ ঢাল, m = -1/2

(গ) y = 2x + 5
∴ ঢাল, m = 2

(ঘ) y = - x/2 + 3
⇒ y = (-1/2)x + 3
∴ ঢাল, m = -1/2

সুতরাং, দেখা যাচ্ছে যে শুধুমাত্র অপশন (গ) এর রেখার ঢাল মূল রেখার ঢাল থেকে ভিন্ন।

১০,৫৭৩.

A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

ক
12 km/h
খ
24 km/h
গ
21 km/h
ঘ
19 km/h

ব্যাখ্যা

Question: A boat travels 18 km downstream in 45 minutes. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

Solution:
স্রোতের অনুকূলে 45 মিনিটে যায় 18 কিমি
স্রোতের অনুকূলে 1 মিনিটে যায় 18/45 কিমি
স্রোতের অনুকূলে 1 ঘণ্টা বা 60 মিনিটে যায় (18 × 60)/45 কিমি
= 24 কিমি

∴ স্রোতের অনুকূলে বেগ = 24 কিমি/ঘণ্টা

দেওয়া আছে,
স্রোতের বেগ = 5 কিমি/ঘণ্টা।

∴ স্থির পানিতে নৌকার বেগ = স্রোতের অনুকূলে বেগ - স্রোতের বেগ
= 24 - 5 = 19 কিমি/ঘণ্টা।

১০,৫৭৪.

In a 300 m race, A beats B by 30 m and C by 40 m. In a race of 540 m, B will beat C by -

ক
ক) 12 m
খ
খ) 16 m
গ
গ) 20 m
ঘ
ঘ) None of these

ব্যাখ্যা

Question: In a 300 m race, A beats B by 30 m and C by 40 m. In a race of 540 m, B will beat C by -

Solution:
Given that,
A : B = 300 : 270
and A : C = 300 : 260

A/B = 300/270
and A/C = 300/260

∴ B/C = (B/A) × (A/C)
⇒(270/300) × (300/260) = 270/260
⇒ (270 × 2)/(260 × 2) = 540/520
⇒ B/C = 540/520

∴ B : C = 540 : 520

∴ In a 360 m race, B beats C by (540 - 520) m = 20 m

১০,৫৭৫.

What is the total number of integers between 100 and 200 that are divisible by 3?

ক
ক) 33
খ
খ) 32
গ
গ) 31
ঘ
ঘ) 30
ঙ
ঙ) 34

ব্যাখ্যা

First, identify the number that is multiple of 3 more than 100.
That type of number is 102.
So, 102//3 = 34.
Second, we have to identify the number that is multiple of 3 but nearest less than 198.
Now, 198/3 = 66.
Answer is (66 - 34) + 1 = 33

১০,৫৭৬.

Find the average of first 40 natural integer numbers.

ক
19.5
খ
20.5
গ
21.5
ঘ
22.5

ব্যাখ্যা

প্রশ্ন: Find the average of first 40 natural integer numbers.

সমাধান:

আমরা জানি,

n সংখ্যক স্বাভাবিক সংখ্যার সমষ্টি = n(n + 1)/2
∴ প্রথম 40 টি স্বাভাবিক সংখ্যার যোগফল = 40 × (40 + 1)/2
= (40 × 41)/2
= 820

∴ গড় = 820/40
= 20.5

১০,৫৭৭.

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

ক
48
খ
56
গ
64
ঘ
None of these

ব্যাখ্যা

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

Solution:

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

Hence,
Number of triangles formed
= ⁸C₃
= 8 × 7 × 6/3 × 2 × 1
= 336/6
= 56

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

১০,৫৭৮.

The investment ratio of two partners, P and Q, is 7 : 9, while their profit ratio is 14 : 27. Given that P invested his funds for 6 months, determine the duration of Q's investment.

ক
7 months
খ
8 months
গ
9 months
ঘ
11 months

ব্যাখ্যা

Question: The investment ratio of two partners, P and Q, is 7 : 9, while their profit ratio is 14 : 27. Given that P invested his funds for 6 months, determine the duration of Q's investment.

Solution:
Let P invested Tk 7x for 6 months
Q invested Tk 9x for y months

Now,
(7x × 6) : (9x × y) = 14 : 27
⇒ (7x × 6)/(9x × y) = 14/27
⇒ 42x/9xy = 14/27
⇒ 42 × 27 = 14 × 9y
⇒ 1134 = 126y
⇒ y = 1134/126
∴ y = 9

So, Q invested for 9 months.

১০,৫৭৯.

(81)^0.25 × (3)^0.5 = ?

ক
√27
খ
√18
গ
√3
ঘ
9

ব্যাখ্যা

Question: (81)^0.25 × (3)^0.5 = ?

Solution:
(81)^0.25 × (3)^0.5
= {(3)⁴}^0.25 × (3)^0.5
= 3^{(4 × 0.25)} × (3)^0.5
= (3)¹ × (3)^0.5
= (3)^{1 + 0.5}
= (3)^1.5
= (3)^15/10
= (3)^3/2
= √3³
= √27

১০,৫৮০.

In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer. (I) 39x² - 31x – 28 = 0 (l) y²- 25y + 114 = 0

ক
ক) x < y
খ
খ) x > y
গ
গ) x ≤ y
ঘ
ঘ) x ≥ y

ব্যাখ্যা

প্রথম সমীকরণ
39x² - 31x - 28 = 0
⇒39x² - 52x + 21x - 28 = 0
⇒13x (3x - 4) + 7 (3x - 4)= 0
⇒(3x - 4) (13x + 7) = 0
হয় অথবা
3x - 4 = 0 13x + 7 = 0
x= 4/3, x = -7/13

দ্বিতীয় সমীকরণ
y²-25y + 114 =0
⇒y² - 19y - 6y + 114 = 0
⇒y(y - 19) - 6 (y - 19) = 0
⇒ (y - 19) (y- 6) = 0

হয় অথবা
y - 19 = 0 y- 6 = 0
y = 19 y= 6

অতএব,
দেখা যাচ্ছে যে
x < y

১০,৫৮১.

Akash can do a piece of work in 30 days. He works at it for 6 days and then Rakib finishes it in 18 days. In what time can Akash and Rakib together finish the work?

ক
ক) 90/7 days
খ
খ) 8 days
গ
গ) 12 days
ঘ
ঘ) 90/11 days

ব্যাখ্যা

Question: Akash can do a piece of work in 30 days. He works at it for 6 days and then Rakib finishes it in 18 days. In what time can Akash and Rakib together finish the work?

Solution:
আকাশ ৩০ দিনে করে সম্পূর্ণ অংশ
১ দিনে করে ১/৩০ অংশ
৬ দিনে করে ৬/৩০ অংশ
= ১/৫ অংশ

বাকি থাকে ১ - ১/৫ অংশ
= ৪/৫ অংশ

রাকিব ১৮ দিনে করে ৪/৫ অংশ
১ দিনে করে ২/৪৫ অংশ

রাকিব ও আকাশ ১ দিনে করে (১/৩০) + (২/৪৫) অংশ
= (৩ + ৪)/৯০
= ৭/৯০

সম্পুর্ণ কাজ করতে সময় লাগে = ৯০/৭ দিন

১০,৫৮২.

∠B is the right angle of a right angles triangle ABC. If tanA = 1, then 2sinACosA = ?

ক
ক) 2
খ
খ) 1/2
গ
গ) 1
ঘ
ঘ) 4

ব্যাখ্যা

Question: ∠B is the right angle of a right angles triangle ABC. If tanA = 1, then 2sinACosA = ?

Solution:

দেওয়া আছে,
tanA = 1
ধরি,
বিপরীত বাহু = সন্নিহিত বাহু = a
অতিভুজ = √(a² + a²) = √2 a

∴ sinA = a/√2 a = 1/√2
cosA = a/√2 a = 1/√2

∴ 2sinACosA = 2 × (1/√2) × (1/√2)
= 2 × 1/2
= 1

১০,৫৮৩.

The average of 7 consecutive numbers is 20. The largest of these number is:

ক
ক) 21
খ
খ) 22
গ
গ) 23
ঘ
ঘ) 24
ঙ
ঙ) 25

ব্যাখ্যা

Let the number be,
x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,
Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.
or 7x + 21 = 140
or 7x = 119
or x =17.
Latest number = x + 6 = 23.

১০,৫৮৪.

At 3:15 on a clock, what is the angle between the hour and the minute hands?

ক
6 degrees
খ
7.5 degrees
গ
30 degrees
ঘ
22 degrees

ব্যাখ্যা

Question: At 3:15 on a clock, what is the angle between the hour and the minute hands?

Solution:
Given:
The hour hand time = 3
The minute hand time = 15

We know,
The angle between the hour hand and minute hand is given by:
= {(60 × hour) − (11 × minute)} / 2
= {(60 ×3) − (11 × 15)} / 2
= 180 - 165 / 2
= 15/2
= 7.5

Therefore, the angle between the hour hand and minute hand is 7.5 degrees.

১০,৫৮৫.

The value of 8^-2/3 lies between -

ক
0 to 1
খ
0.5 to 1
গ
1 to 2
ঘ
2 to 3

ব্যাখ্যা

Question: The value of 8^-2/3 lies between -

Solution:
8^-2/3
= (23)^-2/3
= 1/2²
= 1/4
= 0.25

১০,৫৮৬.

A sum of money invested at compound interest triples itself in 3 years. In how many years will it become 27 times itself?

ক
6 years
খ
8 years
গ
9 years
ঘ
12 years

ব্যাখ্যা

Question: A sum of money invested at compound interest triples itself in 3 years. In how many years will it become 27 times itself?

Solution:
Since the sum triples in 3 years, we can write:

Thus, it will take 9 years for the amount to become 27 times itself.

১০,৫৮৭.

A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?

ক
8 boys
খ
10 boys
গ
13 boys
ঘ
15 boys

ব্যাখ্যা

Question: A man, a woman and a boy can do a piece of work in 6, 9 and 18 days respectively. How many boys must assist one man and one woman to do the work in 1 day ?

Solution:
(1 man + 1 woman)'s 1 day's work
= 1/6 + 1/9
= 5/18
Remaining work=(1 − 5/18)
=13/18

Work done by 1 boy in 1 day = 1/18

∴Number of boys required= (13×18)/18 boys
=13 boys

১০,৫৮৮.

Find which of the following are twin Primes.

ক
(37, 41)
খ
(3 , 7)
গ
(43 , 47)
ঘ
(71, 73)

ব্যাখ্যা

Question: Find which of the following are twin Primes.

Solution:
- A twin prime is a prime number that is either 2 less or 2 more than another prime number.
- The difference between the twin prime number is always two.
- In twin prime number, both the number should be the prime number.
- Twin primes are pairs of successive primes that differ by two.

The primes from 1 to 100 are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

Options:
(37, 41) - Difference between them is 4.
(3, 7) - The difference between them is 4.
(43, 47) - Difference between them is 4.
(71, 73) - Difference between them is 2.

Here, in the given option (71 and 73) are prime numbers and their difference is '2'.

১০,৫৮৯.

A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?

ক
6 days
খ
7 days
ঘ
9 days

ব্যাখ্যা

Question: A, B, C can do a job in 10, 20 and 40 days respectively. In how many days A can complete the job if he is assisted by B and C on every third day?

Solution:

১০,৫৯০.

Half of the people on a bus get off at each stop after the first and no one gets on after the first stop. If only 4 person gets off at stop number 4, how many people got on at the first stop?

ক
16
খ
32
গ
44
ঘ
None of these

ব্যাখ্যা

Question: Half of the people on a bus get off at each stop after the first and no one gets on after the first stop. If only 4 person gets off at stop number 4, how many people got on at the first stop?

Solution:
stop 4 এ যাত্রী ছিলো 4 জন
stop 3 এ যাত্রী ছিলো 8 জন
stop 2 এ যাত্রী ছিলো 16 জন
stop 1 এ যাত্রী ছিলো 32 জন

প্রথম stopageএ কেউ নামেনি। তার পরের প্রতিটিতে অর্ধেক করে নেমে গিয়েছে।
প্রথম স্টেশনে যাত্রী ছিল 32 জন।

১০,৫৯১.

A car moves 550 meters in a minute, and a train travels 72 km in 45 minutes. How much faster is one than the other?

ক
45 km/h
খ
54 km/h
গ
63 km/h
ঘ
74 km/h

ব্যাখ্যা

Question: A car moves 550 meters in a minute, and a train travels 72 km in 45 minutes. How much faster is one than the other?

Solution:
Speed of the car = Distance/Time
= (550/1) meters/minute
= (550/1000)/(1/60) km/h
= (550 × 60)/1000 km/h
= 33 km/h

Speed of the train = Distance/Time
= (72/45) km/minute
= 72/(45/60) km/h
= (72 × 60)/45 km/h
= 96 km/h

∴ Difference in speed between the train and the bus = (96 - 33) km/h = 63 km/h

১০,৫৯২.

How many pairs of natural numbers are there such that the difference of whose squares is 63?

ক
ক) 1
খ
খ) 2
গ
গ) 3
ঘ
ঘ) 5

ব্যাখ্যা

x² - y² = (x + y)(x - y) = 1 × 3 × 3 × 7
= 7 × 6 or 21 × 3 or 9 × 7 or 63 × 1
Both x + y and x - y need to be odd, so we can reject 7 and 6
x + y, x - y as 21, 3 / 9, 7 / 63, 1 means
x, y as 12, 9 or 8, 1 or 32, 31
There are 3 pairs.

১০,৫৯৩.

Given that the milk and water ratio in a 45-liter mixture is 4 : 1, how much additional water is required to achieve a 3 : 2 ratio?

ক
9 litres
খ
10 litres
গ
12 litres
ঘ
15 litres

ব্যাখ্যা

Question: Given that the milk and water ratio in a 45-liter mixture is 4 : 1, how much additional water is required to achieve a 3 : 2 ratio?
(৪৫ লিটার মিশ্রণের মধ্যে দুধ ও পানির অনুপাত ৪:১, তাহলে ৩:২ অনুপাত করার জন্য কতটা পানি আরও যোগ করতে হবে?)

Solution:
৪৫ লিটার মিশ্রণে দুধের পরিমাণ ৪৫ × (৪/৫) লিটার = ৩৬ লিটার
অতএব, মিশ্রণে পানির পরিমাণ = ৪৫ - ৩৬ লিটার = ৯ লিটার

ধরা যাক,
মিশ্রণে x লিটার পানি যোগ করা হয়েছে।
তাহলে,
৩৬ / (৯ + x) = ৩ / ২
⇒ ৭২ = ২৭ + ৩x
⇒ ৩x = ৪৫

অতএব, x = ১৫

১০,৫৯৪.

In an exam, there are 4 multiple choice questions, and each question has 5 choices. Only one answer per question is correct. How many ways can a student fail to get all answers correct?

ক
124
খ
125
গ
625
ঘ
624
ঙ
None

ব্যাখ্যা

Question: In an exam, there are 4 multiple choice questions, and each question has 5 choices. Only one answer per question is correct. How many ways can a student fail to get all answers correct?

Solution:
Each question has 5 options, so the total number of ways to answer all 4 questions is = 5⁴
= 5 × 5 × 5 × 5
= 625

Number of ways, getting correct answers = 1⁴ = 1

∴ Number of ways of not getting all answer correct = 625 - 1 = 624

১০,৫৯৫.

If Ehsan was 22 years old x years ago and Shaon will be 24 years old in y years, what was the average of their ages 4 years ago?

ক
(x - y + 42)/2
খ
(x - y + 38)/2
গ
(x - y )/2
ঘ
(x + y )/2

ব্যাখ্যা

Question: If Ehsan was 22 years old x years ago and Shaon will be 24 years old in y years, what was the average of their ages 4 years ago?

Solution:
Ehsan was 22 years old x years ago
present age = x + 22 years
4 years ago, his age was = x + 22 - 4 = x + 18 years

Shaon will be 24 years old in y years
4 years ago, his age was = 24 - y - 4
= 20 - y years

average 4 years ago = (x + 18 + 20 - y)/2
= (x - y + 38)/2

১০,৫৯৬.

If (x + 3) is a factor of 3x² + ax + b, then find the value of 3a - b.

ক
ক) 21
খ
খ) 23
গ
গ) 25
ঘ
ঘ) 27

ব্যাখ্যা

Question: If (x + 3) is a factor of 3x² + ax + b, then find the value of 3a - b.

Solution:
According to the question,
⇒ (x + 3) = 0
⇒ x = - 3
Now, substitute the value of x = - 3 in the function 3x² + ax + b and then equate to 0.
⇒ 3(- 3)² - 3a + b = 0
⇒ 27 - 3a + b = 0
⇒ - 3a + b = - 27
⇒ - (3a - b) = - 27
⇒ 3a - b = 27

১০,৫৯৭.

Mr. Anwar deposits Tk. 7000 in a bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

ক
ক) 2317
খ
খ) 3197
গ
গ) 9317
ঘ
ঘ) 7317

ব্যাখ্যা

Question: Mr. Anwar deposits Tk. 7000 in a bank at 10% interest rate compounded annually. At the end of the three year, the total amount including interest will become?

Solution:
Given,
Principal, P = 7000 Tk.
Rate of interest, r = 10% = 10/100 = 1/10
Time, n = 3 years.

We know,
Compound Amount = P (1 + r)ⁿ
= 7000 × (1 + 1/10)³
= 7000 × (11/10)³
= 7000 × (11/10) × (11/10) × (11/10)
= 9317

১০,৫৯৮.

The sum of the ages of a mother and daughter is 56 years. Four years ago, the mother was five times as old as her daughter. Find the present age of the daughter is?

ক
12 years
খ
18 years
গ
8 years
ঘ
15 years

ব্যাখ্যা

Question: The sum of the ages of a mother and daughter is 56 years. Four years ago, the mother was five times as old as her daughter. Find the present age of the daughter is?

Solution:
Let daughter's present age = x years
Then mother's present age = (56 - x) years

Four years ago:
Daughter's age = x - 4
Mother's age = (56 - x) - 4 = 52 - x

ATQ,
⇒ 52 - x = 5(x - 4)
⇒ 52 - x = 5x - 20
⇒ 52 + 20 = 5x + x
⇒ 72 = 6x
∴ x = 12

So the daughter's present age is 12 years.

১০,৫৯৯.

In a school library, there are 60 books in total. Among them, 18 books are science fiction. If a student picks one book at random, what is the probability that it is not a science fiction book?

ক
3/10
খ
7/10
গ
3/13
ঘ
10/13

ব্যাখ্যা

Question: In a school library, there are 60 books in total. Among them, 18 books are science fiction. If a student picks one book at random, what is the probability that it is not a science fiction book?

Solution:
Probability of picking a book that is a science fiction book = 18/60
= 3/10

Probability of picking a book that is not a science fiction book = (1 - 3/10)
= (10 - 3)/10
= 7/10

১০,৬০০.

A 150-liter mixture contains 60% milk and the rest water. How many liters of water should be evaporated to make the mixture 75% milk?

ক
25 liters
খ
30 liters
গ
40 liters
ঘ
45 liters
ঙ
50 liters

ব্যাখ্যা

Question: A 150-liter mixture contains 60% milk and the rest water. How many liters of water should be evaporated to make the mixture 75% milk?

Solution:
There is 60% milk in 150 liters of mixture,
That means, (60/100) × 150 = 90 liters of milk.
∴ The amount of water = 150 - 90 = 60 liters.

Let,
x liters of water need to be evaporated.
Then the new volume of the solution will be (150 - x) liters.

ATQ,
90/(150 - x) = 75/100
⇒ 90/(150 - x) = 3/4
⇒ 3(150 - x) = 360
⇒ 450 - 3x = 360
⇒ 3x = 450 - 360
⇒ 3x = 90
⇒ x = 90/3
∴ x = 30

∴ 30 liters of water need to be evaporated so that the milk concentration becomes 75%.