Bank Math

PrepBank · পাতা ১১৮ / ১৬১ · ১১,৭০১–১১,৮০০ / ১৬,১২৪

১১,৭০১.

The length of a garden is thrice its breadth. A playground measuring 180 sq. m occupies (1/15)th of the total area of the garden. The length of the garden is-

ক
81 m
খ
90 m
গ
120 m
ঘ
112 m

সঠিক উত্তর: খ

90 m

উত্তর

সঠিক উত্তর: খ

90 m

খ

ব্যাখ্যা

Question: The length of a garden is thrice its breadth. A playground measuring 180 sq. m occupies (1/15)th of the total area of the garden. The length of the garden is

Solution:
Let L be the length and B is the breadth of the garden.
We have L = 3B.
Total area of the garden = 180 × 15 = 2700 sq m.
⇒ LB = 2700
⇒ 3B² = 2700
⇒ B² = 900
⇒ B = 30m

Hence the length of the garden = 30 × 3 = 90 m

১১,৭০২.

Suppose today is Saturday. What day of the week will it be 65 days from now on?

ক
ক) Saturday
খ
খ) Monday
গ
গ) Sunday
ঘ
ঘ) Friday

সঠিক উত্তর: গ

গ) Sunday

উত্তর

সঠিক উত্তর: গ

গ) Sunday

গ

ব্যাখ্যা

প্রশ্ন : Suppose today is Saturday. What day of the week will it be 65 days from now on?
সমাধান :
Each day of the week is repeated after 7 days.
So, after 63 days [on the 64th Day] it will be Saturday.
∴ 65th day will be Sunday.

১১,৭০৩.

A and B together can complete a task in 12 days. A alone can do it in 20 days. How many days would it take B to do this job alone?

ক
21 days
খ
30 days
গ
27 days
ঘ
35 days
ঙ
40 days

সঠিক উত্তর: খ

30 days

উত্তর

সঠিক উত্তর: খ

30 days

খ

ব্যাখ্যা

Question: A and B together can complete a task in 12 days. A alone can do it in 20 days. How many days would it take B to do this job alone?

Solution:
A একা কাজটি করতে পারে = 20 দিনে
∴ A এর একদিনের কাজ = 1/20 অংশ

A ও B একসাথে কাজটি করতে পারে = 12 দিনে
∴ তাদের একদিনের সম্মিলিত কাজ = 1/12 অংশ

B এর একদিনের কাজ = (A ও B এর সম্মিলিত কাজ) − (A এর একা কাজ)
= (1/12) - (1/20)
= (5 - 3)/60
= 2/60
= 1/30 অংশ

অতএব, B এক দিনে কাজ করে 1/30 অংশ।
∴ B পুরো কাজটি শেষ করবে = 1 ÷ (1/30) = 30 দিনে।

১১,৭০৪.

sin²θ + sinθ = xcosθ - cos²θ, then what is the value of 2tanθ?

ক
ক) (x² - 1)/2x
খ
খ) (x - 1)/x
গ
গ) (x² - 1)/x
ঘ
ঘ) (x² + 1)/x

সঠিক উত্তর: গ

গ) (x² - 1)/x

উত্তর

সঠিক উত্তর: গ

গ) (x² - 1)/x

গ

ব্যাখ্যা

Question: sin²θ + sinθ = xcosθ - cos²θ, then what is the value of 2tanθ?

Solution:
sin²θ + sinθ = xcosθ - cos²θ
⇒ sin²θ + cos²θ + sinθ = xcosθ
⇒ 1 + sinθ = xcosθ
⇒ (1 + sinθ)/cosθ = x
⇒ secθ + tanθ = x.....(1)

sec²θ - tan²θ = 1
⇒ (secθ + tanθ) (secθ - tanθ) = 1
⇒ x (secθ - tanθ) = 1
∴ (secθ - tanθ) = 1/x.......(2)

(1) - (2),
secθ + tanθ - secθ + tanθ = x - (1/x)
⇒ 2tanθ = (x² - 1)/x

১১,৭০৫.

A person rides a bicycle around a circular path of radius 50m. The radius of the bicycle wheel of the bicycle is 50 cm. The cycle comes to the starting point for the first time in 1 hour. What is the number of revolutions of the wheel in 15 minutes?

ক
ক) 20
খ
খ) 25
গ
গ) 30
ঘ
ঘ) 35

সঠিক উত্তর: খ

খ) 25

উত্তর

সঠিক উত্তর: খ

খ) 25

খ

ব্যাখ্যা

দেওয়া আছে,
বৃত্তকার মাঠের ব্যাসার্ধ r₁ = 50 m
বৃত্তকার মাঠের পরিধি, 2πr₁ = 2 × π × 50
= 100π m.
সাইকেলের চাকার ব্যাসার্ধ, r₂ = 50 cm = 0.5 m.
∴ সাইকেলের চাকার পরিধি, 2πr₂ = 2 × π × 0.5
= π m.
এখন চাকাটি π মিটার গেলে ঘুরবে = 1 বার।
∴ চাকাটি 100π গেলে ঘুরবে = 1 × 100×π
= 100 বার।
এখন, 60 মিনিটে চাকাটি ঘুরবে = 100 বার।
∴ 15 মিনিটে চাকাটি ঘুরবে = (100 × 15)/60
= 25 বার।

১১,৭০৬.

A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

ক
ক) Tk. 1000
খ
খ) Tk. 1200
গ
গ) Tk. 1500
ঘ
ঘ) Tk. 2000

সঠিক উত্তর: খ

খ) Tk. 1200

উত্তর

সঠিক উত্তর: খ

খ) Tk. 1200

খ

ব্যাখ্যা

Question: A shopkeeper has sufficient money to buy 50 books. On reduction in the price of each book by Tk. 4, he could buy 10 books more. How much money does he has?

Solution:
১টি বইয়ে দাম কমে ৪ টাকা
∴ ৫০টি বইয়ে দাম কমে (৫০ × ৪) টাকা
= ২০০ টাকা

সে মোট বই কিনে (৫০ + ১০) টি
= ৬০টি

১০টি বইয়ের দাম ২০০ টাকা
∴ ৬০টি বইয়ের দাম (২০০ × ৬০)/১০ টাকা
= ১২০০ টাকা

∴ তার কাছে ১২০০ টাকা আছে।

১১,৭০৭.

P can do a piece of work in 10 days and Q can do the same piece of work in 15days. P and Q together complete the same piece of work and get Tk. 1000 as the combined wages. Q's share of the wages will be-

ক
Tk. 600
খ
Tk. 300
গ
Tk. 500
ঘ
Tk. 400
ঙ
None of these

সঠিক উত্তর: ঘ

Tk. 400

উত্তর

সঠিক উত্তর: ঘ

Tk. 400

ঘ

ব্যাখ্যা

Question: P can do a piece of work in 10 days and Q can do the same piece of work in 15days. P and Q together complete the same piece of work and get Tk. 1000 as the combined wages. Q's share of the wages will be-

Solution:
P এর 1 দিনের কাজ = 1/10
Q এর 1 দিনের কাজ = 1/15

∴ (P + Q) একত্রে 1 দিনের কাজ = (1/10) + (1/15) = (3 + 2)/30 = 5/30 = 1/6

∴ (P + Q) এর 1 দিনের কাজ অনুপাত = (1/10) : (1/15) = 3 : 2

∴ Q এর শেয়ার = {(2/5) × 1000} = 400 টাকা

১১,৭০৮.

If the price of an article is increased by 20% and then decreased by 20%, the net change in the price is -

ক
5% decrease
খ
8% decrease
গ
4% decrease
ঘ
6% decrease

সঠিক উত্তর: গ

4% decrease

উত্তর

সঠিক উত্তর: গ

4% decrease

গ

ব্যাখ্যা

Question: If the price of an article is increased by 20% and then decreased by 20%, the net change in the price is -

Solution:
Let,
The price of an article is 100 Tk.

If the price increased by 20%,
So, the new price will be after increase = 100 + {100 × (20/100)} Tk.
= 100 + 20 Tk.
= 120 Tk.

Then the new price decreased by 20%,
So, the new price will be after decrease = 120 - {120 × (20/100)} Tk.
= 120 - 24 Tk.
= 96 Tk.

∴ The net change in the price of the article is = (100 - 96)
= 4 Taka

So, there is a 4% decrease in the price

১১,৭০৯.

The floor of a room is of size 5 m × 4m and its height is 3m. The walls and ceiling of the room require painting. What is the area to be painted?

ক
ক) 65 m²
খ
খ) 74 m²
গ
গ) 63 m²
ঘ
ঘ) 69 m²

সঠিক উত্তর: খ

খ) 74 m²

উত্তর

সঠিক উত্তর: খ

খ) 74 m²

খ

ব্যাখ্যা

Area of Wall = ( 5 + 4 + 5 + 4 ) m. wall length × 3 m height
= 18 × 3 sq.m.
= 54 sq.m.

Area of Ceiling = 5 m × 4m
= 20 sq.m.

hence total painting area of walls and ceiling = 54 sq m + 20 sq m = 74 sq m
74 square meter area of walls and ceiling to be painted.

১১,৭১০.

A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

ক
ক) 25 hours
খ
খ) 30 hours
গ
গ) 35 hours
ঘ
ঘ) 20 hours

সঠিক উত্তর: গ

গ) 35 hours

উত্তর

সঠিক উত্তর: গ

গ) 35 hours

গ

ব্যাখ্যা

প্রশ্ন: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?

সমাধান:
Suppose,
pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.

Now,
1/x + 2/x + 4/x = 1/5
⇒ 7/x = 1/5
∴ x = 35

∴ pipe A alone takes 35 hours to fill the tank.

১১,৭১১.

X can complete a piece of work in 18 days, Y in 20 days and Z in 30 days, Y and Z together start the work and forced to leave after 2 days. The time taken by X alone to complete the remaining work is:

ক
8 days
খ
12 days
গ
15 days
ঘ
10 days

সঠিক উত্তর: গ

15 days

উত্তর

সঠিক উত্তর: গ

15 days

গ

ব্যাখ্যা

Question: X can complete a piece of work in 18 days, Y in 20 days and Z in 30 days, Y and Z together start the work and forced to leave after 2 days. The time taken by X alone to complete the remaining work is:

Solution:
(Y + Z) 2 day's work:
= 2 × (1/20) + (1/30)
= 2 × (3 + 2)/60
= 1/6 part

Remaining work = 1 - (1/6)
= 5/6 part

X's one day's work = 1/18 part

Time taken to complete the work = (5/6)/(1/18) days

∴ Time taken to complete the work = (5/6) × 18
= 15 days

১১,৭১২.

In an examination, 68 percent of candidates passed in mathematics and 62 percent of the candidates passed in statistics. While 40 percent passed in both the subjects. If 30 candidates failed in both these subjects, then the total number of candidates were-

ক
600
খ
450
গ
300
ঘ
375

সঠিক উত্তর: গ

300

উত্তর

সঠিক উত্তর: গ

300

গ

ব্যাখ্যা

Question: In an examination, 68 percent of candidates passed in mathematics and 62 percent of the candidates passed in statistics. While 40 percent passed in both the subjects. If 30 candidates failed in both these subjects, then the total number of candidates were-

Solution:
68% of candidates passed in mathematics alone
62% of candidates passed in statistics alone
40% of candidates passed in both subjects
30 candidates failed in both the subjects

Let percentage of candidates passed in mathematics = A,
Percentage of candidates passed in statistics = B
According to the question:
n(A ∪ B) = 68% + 62% - 40%
⇒ n(A ∪ B) = 90%

⇒ Percentage of failed students(neither A nor B) = (100 - 90)% = 10%
Also, 10% = 30
∴ Total number of students = 100% = 300

১১,৭১৩.

A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.

ক
2 km/h
খ
1 km/h
গ
3 km/h
ঘ
5 km/h
ঙ
None of these

সঠিক উত্তর: গ

3 km/h

উত্তর

সঠিক উত্তর: গ

3 km/h

গ

ব্যাখ্যা

Question: A boatman can row 2 km against the stream in 20 minutes and return in 10 minutes. Find the rate of flow of the current.

Solution:
Let,
x be the speed of man in still water
and y be the speed of current.

Speed of d/s = (2/10) × 60 = 12 km/hr.
Speed of u/s = (2/20) × 60 = 6 km/hr.

∴ rate of current = (12 - 6)/2 = 3 km/hr.

১১,৭১৪.

Rakib and Tanveer start running towards each other at the same time with speeds in the ratio 3 : 4. If the initial distance between them is 4.2 km and they meet after 3 minutes, what is the difference between their speeds?

ক
16.5 km/h
খ
12 km/h
গ
18.25 km/h
ঘ
14 km/h

সঠিক উত্তর: খ

12 km/h

উত্তর

সঠিক উত্তর: খ

12 km/h

খ

ব্যাখ্যা

Question: Rakib and Tanveer started running simultaneously towards each other with speeds in the ratio 3 : 4 if the initial separation between the two is 4.2 km and they meet in 3 minutes, what is the difference between their speeds?

Solution:
Given that,
Rakib and Tanveer have speeds in the ratio 3 : 4.
The initial distance between them is 4.2 km, and they meet in 3 minutes, which is 3/60 = 1/20 hours

Let,
Rakib's speed be 3x km/h and Josh's speed be 4x km/h.
The relative speed when running towards each other is = 3x + 4x = 7x km/h.

Now we know,
Relative speed × time = distance
7x × (1/20) = 4.2
⇒ x = (4.2 × 20)/7
∴ x = 12

Thus, Rakib's speed is = 3 × 12 = 36 km/h.
And Tanveer's speed is = 4 × 12 = 48 km/h.

So the difference in speeds is = 48 - 36 = 12 km/h.

১১,৭১৫.

A man starts climbing a 20m high wall at 9 am. In each minute, he climbs up 5m but slips down 2m. At what time will he climb the wall?

ক
9 : 05 AM
খ
9 : 06 AM
গ
9 : 07 AM
ঘ
9 : 08 AM

সঠিক উত্তর: খ

9 : 06 AM

উত্তর

সঠিক উত্তর: খ

9 : 06 AM

খ

ব্যাখ্যা

Question: A man starts climbing a 20m high wall at 9 am. In each minute, he climbs up 5m but slips down 2m. At what time will he climb the wall?

Solution:
দেওয়া আছে, দেয়ালের মোট উচ্চতা = 20 মিটার।

প্রতি মিনিটে উপরে ওঠে = 5 মিটার।
প্রতি মিনিটে নিচে নেমে যায় = 2 মিটার।

∴ প্রতি মিনিটে
নিট বা প্রকৃত আরোহণ = 5 মিটার - 2 মিটার
= 3 মিটার।

এখানে, শেষ মিনিটে লোকটি উপরে উঠে যাবে এবং আর পিছলে নামবে না।
তাই, শেষ 5 মিটার বাদ দিয়ে হিসাব করতে হবে।

যে উচ্চতা পর্যন্ত তাকে পিছলে নামতে হবে = 20 - 5 = 15 মিটার।

3 মিটার উঠতে সময় লাগে = 1 মিনিট।
∴ 15 মিটার উঠতে সময় লাগে = 15/3 মিনিট
= 5 মিনিট।

সবশেষে 5 মিটার সে পরের মিনিটে উঠে যাবে এবং দেয়ালের শীর্ষে পৌঁছাবে।
সুতরাং, মোট সময় লাগবে = 5 মিনিট + 1 মিনিট = 6 মিনিট।

যেহেতু লোকটি সকাল 9টায় আরোহণ শুরু করেছিল, তাই সে সকাল 9টা 6 মিনিটে দেয়ালে পৌঁছাবে।

১১,৭১৬.

A train moving at speed of 72 km/hr crosses a pole in 10 seconds. Find the length of the train.

ক
180 meters
খ
190 meters
গ
200 meters
ঘ
220 meters

সঠিক উত্তর: গ

200 meters

উত্তর

সঠিক উত্তর: গ

200 meters

গ

ব্যাখ্যা

Question: A train moving at speed of 72 km/hr crosses a pole in 10 seconds. Find the length of the train.

Solution:
Length of the train is equal to the distance covered by train to cross the pole.
So, we will find the distance travelled by the train in 10 seconds by applying the following formula:
Distance = Speed × Time
Speed is given in Km/hr so we will convert it into m/s
Speed = 72 × (5/18) = 20 m/s
Time = 10 seconds
Distance = 20 × 10 = 200 meters

১১,৭১৭.

If 40% of a number is equal to two - third of another number, what is the ratio of first number to the second number?

ক
2 : 5
খ
5 : 4
গ
5 : 3
ঘ
7 : 3

সঠিক উত্তর: গ

5 : 3

উত্তর

সঠিক উত্তর: গ

5 : 3

গ

ব্যাখ্যা

Question: If 40% of a number is equal to two - third of another number, what is the ratio of first number to the second number?

Solution:
Suppose, 40% of A = 2B/3
⇒ 2A/5 = 2B/3
⇒ A/B = 5/3
⇒ A : B = 5 : 3

১১,৭১৮.

A person has deposited Tk. 13200 in a bank which pays 14% interest. He withdraws the money and invests in Tk. 100 stock at Tk. 110 which pays a dividend of 15%. How much does he gain or lose?

ক
ক) Loses Tk. 24
খ
খ) Gains Tk. 28
গ
গ) Loses Tk. 48
ঘ
ঘ) Gains Tk. 32

সঠিক উত্তর: গ

গ) Loses Tk. 48

উত্তর

সঠিক উত্তর: গ

গ) Loses Tk. 48

গ

ব্যাখ্যা

Income from bank = 14% of Tk. 13200 = Tk. 1848
Number of shares purchased
= Tk. (13200/110)
= Tk. 120
Income from stock
= (15% of Tk. 100) × 120
= Tk. (15 × 20)
= Tk. 1800
∴ Loss = Tk. (1848 - 1800)
= Tk. 48

১১,৭১৯.

A 120 meters long train is running at a speed of 108 km per hour. It will cross a railway platform 210 m long in-

ক
11 sec
খ
13 sec
গ
15 sec
ঘ
12 sec

সঠিক উত্তর: ক

11 sec

উত্তর

সঠিক উত্তর: ক

11 sec

ক

ব্যাখ্যা

Question: A 120 meters long train is running at a speed of 108 km per hour. It will cross a railway platform 210 m long in-

Solution:
Here,
Speed of the running train = 108 km/hr
= {108 × (5/18)} m/sec
= 30 m/sec

And length of the train is = 120 metres
Length of platform = 210 m

So, the time will taken by the train = (Length of train + Length of platform)/Speed
= (120 + 210)/30
= 330/30
= 11 sec

১১,৭২০.

If p is an even integer, which of the following must be an even integer?

ক
p² - p
খ
p + 2
গ
3p³
ঘ
All of the above

সঠিক উত্তর: ঘ

All of the above

উত্তর

সঠিক উত্তর: ঘ

All of the above

ঘ

ব্যাখ্যা

Question: If p is an even integer, which of the following must be an even integer?

Solution:
ধরি,
p = 2

ক) p² - p = 22 - 2 = 4 - 2 = 2 [যা জোড়]
খ) 3n³ = 3 × 2³ = 24 [যা জোড়]
গ) p + 2 = 2 + 2 = 4 [যা জোড়]
∴ সঠিক উত্তর হচ্ছে ঘ) All of the above

১১,৭২১.

Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 8 hours. Another pipe alone can fill two tanks in -

ক
28 hours
খ
48 hours
গ
44 hours
ঘ
56 hours

সঠিক উত্তর: খ

48 hours

উত্তর

সঠিক উত্তর: খ

48 hours

খ

ব্যাখ্যা

Question: Two pipes together can fill a tank in 6 hours. One pipe alone can do it in 8 hours. Another pipe alone can fill two tanks in -

Solution:
Let, the second pipe fill the tank in X hours.

in one hour both pipes can fill = 1/8 + 1/X
= (X + 8)/8X

ATQ,
⇒ 8X/(X + 8) = 6
⇒ 8X = 6 × (X + 8) hours.
⇒ 2X = 48
⇒ X = 24

∴ to fill two tanks it will take = 48 hours

১১,৭২২.

By selling a laptop for Tk. 4,500, a shopkeeper gains 20%. If the profit is reduced to 10%, then the selling price will be?

ক
4125
খ
4250
গ
4200
ঘ
4050

সঠিক উত্তর: ক

4125

উত্তর

সঠিক উত্তর: ক

4125

ক

ব্যাখ্যা

Question: By selling a laptop for Tk. 4,500, a shopkeeper gains 20%. If the profit is reduced to 10%, then the selling price will be?

Solution:
Let the cost price be x

According to the question,
x + 20% of x = 4500
⇒ x + 20x/100= 4500
⇒ x + 0.20x = 4500
⇒ 1.20x = 4500
⇒ x = 4500/1.20
∴ x = 3750

So, cost price = Tk. 3750

Now, Selling price when profit is 10%,
SP = 3750 + 10% of 3750
= 3750 + 375
= 4125
∴ The new selling price will be Tk. 4,125.

১১,৭২৩.

A man can row 6 km/hr in still water. If the speed of the current is 2 km / hr. It takes 3 hrs more in upstream than in the downstream for the same distance. The distance is -

ক
ক) 30 km
খ
খ) 24 km
গ
গ) 20 km
ঘ
ঘ) 32 km

সঠিক উত্তর: খ

খ) 24 km

উত্তর

সঠিক উত্তর: খ

খ) 24 km

খ

ব্যাখ্যা

Speed of man in still water, x = 6 km/h
Speed of current, y = 2 km/h

Let Distance = M
Upstream time = Downstram time + 3
M/4 = M/8 + 3 [As, speed of the boat upstream = 6 + 2 = 8 km/h; and downstream = 6 - 2 = 4 km/h]
M/4 - M/8 = 3
M/8 = 3
∴ M = 24
∴ Distance = 24 km

১১,৭২৪.

What is the solution of the inequality ।5x - 3। < 4?

ক
- 7/5 < x < 7/5
খ
- 3/5 < x < 1/5
গ
- 7/5 < x < 1/5
ঘ
- 1/5 < x < 7/5

সঠিক উত্তর: ঘ

- 1/5 < x < 7/5

উত্তর

সঠিক উত্তর: ঘ

- 1/5 < x < 7/5

ঘ

ব্যাখ্যা

Question: What is the solution of the inequality ।5x - 3। < 4?

Solution:
।5x - 3। < 4
⇒ - 4 < 5x - 3 < 4
⇒ - 4 + 3 < 5x - 3 + 3 < 4 + 3
⇒ - 1 < 5x < 7
⇒ - 1/5 < 5x/5 < 7/5
⇒ - 1/5 < x < 7/5

১১,৭২৫.

An UberX car charges Tk. 40 as base fare, Tk. 3.6 for each 0.2 of a kilometre and Tk. 180/hour as the travelling time charge. What will be the fare for a 6 kilometre trip if the travelling time is 110 minutes.

ক
ক) 230
খ
খ) 340
গ
গ) 460
ঘ
ঘ) 478

সঠিক উত্তর: ঘ

ঘ) 478

উত্তর

সঠিক উত্তর: ঘ

ঘ) 478

ঘ

ব্যাখ্যা

Base fare = Tk. 40
Distance Charge = Tk. 3.6 per 0.2 km = Tk. 18 per km
Travelling Time Charge = Tk. 180/1 hour
= 180/60
= Tk. 3 per minute
Total Distance = 6 kms
Total Time = 110 mins
Total Charge = Tk. 40 + Tk. (6 × 18) + Tk. (110 × 3)
= Tk. 478.

১১,৭২৬.

A committee of 3 members is selected out of 4 men and 3 women. What is the probabiity that the comittee has at least 1 man?

ক
ক) 1/35
খ
খ) 1/7
গ
গ) 34/35
ঘ
ঘ) 3/8

সঠিক উত্তর: গ

গ) 34/35

উত্তর

সঠিক উত্তর: গ

গ) 34/35

গ

ব্যাখ্যা

Question: A committee of 3 members is selected out of 4 men and 3 women. What is the probabiity that the comittee has at least 1 man?

Solution:
৭ জন থেকে ৩ জন বাছাই করার উপায় = ⁷C₃
= 35

৩ জন মহিলা থেকে ৩ জনই বাছাই করার উপায় = ³C₃
= 1

কমিটির ৩ জনই মহিলা হওয়ার সম্ভাবনা = 1/35

∴ কমপক্ষে ১ জন পুরুষ নিয়ে ৩ জনের কমিটি করার সম্ভাবনা = 1 - (1/35)
= (35 - 1)/35
= 34/35

১১,৭২৭.

All possible three digit numbers are formed by 1, 3, 5. If one number is chosen randomly, the probability that it would be divisible by 5 is –

ক
ক) 1/9
খ
খ) 2/9
গ
গ) 1/3
ঘ
ঘ) 1/4

সঠিক উত্তর: গ

গ) 1/3

উত্তর

সঠিক উত্তর: গ

গ) 1/3

গ

ব্যাখ্যা

1, 3, 5 এই তিনটি অংক দ্বারা 3! = 6 উপায়ে সংখ্যা গঠন করা যায়
5 দ্বারা বিভাজ্য হতে হলে শেষের অংক 5 রেখে সংখ্যার প্রথম দুটি স্থান বাকি দুইটি অংক দিয়ে 2! = 2 উপায়ে গঠন করা যায়।
∴ সংখ্যাটি 5 দ্বারা বিভাজ্য হবার সম্ভাবনা = 2/6 = 1/3

১১,৭২৮.

Two outgoing pipes, where the first one is double the efficiency of the second one. Both pipes together can empty a tank in just 4 hours. What is the pouring capacity of the first pipe in one hour?

ক
1/8
খ
1/4
গ
1/10
ঘ
1/6

সঠিক উত্তর: ঘ

1/6

উত্তর

সঠিক উত্তর: ঘ

1/6

ঘ

ব্যাখ্যা

Question: Two outgoing pipes, where the first one is double the efficiency of the second one. Both pipes together can empty a tank in just 4 hours. What is the pouring capacity of the first pipe in one hour?

Solution:
Let the second pipe empty the tank in 2X hours.
so, the first pipe can do it in X hours.

total pouring in one hour
= 1/X + 1/2X
= 3/2X

ATQ,
2X/3 = 4
X = 6 hours.

so, the first pipe can pour 1/6 of the tank water in one hour.

১১,৭২৯.

If 10 person shake their hands with each other, then total number of handshakes are -

ক
ক) 100
খ
খ) 20
গ
গ) 50
ঘ
ঘ) 45

সঠিক উত্তর: ঘ

ঘ) 45

উত্তর

সঠিক উত্তর: ঘ

ঘ) 45

ঘ

ব্যাখ্যা

Question: If 10 persons shake their hands with each other, then total number of handshakes are -

Solution:
n সংখ্যক মানুষ নিজেদের মধ্যে n(n - 1)/2 ভাবে হ্যান্ডশেক করতে পারবে।

∴ ১০ জন মানুষ নিজেদের মধ্যে ১০(১০ - ১)/২ বা, ৪৫ ভাবে হ্যান্ডশেক করতে পারবে।

১১,৭৩০.

A rectangular floor is covered by a rug except for a strip p meters along each of the four edges. If the floor is m meters by n meters, What is the area of the rug in square meters?

ক
mn – 2p(m+n)
খ
mn – p²
গ
mn - p(m+n)
ঘ
(m - 2p)(n - 2p)
ঙ
(m - p)(n - p)

সঠিক উত্তর: ঘ

(m - 2p)(n - 2p)

উত্তর

সঠিক উত্তর: ঘ

(m - 2p)(n - 2p)

ঘ

ব্যাখ্যা

Question: A rectangular floor is covered by a rug except for a strip p meters along each of the four edges. If the floor is m meters by n meters, What is the area of the rug in square meters?

Solution:

The area of the floor is mn
Length of rug = m - 2p (Distance of p on each side)
Width of rug = n - 2p (Distance of p on each side)

Thus area of rug = (m-2p)(n-2p)

১১,৭৩১.

If the height of a right square pyramid is increased by 12% by what percent must the side of the base be increased, so that the volume of the pyramid is increased by 28%?

ক
ক) 3%
খ
খ) 7%
গ
গ) 10%
ঘ
ঘ) 36%

সঠিক উত্তর: খ

খ) 7%

উত্তর

সঠিক উত্তর: খ

খ) 7%

খ

ব্যাখ্যা

আমরা জানি,
পিরামিডের ভূমি (base) বর্গাকৃতি
∴ (1/3×base₂×h₂) / (1/3×base₁×h₁) = 128/100
⇒ base₂×1.12h₁/base1×h1 = 128/100 [As, the height is increased by 12%, so h₂ = 1.12h₁]
⇒ base₂/base₁ = 128/(100×1.12)
⇒ x₂²/x₁² = 128/112 [ x₁, x₂ হলো বর্গাকৃতি ভূমি (base) ]
⇒ x₂/x₁ = √(128/112) = 1.07

∴ % = 100×1.07 = 107

সুতরাং, ভূমি (base) বৃদ্ধি করতে হবে = ( 107 - 100 )% = 7%

১১,৭৩২.

What is the value of [log₅(5log₅3125)]² ?

ক
4
খ
2
গ
6
ঘ
16

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: What is the value of [log₅(5log₅3125)]² ?

Solution:
Given that,
= [log₅(5log₅3125)]²
= [log₅(5log₅5⁵)]²
= [log₅(5 × 5log₅5)]²
= [log₅25]² ; [ log₅5 = 1 ]
= [log₅5²]²
= [2log₅5]²
= 2²
= 4

১১,৭৩৩.

The difference between the circumference and the radius of a circle is 185 cm. Find the diameter of the circle.

ক
ক) 30 cm
খ
খ) 35 cm
গ
গ) 60 cm
ঘ
ঘ) 70 cm

সঠিক উত্তর: ঘ

ঘ) 70 cm

উত্তর

সঠিক উত্তর: ঘ

ঘ) 70 cm

ঘ

ব্যাখ্যা

Question: The difference between the circumference and the radius of a circle is 185 cm. Find the diameter of the circle.

Solution:
Let r be the radius of circle

Given that,
2πr - r = 185
⇒ r(2π - 1) = 185
⇒ r{(44/7) - 1} = 185
⇒ r (44 - 7)/7 }= 185
⇒ r(37/7) = 185
⇒ r = 185 (7/37)
∴ r = 35

The radius of the circle is 35 cm.
∴ Diameter = 2 × 35
= 70 cm

১১,৭৩৪.

A customer deposits Tk 2000 at the beginning of a year. How much total interest would he have gained after end of the year if the bank offers 10% compound interest calculated on a half-yearly basis?

ক
ক) 200 Tk
খ
খ) 205 Tk
গ
গ) 210 Tk
ঘ
ঘ) 220 Tk

সঠিক উত্তর: খ

খ) 205 Tk

উত্তর

সঠিক উত্তর: খ

খ) 205 Tk

খ

ব্যাখ্যা

Question: A customer deposits Tk 2000 at the beginning of a year. How much total interest would he have gained after end of the year if the bank offers 10% compound interest calculated on a half-yearly basis?

Solution:
Given,
Principal = 2000 Tk
Rate of Interest = 10% = 10/100 = 1/10

So, after 1 year he would have gained,
= 2000 × {1 + 1/(2 × 10)}²
= 2000 × (21/20)²
= 2000 × {( 21 × 21) / (20 × 20)}
= 2205

So, compound interest = 2205 - 2000 = 205 Tk

১১,৭৩৫.

4 men can repair a road in 7 hours. How many men are required to repair the road in 2 hours?

ক
ক) 17 men
খ
খ) 14 men
গ
গ) 13 men
ঘ
ঘ) 16 men
ঙ
ঙ) None of these

সঠিক উত্তর: খ

খ) 14 men

উত্তর

সঠিক উত্তর: খ

খ) 14 men

খ

ব্যাখ্যা

4 men can repair a road in 7 hours
1 men can repair a road in 7 × 4hours = 28 hours
28 hours is required by 1 men
2 hours is required by 28/2 men = 14 men

১১,৭৩৬.

If α, β are the roots of the equation x² - 4x - 5 = 0 then α² + β² equals to:

ক
26
খ
14
গ
16
ঘ
24

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: If α, β are the roots of the equation x² - 4x - 5 = 0 then α² + β² equals to:

Solution:
x² - 4x - 5 = 0
⇒ x² - 5x + x - 5 = 0
⇒ x(x - 5) + 1(x - 5) = 0
⇒ (x - 5)(x + 1) = 0
∴ x = 5, -1

Hence, α = 5 , β = -1 Hence, The value of α² + β² = 5² + (-1)² = 25 + 1 = 26

১১,৭৩৭.

The sum of two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is-

ক
280
খ
240
গ
270
ঘ
290

সঠিক উত্তর: খ

240

উত্তর

সঠিক উত্তর: খ

240

খ

ব্যাখ্যা

Question: The sum of two numbers is 520. If the bigger number is decreased by 4% and the smaller number is increased by 12%, then the numbers obtained are equal. The smaller number is-

Solution:
Let,
Larger number = x and smaller number = 520 – x

According to the question
⇒ 96x/100 = {(520 - x)/100} × 112
⇒ 96x = (520 - x) × 112
⇒ 96x = 520 × 112 - 112x
⇒ 112x + 96x = 520 × 112
⇒ 208x = 520 × 112
⇒ x= (520×112)/208
⇒ x = 280

∴ Smaller number = 520 - 280 = 240

১১,৭৩৮.

If (sinθ + cosθ)/(sinθ - cosθ) = 7 then, secθ =?

ক
±1/3
খ
±2/3
গ
±5/3
ঘ
±5/2

সঠিক উত্তর: গ

±5/3

উত্তর

সঠিক উত্তর: গ

±5/3

গ

ব্যাখ্যা

প্রশ্ন: If (sinθ + cosθ)/(sinθ - cosθ) = 7 then, secθ =?

সমাধান:
দেয়া আছে,
(Sinθ + Cosθ)/(Sinθ - Cosθ) = 7
⇒ (Sinθ + Cosθ) + (Sinθ - Cosθ)/(Sinθ + Cosθ) - (Sinθ - Cosθ) = (7 + 1)/(7 - 1)
⇒ (Sinθ + Cosθ + Sinθ - Cosθ)/(Sinθ + Cosθ - Sinθ + Cosθ) = 8/6
⇒ 2Sinθ/2Cosθ = 4/3
⇒ Sinθ/Cosθ = 4/3
⇒ tanθ = 4/3
⇒ tan²θ = 16/9
⇒ Sec²θ - 1 = 16/9
⇒ Sec²θ = (16/9) + 1
⇒ Sec²θ = (16 + 9)/9
⇒ Sec²θ = 25/9
⇒ Sec²θ = (16 + 9)/9
⇒ Sec²θ = 25/9
Secθ = ±5/3

১১,৭৩৯.

Find the number of terms in geometric progression 3, 6, 12, 24, ........... , 384.

ক
ক) 10
খ
খ) 11
গ
গ) 9
ঘ
ঘ) 8

সঠিক উত্তর: ঘ

ঘ) 8

উত্তর

সঠিক উত্তর: ঘ

ঘ) 8

ঘ

ব্যাখ্যা

Question: Find the number of terms in geometric progression 3, 6, 12, 24, .......... , 384.

Solution:
Here, a = 3,
r = 6/3 = 2

We have to find the number of terms
n^th term = 384
n^thterm = ar^{(n -1)}

384 = 3 × 2^{(n -1)}⇒ 2^{(n – 1)} = 384/3
⇒ 2^{(n -1)} = 128
⇒ 2^{(n - 1)} = 2⁷
Therefore,
n - 1 = 7
⇒ n = 7 + 1
∴ n = 8

Hence, number of terms = 8

১১,৭৪০.

The three sides of a triangle are x + 1, 2x - 1, and 3x + 1, respectively and the perimeter is 25cm. The length of the smallest side is-

ক
5cm
খ
3cm
গ
4cm
ঘ
7cm
ঙ
9cm

সঠিক উত্তর: ক

5cm

উত্তর

সঠিক উত্তর: ক

5cm

ক

ব্যাখ্যা

A/Q, x+1 + 2x-1 + 3x+1 = 25
So, x = 4
Hence, 1st side = 4 + 1 = 5
2nd side = 2 × 4 - 1 = 7
3rd side = 3 × 4 + 1 = 13

১১,৭৪১.

A car reaches from City A to City B in 9 hours travelling at a speed of 40 km/hr. If its speed is increased by 20 km/hr, then the time of journey is reduced by-

ক
45 minutes
খ
2 hours
গ
1.5 hours
ঘ
3 hours

সঠিক উত্তর: ঘ

3 hours

উত্তর

সঠিক উত্তর: ঘ

3 hours

ঘ

ব্যাখ্যা

Question: A car reaches from City A to City B in 9 hours travelling at a speed of 40 km/hr. If its speed is increased by 20 km/hr, then the time of journey is reduced by-

Solution:
দুটি শহরের মধ্যে মোট দূরত্ব = গতিবেগ × সময়
= 40 কিমি/ঘন্টা × 9 ঘন্টা
= 360 কিমি

এখন, গতিবেগ 20 কিমি/ঘন্টা বৃদ্ধি করা হলে,
নতুন গতিবেগ = (40 + 20) কিমি/ঘন্টা
= 60 কিমি/ঘন্টা

এই নতুন গতিবেগে একই দূরত্ব অতিক্রম করতে,
নতুন সময় = মোট দূরত্ব/নতুন গতিবেগ
= 360 কিমি/60 কিমি/ঘন্টা
= 6 ঘন্টা

সুতরাং, সময় কমেছে = (আসল সময় - নতুন সময়)
= (9 - 6) ঘন্টা
= 3 ঘন্টা

অর্থাৎ, ভ্রমণের সময় 3 ঘন্টা কমেছে।

১১,৭৪২.

A tree casts a shadow 15√3 meters long when the sun's angle of elevation is 60°. Find the height of the tree.

ক
30 m
খ
45 m
গ
60 m
ঘ
40 m

সঠিক উত্তর: খ

45 m

উত্তর

সঠিক উত্তর: খ

45 m

খ

ব্যাখ্যা

Question: A tree casts a shadow 15√3 meters long when the sun's angle of elevation is 60°. Find the height of the tree.
(সূর্যের উন্নতি কোণ 60° হলে একটি গাছের ছায়ার দৈর্ঘ্য 15√3 মিটার হয়। গাছটির উচ্চতা কত?)

Solution:

ধরি,
উচ্চতা = h
tan60° = h/15√3
⇒ √3 = h/15√3
⇒ h = 3 × 15
∴ h = 45

১১,৭৪৩.

Which of the following is not a leap year?

ক
2008
খ
2012
গ
2020
ঘ
2022
ঙ
None of these

সঠিক উত্তর: ঘ

2022

উত্তর

সঠিক উত্তর: ঘ

2022

ঘ

ব্যাখ্যা

Question: Which of the following is not a leap year?

Solution:
A leap year is divisible by 4.

Here,
2008 ÷ 4 = 502, divisible by 4 , so leap year.
2012 ÷ 4 = 503, divisible by 4 , so leap year.
2020 ÷ 4 = 505, divisible by 4 , so leap year.
2022 ÷ 4 = 505, remainder 2, so not leap year.

১১,৭৪৪.

If (7x - 3y) : (x - 3y) = 5 : 11, find the value of x/y.

ক
1/2
খ
2/3
গ
3/4
ঘ
1/4

সঠিক উত্তর: ঘ

1/4

উত্তর

সঠিক উত্তর: ঘ

1/4

ঘ

ব্যাখ্যা

Question: If (7x - 3y) : (x - 3y) = 5 : 11, find the value of x/y.

Solution:
Given that,
(7x - 3y) : (x - 3y) = 5 : 11
⇒ (7x - 3y)/(x - 3y) = 5/11
⇒ 77x - 33y = 5x - 15y
⇒ 77x - 5x = 33y - 15y
⇒ 72x = 18y
⇒ x/y = 18/72
∴ x/y = 1/4

১১,৭৪৫.

Three partners A, B, and C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk 16500 at the end of a year, Find out A's share in it.

ক
6000
খ
9000
গ
11000
ঘ
12000
ঙ
None

সঠিক উত্তর: খ

9000

উত্তর

সঠিক উত্তর: খ

9000

খ

ব্যাখ্যা

Question: Three partners A, B, and C start a business. B's Capital is four times C's capital and twice A's capital is equal to thrice B's capital. If the total profit is Tk 16500 at the end of a year, Find out A's share in it.

Solution:
Let,
C's capital = x then
B's capital = 4x
A's capital = 6x

Now,
A : B : C = 6x : 4x : x
= 6 : 4 : 1

∴ A's share = 16500 × (6/11)
= 9000

১১,৭৪৬.

Any sold her bicycle for Taka. 5000 while making a profit of Taka. 70. Then what is the price at which she bought that cycle?

ক
4930 Taka
খ
4530 Taka
গ
4030 Taka
ঘ
493 Taka

সঠিক উত্তর: ক

4930 Taka

উত্তর

সঠিক উত্তর: ক

4930 Taka

ক

ব্যাখ্যা

Question: Any sold her bicycle for Taka. 5000 while making a profit of Taka. 70. Then what is the price at which she bought that cycle?

Solution:
Given,
Selling Price (SP) = Taka. 5000
Profit = 70 Taka

Thus,
Cost Price = Selling Price - Profit
⇒ Cost Price = 5000 - 70
⇒ Cost Price = 4930 Taka

Thus, cost price of the bicycle is Taka 4930

১১,৭৪৭.

Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9), and D(5, 4). What is the shape of the quadrilateral?

ক
Square
খ
Parallelogram but not a rhombus
গ
Rectangle but not a square
ঘ
Rhombus

সঠিক উত্তর: ঘ

Rhombus

উত্তর

সঠিক উত্তর: ঘ

Rhombus

ঘ

ব্যাখ্যা

Question: Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9), and D(5, 4). What is the shape of the quadrilateral?

Solution:

∴ The shape of the quadrilateral is Rhombus.

১১,৭৪৮.

What is the least number of people who can be arranged in certain places of 12, 15, 18 and 20 people and also in form of a solid square?

ক
180
খ
450
গ
900
ঘ
1800
ঙ
2700

সঠিক উত্তর: গ

900

উত্তর

সঠিক উত্তর: গ

900

গ

ব্যাখ্যা

In this type of question, We need to find out the L.C.M. of the given numbers.
L.C.M. of 12, 15, 18 and 20 = 180 = 3×3×2×2×5
L.C.M. must be a perfect square. To make the L.C.M. a perfect square, We have to multiply it by 5,
The required number of soldiers = 3×3×2×2×5×5 = 30² = 900

১১,৭৪৯.

One of the four angles of a rhombus is 90 degrees. If each side of the rhombus is 20 cm, what will be the length of the longer diagonal?

ক
20√2 cm
খ
25√2 cm
গ
30√2 cm
ঘ
35√2 cm
ঙ
None of these

সঠিক উত্তর: ক

20√2 cm

উত্তর

সঠিক উত্তর: ক

20√2 cm

ক

ব্যাখ্যা

Question: One of the four angles of a rhombus is 90 degrees. If each side of the rhombus is 20 cm, what will be the length of the longer diagonal?

Solution:
A rhombus with one of its angle 90 degrees is a square. So, both the diagonals are of equal length.

Now, Diagonal of a square= √2 × side
Given Side = 20 cm
So, Diagonal = 20√2 cm

১১,৭৫০.

The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?

ক
30
খ
20
গ
60
ঘ
80
ঙ
None of these

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: The average of 4 terms is 20 and the 1st term is 1/3 of the remaining terms. What will be the first number?

Solution:

Average of 4 terms = 20

Hence, the total sum of 4 terms = 80

Let terms be A, B, C, D

So, the sum will be A + B + C + D = 80

Given,
3A = B + C + D
3A + A = A + B + C + D
4A = A + B + C + D

So, 4A = 80,

A = 20

১১,৭৫১.

Determine the side length of the largest square tile that can completely cover a room measuring 5.44 meters in length and 3.74 meters in width.

ক
36 cm
খ
24 cm
গ
34 cm
ঘ
44 cm

সঠিক উত্তর: গ

34 cm

উত্তর

সঠিক উত্তর: গ

34 cm

গ

ব্যাখ্যা

Question: Determine the side length of the largest square tile that can completely cover a room measuring 5.44 meters in length and 3.74 meters in width.

Solution:
long = 5 meters 44 cm = 500 + 44 cm = 544 cm
broad = 3 meters 74 cm = 300 + 74 = 374 cm

∴ The side of the square slab is the H.C.F. of 544 and 374 cm i.e. 34.

১১,৭৫২.

Rakin's regular pay is 30 Taka per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid 1680 Taka, how many hours of overtime did Rakin work?

ক
ক) 5 hr
খ
খ) 6 hr
গ
গ) 8 hr
ঘ
ঘ) 10 hr

সঠিক উত্তর: গ

গ) 8 hr

উত্তর

সঠিক উত্তর: গ

গ) 8 hr

গ

ব্যাখ্যা

Question: Rakin's regular pay is 30 Taka per hour up to 40 hours. Overtime is twice the payment for regular time. If he was paid 1680 Taka, how many hours of overtime did Rakin work?

Solution:
40 ঘন্টার জন্য রাকিনের নিয়মিত বেতন = (30 × 40) = 1200 টাকা।
Overtime এর টাকার পরিমান = (1680 - 1200) টাকা = 480 টাকা
যেহেতু, Overtime এর প্রতিদিনের টাকার পরিমান নিয়মিত বেতন এর দ্বিগুন,
সেহেতু মোট overtime কাজ করার সময় = 480 ÷ (30×2) ঘন্টা = 8 ঘন্টা।

১১,৭৫৩.

On Tuesday Ray rode his bike 10 miles, On Wednesday he increased Tuesday's distance by 5 miles. On Thursday he decreased Wednesday's distance by 7 miles. On Friday he increased Thursday's by 12 miles. How many total miles did Ray ride over the 4 day period?

ক
ক) 50
খ
খ) 51
গ
গ) 52
ঘ
ঘ) 53

সঠিক উত্তর: ঘ

ঘ) 53

উত্তর

সঠিক উত্তর: ঘ

ঘ) 53

ঘ

ব্যাখ্যা

Question: On Tuesday Ray rode his bike 10 miles, On Wednesday he increased Tuesday's distance by 5 miles. On Thursday he decreased Wednesday's distance by 7 miles. On Friday he increased Thursday's by 12 miles. How many total miles did Ray ride over the 4-day period?

Solution:
On Tuesday, Ray goes = 10 miles
On Wednesday, Ray goes = 10 + 5 = 15 miles
On Thursday, Ray goes = 15 - 7 = 8 miles
On Friday, Ray goes = 8 + 12 = 20 miles

∴ Total distance = 10 + 15 + 8 + 20
= 53 miles

১১,৭৫৪.

If 'TEST' is coded as '64' then 'EXAM' is coded as -

ক
ক) 41
খ
খ) 43
গ
গ) 32
ঘ
ঘ) 37

সঠিক উত্তর: খ

খ) 43

উত্তর

সঠিক উত্তর: খ

খ) 43

খ

ব্যাখ্যা

চিত্র অনুসারে

TEST => T (20) + E (5) + S (19) + T (20) = 64

অনুরূপভাবে,

EXAM => E (5) + X (24) + A (1) + M (13) = 43

১১,৭৫৫.

P, Q and R can do work in 20 , 30 and 60 days respectively. How many days does it take to complete the work if P does the work and he is assisted by Q and R on every third day?

ক
15 days
খ
9 days
গ
10 days
ঘ
14 days
ঙ
18 days

সঠিক উত্তর: ক

15 days

উত্তর

সঠিক উত্তর: ক

15 days

ক

ব্যাখ্যা

Amount of work P can do in 1 day = 1/ 20
Amount of work Q can do in 1 day = 1/ 30
Amount of work R can do in 1 day = 1 /60
P is working alone and every third day Q and R is helping him.

Work completed in every three days = 3 × 1/20 + 1/30 + 1/60 = 1/5
So, work completed in 15 days = 5 × 1/5 = 1
That is, the work will be done in 15 days

১১,৭৫৬.

What is the solution of the inequality ।1 - 2x। < 3 ?

ক
ক) - 1 < x < 1
খ
খ) - 2 < x < 2
গ
গ) - 2 < x < 1
ঘ
ঘ) - 1 < x < 2

সঠিক উত্তর: ঘ

ঘ) - 1 < x < 2

উত্তর

সঠিক উত্তর: ঘ

ঘ) - 1 < x < 2

ঘ

ব্যাখ্যা

Question: What is the solution of the inequality ।1 - 2x। < 3 ?

Solution:
।1 - 2x। < 3
= - 3 < 1 - 2x < 3
= - 3 - 1 < 1 - 2x < 3 - 1
= - 4 < - 2x < 2
= - 4/2 < - 2x/2 < 2/2
= - 2 < - x < 1
= (- 2)(- 1) > ( - x) (- 1) > 1(- 1)
= 2 > x > - 1
= - 1 < x < 2

১১,৭৫৭.

A certain company retirement plan has a "rule of 70" provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?

ক
2023
খ
2004
গ
2005
ঘ
2006
ঙ
2024

সঠিক উত্তর: গ

2005

উত্তর

সঠিক উত্তর: গ

2005

গ

ব্যাখ্যা

Question: A certain company retirement plan has a "rule of 70" provision that allows an employee to retire when the employee's age plus years of employment with the company total at least 70. In what year could a female employee hired in 1986 on her 32nd birthday first be eligible to retire under this provision?

Solution:
She must gain at least 70 points, now she has 32 and every year gives her two more points: one for age and one for additional year of employment.

Let, X is the years worked

32 + x + x = 70
⇒ 2x = 38,
∴ x = 19

1986 + 19 = 2005

১১,৭৫৮.

How much time will taken by a train to cross a total distance of 500km if 1/4 of the distance is covered at 62.5kmph and the rest of the distance is at 37.5kmph.

ক
8 hour.
খ
10 hour.
গ
12 hour.
ঘ
15 hour.

সঠিক উত্তর: গ

12 hour.

উত্তর

সঠিক উত্তর: গ

12 hour.

গ

ব্যাখ্যা

Question: How much time will taken by a train to cross a total distance of 500km if 1/4 of the distance is covered at 62.5kmph and the rest of the distance is at 37.5kmph.

Solution:
1/4 of 500km = (500 × 1/4) = 125km
time = 125/62.5 = 2 hour.

remaining distance = 500 - 125 = 375km
time = 375/37.5 = 10 hour.

total time = 10 + 2 = 12 hour.

১১,৭৫৯.

The average height of girls in a class is 5 feet and that of boys is 5.7 feet. If the average height of the students in class is 5.5 feet. What could be the possible strength of boys and girls respectively in the class:

ক
ক) 50, 25
খ
খ) 30, 20
গ
গ) 20, 30
ঘ
ঘ) 60, 50
ঙ
ঙ) 50, 20

সঠিক উত্তর: ঙ

ঙ) 50, 20

উত্তর

সঠিক উত্তর: ঙ

ঙ) 50, 20

ঙ

ব্যাখ্যা

The number of boys = B
The number of Girls = G
According to question, 5G + 5.7B = 5.5(B + G)
Or, 0.2B = 0.5G
Or, B:G = 5:2
Now, sum of the ratio= 7.
Sum of one option is divisible by 7 that is = 50 + 20
= 70

১১,৭৬০.

One card is drawn at random from a pack of 52 cards. What is the probability that it is not a face card?

ক
12/13
খ
1/52
গ
3/52
ঘ
10/13

সঠিক উত্তর: ঘ

10/13

উত্তর

সঠিক উত্তর: ঘ

10/13

ঘ

ব্যাখ্যা

Question: One card is drawn at random from a pack of 52 cards. What is the probability that it is not a face card?

Solution:
Here,
Face card refers to Jack, Queen and King

Now,
Total cards = 52
Total face card = Number of Jack, Queen and King
= 4 + 4 + 4
= 12

∴ Probability of getting a face card = 12/52
= 3/13

∴ Probability of not getting a face card = 1 - 3/13
= (13 - 10)/13
= 10/13

১১,৭৬১.

Which of the following is the polynomial equation 2x⁴ - 5x³ + 9x² - 4 = 0?

ক
ক) Linear Equation
খ
খ) Quadratic Equation
গ
গ) Cubic Equation
ঘ
ঘ) Biquadratic Equation

সঠিক উত্তর: ঘ

ঘ) Biquadratic Equation

উত্তর

সঠিক উত্তর: ঘ

ঘ) Biquadratic Equation

ঘ

ব্যাখ্যা

Question: Which of the following is the polynomial equation 2x⁴ - 5x³ + 9x² - 4 = 0?

Solution:
The given polynomial equation is in terms of x.
The highest power of x is 4 and hence the degree of the equation is 4.
Hence, it is a biquadratic equation.

১১,৭৬২.

1050 tk are divided among P, Q and R. The share of Q is 2/5 of the combined share of P and R. Q gets-

ক
ক) 750 tk
খ
খ) 300 tk
গ
গ) 350 tk
ঘ
ঘ) 900 tk

সঠিক উত্তর: খ

খ) 300 tk

উত্তর

সঠিক উত্তর: খ

খ) 300 tk

খ

ব্যাখ্যা

Question: 1050 tk are divided among P, Q and R. The share of Q is 2/5 of the combined share of P and R. Q gets-

Solution:
let, combined share of P and R is x
share of Q is 2x/5

x + 2x/5 = 1050
⇒ (5x + 2x)/5 = 1050
⇒ 7x/5 = 1050
⇒ x = 1050 × 5/7
∴ x = 750 tk

Q gets - 750 × 2/5
= 300 tk

১১,৭৬৩.

A can complete a work in 12 days, and B can do the same work in 18 days. If they work together for 3 days, what fraction of the work is left?

ক
5/12 part
খ
4/11 part
গ
3/11 part
ঘ
7/12 part

সঠিক উত্তর: ঘ

7/12 part

উত্তর

সঠিক উত্তর: ঘ

7/12 part

ঘ

ব্যাখ্যা

Question: A can complete a work in 12 days, and B can do the same work in 18 days. If they work together for 3 days, what fraction of the work is left?

Solution:
Given,
A can do the work in 12 days
A’s 1 day work = 1/12 part

B can do the work in 18 days
B’s 1 day work = 1/18 part

A and B's 1 day work = (1/12 + 1/18) part
= (3 + 2)/36 part
= 5/36 part

∴ Work done in 3 days = {(5/36) × 3} part
= 5/12 part

∴ Remaining work = (1 - 5/12) part
= 7/12 part

১১,৭৬৪.

After a 20% price decrease, a computer monitor is on sale for Tk. 7200. What is its original price?

ক
ক) Tk. 9000
খ
খ) Tk. 10,000
গ
গ) Tk. 11,000
ঘ
ঘ) Tk. 12,000

সঠিক উত্তর: ক

ক) Tk. 9000

উত্তর

সঠিক উত্তর: ক

ক) Tk. 9000

ক

ব্যাখ্যা

At 20% decrease,
The price is = 80% = 7200
So, 100% = (7200×100) / 80
= 9000

১১,৭৬৫.

A hall, 20m long and 15m broad, is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at Tk. 3.50 per square meter is

ক
ক) Tk. 500
খ
খ) Tk. 700
গ
গ) Tk. 600
ঘ
ঘ) Tk. 800

সঠিক উত্তর: খ

খ) Tk. 700

উত্তর

সঠিক উত্তর: খ

খ) Tk. 700

খ

ব্যাখ্যা

Question: A hall, 20m long and 15m broad, is surrounded by a verandah of uniform width of 2.5m. The cost of flooring the verandah at Tk. 3.50 per square meter is-

Solution:
হলের দৈর্ঘ্য = 20 মিটার
হলের প্রস্থ = 15 মিটার
হলের ক্ষেত্রফল = 300 বর্গমিটার

বারান্দাসহ হলের দৈর্ঘ্য = 20 + (2 × 2.5) মিটার
= 25 মিটার
বারান্দাসহ হলের প্রস্থ = 15 + (2 × 2.5) মিটার
= 20 মিটার

বারান্দাসহ হলের ক্ষেত্রফল = 500 বর্গমিটার

বারান্দার ক্ষেত্রফল = (500 - 300) বর্গমিটার
= 200 বর্গমিটার

1 বর্গমিটারে খরচ = 3.5 টাকা
200 বর্গমিটারে খরচ = 3.5 × 200 = 700 টাকা

১১,৭৬৬.

The average of x numbers is y² and the average of y numbers is x². So the average of all the numbers taken together is

ক
(x³ + y³)/(x + y)
খ
(x² + y²)/(x + y)
গ
xy² + x²y
ঘ
xy

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The average of x numbers is y² and the average of y numbers is x². So the average of all the numbers taken together is

Solution:
ATQ,
Average of x number is y²
∴ Sum of x number is = xy²

Average of y number is = x²
∴ Sum of y number is = yx²

Average of all number is = (xy²+ yx²)/(x + y)
= xy(y + x)/(x + y)
= xy

১১,৭৬৭.

Fardin starts climbing a 11 m high wall at 4 pm. In each minute he climbs up 1 m but slips down 50 cm. At what time will he climb the wall?

ক
ক) 4.20 p.m.
খ
খ) 4.21 p.m.
গ
গ) 4.25 p.m.
ঘ
ঘ) 5.20 p.m.

সঠিক উত্তর: খ

খ) 4.21 p.m.

উত্তর

সঠিক উত্তর: খ

খ) 4.21 p.m.

খ

ব্যাখ্যা

Question: Fardin starts climbing a 11 m high wall at 4 pm. In each minute he climbs up 1 m but slips down 50 cm. At what time will he climb the wall?

Solution:
প্রতি মিনিটে উঠে ১ মিটার বা ১০০ সেমি, নামে ৫০ সেমি
প্রতি মিনিটে উঠে ১০০ - ৫০ সেমি = ৫০ সেমি বা ১/২ মিটার

১/২ মিটার উঠতে সময় লাগে ১ মিনিট
১ মিটার উঠতে সময় লাগে ২ মিনিট
১০ মিটার উঠতে সময় লাগে ২০ মিনিট

পরের ১ মিটার ১ মিনিটে উঠে যায়।

সময় লাগে = ২০ + ১ মিনিট
= ২১ মিনিট

১১,৭৬৮.

It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

ক
Tk. 3920
খ
Tk. 4920
গ
Tk. 5000
ঘ
Tk. 4900

সঠিক উত্তর: খ

Tk. 4920

উত্তর

সঠিক উত্তর: খ

Tk. 4920

খ

ব্যাখ্যা

Question: It costs Tk. 1 to photocopy a sheet of paper. However, 2% discount is allowed on all photocopies done after the first 1000 sheets. How much will it cost to copy 5000 sheets of paper?

Solution:
For the first 1000 sheets, cost = 1000 × 1 = Tk. 1000

Cost for rest (5000 - 1000) or 4000 sheets = 4000 × (1 - 0.02)
= 4000 × 0.98
= Tk. 3920

Total cost = 3920 + 1000
= Tk. 4920

১১,৭৬৯.

A trader sells an article and losses (25/2)% . The ratio of cost price to the selling price is-

ক
ক) 7 : 5
খ
খ) 8 : 7
গ
গ) 7 : 6
ঘ
ঘ) 9 : 7

সঠিক উত্তর: খ

খ) 8 : 7

উত্তর

সঠিক উত্তর: খ

খ) 8 : 7

খ

ব্যাখ্যা

Let
cost price is x
Loss = (25/2)%

S. P = {100 - (25/2)}% of x
= (175/2) × (1/100) × x
= 7x/8

Required ratio = x : 7x/8
= 1 : 7/8
= 8 : 7

১১,৭৭০.

4³ × (16)² ÷ (4)⁵ = (2)^?

ক
ক) 1
খ
খ) 2
গ
গ) 3
ঘ
ঘ) 4

সঠিক উত্তর: ঘ

ঘ) 4

উত্তর

সঠিক উত্তর: ঘ

ঘ) 4

ঘ

ব্যাখ্যা

Question: 4³ × (16)² ÷ (4)⁵ = (2)^?

Solution:
ধরি,
4³ × (16)² ÷ (4)⁵ = (2)^x
⇒ (2²)³ × (2⁴)² ÷ (2²)⁵ = 2^x
⇒ (2⁶ × 2⁸) ÷ 2¹⁰ = 2^x
⇒ 2^{6 + 8} ÷ 2¹⁰ = 2^x
⇒ 2¹⁴ ÷ 2¹⁰ = 2^x
⇒ 2^{14 - 10} = 2^x
⇒ 2^x = 2⁴
∴ x = 4

১১,৭৭১.

Meena and Rupa entered into a business with a capital of Tk. 15,000 and Tk. 12,000 and they made a total profit of Tk. 9,000. Find the amount of Rupa's share -

ক
Tk. 4500
খ
Tk. 5000
গ
Tk. 4000
ঘ
Tk. 5500

সঠিক উত্তর: গ

Tk. 4000

উত্তর

সঠিক উত্তর: গ

Tk. 4000

গ

ব্যাখ্যা

Meena and Rupa invested Tk. 15,000 and Tk. 12,000 respectively
The ratio of their investment is = 15,000 : 12,000
= 5 : 4
Total profit is Tk. 9000
Rupa's share = Tk. [4/9 x 9000]
= Tk. 4000
Hence the answer is Tk. 4000

১১,৭৭২.

A committee of 5 persons is to be formed from 6 men and 4 women. In how many ways can this be done when at least 2 women are included?

ক
ক) 196
খ
খ) 186
গ
গ) 190
ঘ
ঘ) 200
ঙ
ঙ) None of these

সঠিক উত্তর: খ

খ) 186

উত্তর

সঠিক উত্তর: খ

খ) 186

খ

ব্যাখ্যা

When at least 2 women are included.
The committee may consist of 3 women, 2 men : It can be done in ⁴C₃ × ⁶C₂ ways
or, 4 women, 1 man : It can be done in ⁴C₄ × ⁶C₁ ways
or, 2 women, 3 men : It can be done in ⁴C₂ × ⁶C₃ ways.
Total number of ways of forming the committees
= ⁴C₂ × ⁶C₃ + ⁴C₃ × ⁶C₂ + ⁴C₄ × ⁶C₁
= 6 x 20 + 4 x 15 + 1 x 6
= 120 + 60 + 6
= 186

১১,৭৭৩.

The ages of five persons are 54, 82, 45, 55, and 59 years. What should be the age of a sixth person so that the average age becomes 61 years?

ক
65
খ
61
গ
75
ঘ
71

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: The ages of five persons are 54, 82, 45, 55, and 59 years. What should be the age of a sixth person so that the average age becomes 61 years?

Solution:
Let the age of the sixth person be x.
The average of six persons = Total age of 6 person/ 6

Accordingly:
(54 + 82 + 45 + 55 + 59 + x) / 6 = 61
⇒ (295 + x) / 6 = 61
⇒ 295 + x = 366
⇒ x = 366 - 295
⇒ x = 71

১১,৭৭৪.

A pipe can fill a tank in 3 hours but an outlet B can empty the tank in 10 hours. If both the pipes are opened simultaneously, then the tank will be filled in -

ক
ক) 20/5 hours
খ
খ) 20/7 hours
গ
গ) 30/8 hours
ঘ
ঘ) 30/7 hours

সঠিক উত্তর: ঘ

ঘ) 30/7 hours

উত্তর

সঠিক উত্তর: ঘ

ঘ) 30/7 hours

ঘ

ব্যাখ্যা

Question: A pipe can fill a tank in 3 hours but an outlet B can empty the tank in 10 hours. If both the pipes are opened simultaneously, then the tank will be filled in -

Solution:
in 1 hour, A fills = 1/3
but B reject = 1/10

so, in 1 hour the net fill-up is = 1/3 - 1/10 = 7/30

hence,
It will take 30/7 hours to fill the tank if both the pipes are opened.

১১,৭৭৫.

In a river flowing at 2 km/hr, a boat travels 40 km upstream and then returns downstream to the starting point. If its speed in still water is 6 km/hr, find the total journey time.

ক
ক) 15 hours
খ
খ) 13 hours
গ
গ) 12 hours
ঘ
ঘ) 11 hours

সঠিক উত্তর: ক

ক) 15 hours

উত্তর

সঠিক উত্তর: ক

ক) 15 hours

ক

ব্যাখ্যা

Speed of the boat in still water = 6 km/hr
Speed of the stream = 2 km/hr
Speed downstream = (6 + 2) = 8 km/hr
Speed upstream = (6 − 2) = 4 km/hr
Total journey time = 40/8 + 40/4 = 15 hr

১১,৭৭৬.

What number should come next in the series:
4, 7, 13, 25, 49,.......?

ক
85
খ
90
গ
97
ঘ
101

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: What number should come next in the series:
4, 7, 13, 25, 49,.......?

Solution:
দেওয়া আছে,
সিরিজটি হলো: 4, 7, 13, 25, 49,.......

পার্থক্যগুলোর মধ্যে একটি প্যাটার্ন রয়েছে। প্রতিটি পার্থক্য আগের পার্থক্যের 2 গুণ।

4 থেকে 7 পর্যন্ত পার্থক্য: 3
7 থেকে 13 পর্যন্ত পার্থক্য: 6 (3 × 2)
13 থেকে 25 পর্যন্ত পার্থক্য: 12 (6 × 2)
25 থেকে 49 পর্যন্ত পার্থক্য: 24 (12 × 2)

সুতরাং, পরবর্তী পার্থক্যটি হবে: 24 × 2 = 48
পরবর্তী সংখ্যাটি হবে শেষ সংখ্যা এবং এই পার্থক্যের যোগফল:
49 + 48 = 97

অতএব, পরবর্তী সংখ্যাটি হলো 97।

১১,৭৭৭.

The difference between the radii of the bigger circle and the smaller circle is 14 cm and the difference between their areas is 1,056 cm2. The radius of the smaller circle is -

ক
ক) 7 cm
খ
খ) 5 cm
গ
গ) 9 cm
ঘ
ঘ) 3 cm

সঠিক উত্তর: খ

খ) 5 cm

উত্তর

সঠিক উত্তর: খ

খ) 5 cm

খ

ব্যাখ্যা

ধরি,
ক্ষুদ্রতর বৃত্তের ব্যাসার্ধ r cm
∴ বৃহত্তর বৃত্তের ব্যাসার্ধ = (r + 14) cm
প্রশ্নমতে, Π(r + 14)²-Πr² = 1056
Π{r² + 2b × r × 14 + (14)² - r²} = 1056
r² + 28r + 196 - r² = 1056/Π
28r + 196 = 1056/(22/7)
= 1056 × (7/22)
= 336
28r = 336 - 196
= 140
∴ r = 140/28
= 5
অতএব, ক্ষুদ্রতর বৃত্তের ব্যাসার্ধ 5 cm.

১১,৭৭৮.

In the figure, if AB = 8, BC = 6, AC = 10 and CD = 9, then AD = ?

ক
ক) 12
খ
খ) 11
গ
গ) 13
ঘ
ঘ) 17

সঠিক উত্তর: ঘ

ঘ) 17

উত্তর

সঠিক উত্তর: ঘ

ঘ) 17

ঘ

ব্যাখ্যা

From the measure of various sites of triangle ABC, we can see that it is a right angle triangle whose right angle is at Angle B.
Applying Pythagoras theorem to triangle ABD: we can find the measure of AD.

AD²=AB² + BD²
AD²= 8 × 8 + 15 × 15
AD = 17,
hence option D is the correct one.

১১,৭৭৯.

A man swimming in a stream which flows 3/2 km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

ক
5 km/hr
খ
4.5 km/hr
গ
8 km/hr
ঘ
9 km/hr

সঠিক উত্তর: খ

4.5 km/hr

উত্তর

সঠিক উত্তর: খ

4.5 km/hr

খ

ব্যাখ্যা

Question: A man swimming in a stream which flows 3/2 km/hr finds that in a given time he can swim twice as far with the stream as he can against it. At what rate does he swim?

Solution:
Let, speed upstream = x km/hr.
Speed downstream = 2x km/hr.

Speed of stream = (2x - x)/2 km/hr. = x/2 km/hr

ATQ,
x/2 = 3/2
∴ x = 3

speed upstream = 3 km/hr.
Speed downstream = 2 × 3 = 6 km/hr.

Rate of swimming = (3 + 6)/2 = 9/2 = 4.5 km/hr

১১,৭৮০.

Six times the average of six consecutive even integers is 18 more than the four times the largest integer. What is the average of the consecutive integers?

ক
ক) 19
খ
খ) 20
গ
গ) 21
ঘ
ঘ) 22

সঠিক উত্তর: ক

ক) 19

উত্তর

সঠিক উত্তর: ক

ক) 19

ক

ব্যাখ্যা

Let the first even integer be y.
Therefore, 6(y + y + 2 + y + 4 + y + 6 + y + 8 + y + 10)/6 = 4(y + 10) + 18
⇒ 6y + 30 = 4y + 58
⇒ 2y = 28
⇒ y = 14
Therefore, the required average
= (6y + 30)/6
= (6 × 14 + 30)/6
= 114/6
= 19
----------------------------------------
৬ টি ক্রমিক জোড় পূর্ণ সংখ্যার গড়ের ৬ গুণ বৃহত্তম পূর্ণ সংখ্যার ৪ গুনের চেয়ে ১৮ বেশি হলে, সংখ্যা গুলোর গড় কত?

১ম জোড় পূর্ণ সংখ্যা y হলে,
6(y + y + 2 + y + 4 + y + 6 + y + 8 + y + 10)/6 = 4(y + 10) + 18
⇒ 6y + 30 = 4y + 58
⇒ 2y = 28
⇒ y = 14
অতএব, নির্ণেয় গড়
= (6y + 30)/6
= (6 × 14 + 30)/6
= 114/6
= 19

১১,৭৮১.

In a simultaneous throw of a pair of dice, find the probability of getting a total more than 9.

ক
1/4
খ
2/3
গ
1/6
ঘ
1/9

সঠিক উত্তর: গ

1/6

উত্তর

সঠিক উত্তর: গ

1/6

গ

ব্যাখ্যা

Question: In a simultaneous throw of a pair of dice, find the probability of getting a total more than 9.

Solution:
When two fair six-sided dice are thrown together, the total number of possible outcomes = 6 × 6 = 36.
We need the cases where the sum is more than 9, i.e., 10, 11, or 12.
Here are all favorable outcomes, (4, 6), (5, 5), (6, 4), (5, 6), (6, 5), (6, 6) = 6

∴ Probability = (number of favorable outcomes)/(total possible outcomes)
= 6/36
= 1/6

So the probability of getting a total more than 9 is 1/6.

১১,৭৮২.

If y : x = 1 : 5 and 2x + y = 22, then what is the value of y?

ক
0
খ
1
গ
2
ঘ
5
ঙ
10

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: If y : x = 1 : 5 and 2x + y = 22, then what is the value of y?

Solution:
Given,
y : x = 1 : 5
⇒ y/x = 1/5
∴ y = x/5 ..........(1)

and,
2x + y = 22
⇒ 2x + (x/5) = 22
⇒ (10x + x)/5 = 22
⇒ 11x = 22 × 5
⇒ 11x = 110
⇒ x = 110/11
∴ x = 10

From equation (1),
y = 10/5 = 2

১১,৭৮৩.

A fruit seller had some apples. He sells 40% apples and still has 420 apples. Originally, he had:

ক
ক) 450
খ
খ) 588
গ
গ) 600
ঘ
ঘ) 672
ঙ
ঙ) 700

সঠিক উত্তর: ঙ

ঙ) 700

উত্তর

সঠিক উত্তর: ঙ

ঙ) 700

ঙ

ব্যাখ্যা

He has = 100 - 40 = 60% apples
60% apples is equal to 420
1%. apples is equal to (420/60%)
100% apples is equal to (420/60%) × 100
= 700

১১,৭৮৪.

How many terms are there in the GP 5, 20, 80, 320,..........., 20480?

ক
6
খ
7
গ
8
ঘ
9

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: How many terms are there in the GP 5, 20, 80, 320,..........., 20480?

Solution:
Common ratio, r = 20/5
= 4

Last term or nth term of GP = ar^{n - 1}
⇒ 20480 = 5 × (4^{n - 1})
⇒ 4^{n - 1} = 20480/5
⇒ 4^{n - 1} = 4096
⇒ 4^{n - 1} = 4⁶
So, comparing the power,
Thus, n - 1 = 6
∴ n = 7

Number of terms = 7

১১,৭৮৫.

How many days are there in x weeks 3x days?

ক
5x²
খ
7x
গ
11x²
ঘ
10x

সঠিক উত্তর: ঘ

10x

উত্তর

সঠিক উত্তর: ঘ

10x

ঘ

ব্যাখ্যা

Question: How many days are there in x weeks 3x days?

Solution:
x weeks 3x days = (7x + 3x) days = 10x days.

১১,৭৮৬.

P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?

ক
8
খ
6
গ
12
ঘ
4

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: P and Q together complete a piece of work in x days. If P alone completes the work in (x + 3) days and Q alone completes the piece of work in (x + 12) days, what is the value of 'x'?

Solution:
P's 1 day's work = 1/(x + 3) part
Q's 1 day's work = 1/(x + 12) part
and (P + Q)'s 1 day's work = 1/x

ATQ,
1/(x + 3) + 1/(x + 12) = 1/x
⇒ (x + 12 + x + 3)/(x + 3)(x + 12) = 1/x
⇒ (2x + 15)/(x² + 15x + 36) = 1/x
⇒ 2x² + 15x = x² + 15x + 36
⇒ 2x² + 15x - x² - 15x = 36
⇒ x² = 36
∴ x = 6

১১,৭৮৭.

If x⁴ + y⁴ = 17 and x + y = 1, then the value of x²y² - 2xy?

ক
ক) 4
খ
খ) 8
গ
গ) 12
ঘ
ঘ) 16

সঠিক উত্তর: খ

খ) 8

উত্তর

সঠিক উত্তর: খ

খ) 8

খ

ব্যাখ্যা

Question: If x⁴ + y⁴ = 17 and x + y = 1, then the value of x²y² - 2xy?

Solution:
Given,
x + y = 1
Or, (x + y)² = 1²
Or, x² + 2xy + y² = 1
Or, x² + y² = 1 - 2xy
Or, (x² + y²)²= (1 - 2xy)²
Or, x⁴+ 2 . x²y² + y⁴ = 1 - 4xy + (2xy)²
Or, x⁴ + y⁴ + 2x²y² = 1 - 4xy + 4x²y²
Or, 17 = 1 - 4xy + 2x²y²
Or, 2x²y² - 4xy = 17 - 1
Or, 2x²y² - 4xy = 16
∴ x²y² - 2xy = 8

১১,৭৮৮.

If A stands for +, B stands for -, C stands for ×, then what is the value of (10 C 4) A (4 C 4) B 6 ?

ক
60
খ
55
গ
50
ঘ
40

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: If A stands for +, B stands for -, C stands for ×, then what is the value of (10 C 4) A (4 C 4) B 6 ?

Solution:
(10 C 4) A (4 C 4) B 6
= (10 × 4) + (4 × 4) - 6
= 40 + 16 - 6
= 56 - 6
= 50

১১,৭৮৯.

In a certain code, MASTER = 582467 and CROWD = 17936, how is DREAM coded in the language?

ক
67568
খ
76568
গ
67685
ঘ
76865

সঠিক উত্তর: গ

67685

উত্তর

সঠিক উত্তর: গ

67685

গ

ব্যাখ্যা

Question: In a certain code, MASTER = 582467 and CROWD = 17936, how is DREAM coded in the language?

Solution:
Given,
M A S T E R
↓ ↓ ↓ ↓ ↓ ↓
5 8 2 4 6 7

and
C R O W D
↓ ↓ ↓ ↓ ↓
1 7 9 3 6

So
D R E A M
↓ ↓ ↓ ↓ ↓
6 7 6 8 5

১১,৭৯০.

Three pipes A, B and C can fill a tank in 8 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. The number of hours taken by C alone to fill the tank is?

ক
21 hours
খ
18 hours
গ
28 hours
ঘ
24 hours

সঠিক উত্তর: ঘ

24 hours

উত্তর

সঠিক উত্তর: ঘ

24 hours

ঘ

ব্যাখ্যা

Question: Three pipes A, B and C can fill a tank in 8 hours. After working at it together for 2 hours, C is closed and A and B can fill the remaining part in 9 hours. The number of hours taken by C alone to fill the tank is?

Solution:
Part filled in 2 hours = 2/8 = 1/4
Remaining part = 1 - (1/4) = 3/4

(A + B)'s 9 hour's work = 3/4
(A + B)'s 1 hour's work = 3/36 = 1/12

∴ C's 1 hour's work = {(A + B + C)'s 1 hour's work } - {(A + B)'s 1 hour's work }
= (1/8) - (1/12)
= (3 - 2)/24
= 1/24
∴ C alone can fill the tank in 24 hours.

১১,৭৯১.

A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least woman?

ক
ক) 9/20
খ
খ) 1/10
গ
গ) 9/10
ঘ
ঘ) 1/20

সঠিক উত্তর: গ

গ) 9/10

উত্তর

সঠিক উত্তর: গ

গ) 9/10

গ

ব্যাখ্যা

Question: A committee of 3 members is to be selected out of 3 men and 2 women. What is the probability that the committee has at least woman?

Solution:
Total Person = 3 + 2 = 5
Committee can be form

Men (3) - Women (2)
1) 2 1
2) 1 2

∴ Expected events = (³C₂ × ²C₁) + (³C₁ × ²C₂)
= (3 × 2) + (3 × 1)
= 6 + 3
= 9

Total events = ⁵C₃ = 10

∴ Probability = 9/10

১১,৭৯২.

ক
0.86
খ
0.101
গ
0.842
ঘ
0.97
ঙ
None

সঠিক উত্তর: ক

0.86

উত্তর

সঠিক উত্তর: ক

0.86

ক

১১,৭৯৩.

A student scores 70% marks in 10 papers of 100 marks each. He scores 14% of the total obtained marks in Math. How much does he score in Math?

ক
99
খ
98
গ
88
ঘ
70

সঠিক উত্তর: খ

উত্তর

সঠিক উত্তর: খ

খ

ব্যাখ্যা

Question: A student scores 70% marks in 10 papers of 100 marks each. He scores 14% of the total marks in Math. How much does he score in Math?

Solution:
Here,
Total marks in 10 subjects = 10 × 100
= 1000

∴ He scores = 70% of 1000
= (70/100) of 1000
= 700

∴ He scores in Math = 14% of 700
= (14/100) of 700
= 98

১১,৭৯৪.

If u > t, r > q, s > t, t > r. Which of the following must be true?
(i) u > s (ii) s > q (iii) u > r

ক
ক) i only
খ
খ) ii only
গ
গ) iii Only
ঘ
ঘ) i & ii only
ঙ
ঙ) ii & iii only

সঠিক উত্তর: ঙ

ঙ) ii & iii only

উত্তর

সঠিক উত্তর: ঙ

ঙ) ii & iii only

ঙ

ব্যাখ্যা

Question: If u > t, r > q, s > t, t > r. Which of the following must be true?
(i) u > s (ii) s > q (iii) u > r

Solution:
u > t
s > t
u, s এর মধ্যে সরাসরি সম্পর্ক নেই। u > s বা u < s দুটিই হতে পারে।

u > t > r > q
⇒ t > q

s > t
∴ s > q

আবার, u > t > r > q
∴ u > r

১১,৭৯৫.

If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?

ক
1480 chairs
খ
1380 chairs
গ
1320 chairs
ঘ
1410 chairs

সঠিক উত্তর: খ

1380 chairs

উত্তর

সঠিক উত্তর: খ

1380 chairs

খ

ব্যাখ্যা

Question: If 12 carpenters, working 6 hours a day, can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day?

Solution:
12 carpenters, working 6 hours for 24 days makes (12 × 6 × 24) or, 1728 working hours.
18 carpenters working 8 hours for 36 days makes (18 × 8 × 36) or, 5184 working hours.

1728 working hours = 460 chairs
∴ 5184 working hours = ( 460 × 5184 ) / 1728 chairs
= 1380 chairs

১১,৭৯৬.

The length of a rectangle is twice than that of its breadth. If the length of the rectangle is increased by 10%, while its breadth is decreased by 10% what is the percentage change in the perimeter?

ক
ক) 3(1/3) %
খ
খ) 3(2/3) %
গ
গ) 4%
ঘ
ঘ) No change

সঠিক উত্তর: ক

ক) 3(1/3) %

উত্তর

সঠিক উত্তর: ক

ক) 3(1/3) %

ক

ব্যাখ্যা

Let, breadth = x unit & length = 2x unit
∴ Perimeter = 2(2x + x) unit = 6x unit
10% হ্রাসে, breadth = (x - 10x/100) = 9x/10 unit
10% বৃদ্ধিতে length (2x + 20x/100) = 11x/5 unit
∴ Perimeter = 2(9x/10 + 11x/5) unit = 2 × 31x/10 = 31x/5 unit
∴ Perimeter এর পরিবর্তনের হার = {(31x/5 - 6x) / 6x} × 100 %
= [{(31x - 30x)/5}/6x × 100] %
= 10/3 %
= 3(1/3)%; increase

১১,৭৯৭.

The ratio 5 : 4 expressed as a percent equals

ক
ক) 125%
খ
খ) 40%
গ
গ) 80%
ঘ
ঘ) 12.5%

সঠিক উত্তর: ক

ক) 125%

উত্তর

সঠিক উত্তর: ক

ক) 125%

ক

ব্যাখ্যা

Question: The ratio 5 : 4 expressed as a percent equals

Solution:
5 : 4 = 5/4
= (5/4) × (100/100)
= (5 × 100)/4 × (1/100)
= 125 × (1/100)
= 125%

১১,৭৯৮.

a is greater than b by 2 and b is greater than c by 10. If (a + b + c) = 130, then b + c - a=?

ক
ক) 34
খ
খ) 36
গ
গ) 38
ঘ
ঘ) 39

সঠিক উত্তর: ক

ক) 34

উত্তর

সঠিক উত্তর: ক

ক) 34

ক

ব্যাখ্যা

Question: a is greater than b by 2 and b is greater than c by 10. If (a + b + c) = 130, then b + c - a=?

Solution:
b = c + 10
a = b + 2
= c + 10 + 2
= c + 12

(a+b+c) = 130
⇒ c + 12 + c + 10 + c = 130
⇒ 3c + 22 = 130
⇒ 3c = 130 - 22
⇒ 3c = 108
∴ c = 108/3
= 36

b = 36 + 10 = 46
a = 36 + 12 = 48

b + c - a = 46 + 36 - 48
= 34

১১,৭৯৯.

In doing a question of division with zero remainder, a candidate took 12 divisor instead of 15. The quotient obtained by him was 35. The correct quotient is-

ক
17
খ
20
গ
24
ঘ
28

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: In doing a question of division with zero remainder, a candidate took 12 divisor instead of 15. The quotient obtained by him was 35. The correct quotient is-

Solution:
Divisor taken = 12
Quotient obtained = 35,
Remainder = 0
∴ Dividend = (12 × 35) = 420

Now, Dividend = 420,
Divisor = 15
Remainder = 0
∴ Quotient = 420/15
= 28

১১,৮০০.

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

ক
240
খ
250
গ
280
ঘ
320

সঠিক উত্তর: খ

250

উত্তর

সঠিক উত্তর: খ

250

খ

ব্যাখ্যা

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

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

20% বৃদ্ধিতে ,
প্রতি পিস পাউরুটির বর্তমানমূল্য ছিল = 100 + 20 টাকা
= 120 টাকা

∴ বর্তমান মূল্যে 30000 টাকা দিয়ে পাউরুটি কেনা যাবে = 30000/120 টাকা
= 250 টাকা