ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: If A + B = 2C and C + D = 2A, then-

Solution: 
Let
 A + B = 2C.............(1)
C + D = 2A.............(2)

(1) + (2)⇒
A + B + C + D = 2C + 2A
A + B + C + D  - A - C = 2C + 2A - A - C
B + D = C + A

অপশনে সঠিক উত্তর না থাকায় বাতিল করা হলো।
সঠিক উত্তর হবে -  188
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Question: The sum of four consecutive even numbers (A, B, C, and D) is 156. What is the sum of the set of the next four consecutive even numbers?

Solution: 
Let
A = x ,B= x + 2,C = x + 4, D = x + 6;

Now
x + x + 2 + x + 4 + x + 6=156
⇒ 4x + 12 = 156
⇒ 4x = 156 - 12
⇒ 4x = 144
     x= 36

This shows A = 36,B = 38,C = 40,D = 42
Next consecutive even numbers will be 44, 46, 48, 50
Therefore 44 + 46 + 48 + 50 = 188

This shows sum of next four consecutive is 188

Question: The HCF and LCM of two numbers are 8 and 96 respectively. If one of the two numbers is 24, what is the other one?

Solution: 
Let the other number be x.

We know that,
H.C.F.× L.C.M.=Product of two numbers
⇒8 × 96 = 24 × x
⇒x = 32

Question: The average of 12 numbers is 16 and the average of the first two is 14. What is the average for the rest?

Solution: 
Average of twelve numbers = 16
Sum of twelve numbers = 16 × 12 = 192
Average of first two numbers = 14
Sum of first two numbers = 14 × 2 = 28

Total of remaining ten numbers = 192 - 28 = 164
Average of rest = 164/10
                         = 82/5

Question: √(4/3) - √(3/4) = ?

Solution:
= (√4.√4 - √3.√3)/√3.√4
=(4 - 3)/2√3
=1/2√3

Question: Two numbers are in the ratio 3 : 4. If the difference of their squares is 63, then the smallest number is -

Solution:
Let
the numbers are 3x, 4x

Now 
(4x)² - (3x)² = 63
16x² - 9x² = 63
7x² = 63 
x² = 9
x = 3

The smallest number is = 3 × 3 = 9

Question: 12 men complete a work in 9 days. After they have worked for 6 days 6 more men join them. How many days will they take to complete the remaining work? 

Solution:
12 men's 9 days work = 1
1 man's 1 day's work = 1/108
12 men's 6 day's work = (12 × 6)/108
                                     = 2/3

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

18 men's 1 day's work =18/108 = 1/6

1/6 work is done by them in 1 day 
1/3 work is done by them in 6/3 = 2 days 

Question: If (5√5 × 5³)/5 ^{- 3/2} = 5^{a + 2}, then the value of a is-

Solution:
Given that 
(5√5 × 5³)/5 ^{- 3/2} = 5^{a + 2}
⇒ (5^{1 + (1/2) + 3})/5 ^{- 3/2} =5^{a + 2}
⇒ 5^{1 + (1/2) + 3 + (3/2)} = 5^{a + 2}
⇒ 1 + (1/2) + 3 + (3/2) = a + 2
⇒ (2 + 1 + 6 + 3)/2 = a + 2
⇒ 12/2 = a + 2
⇒ 6 = a + 2
    a = 4

Question: A man complete a journey in 5 hours. He travels first half of the journey at the rate of 16 km/hr and second half at the rate of 24 km/hr. Find the total journey in km.

Solution: 
Let 
The total journey x km
Now
 {(1/2)x/16} + {(1/2)x/24} = 5
⇒ (x/16) + (x/24) = 10
⇒ (3x + 2x)/48 = 10
⇒ 5x/48 = 10
⇒ x = (10 × 48)/5
    x = 96km

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

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

Question: Which of the following is a factor of x³ - x - 24?

Solution: 
f(x) = x³ - x - 24
f(3) = 3³ - 3 - 24
f(3) =27 - 27
      = 0
(x - 3) is a factor of x³ - x - 24.

Question: If log_x4 = 0.4, then the value of x is-

Solution: 
Given that
 log_x4 = 0.4
log_x4 = 4/10
log_x4 = 2/5
x^2/5 = 4
x = 4^5/2
x = (2²)^5/2
x = 2⁵
x = 32

Question: The sum of the numerator and denominator of a real fraction is 7 and their difference is 1. What is the fraction?

Solution: 
Let
Denominator of fraction = x
The numerator of the fraction = y

According to question,
x + y = 7.............(1)
x - y = 1.............(2)

(1) + (2) ⇒
x + y + x - y = 7 + 1
2x = 8
x = 4
From (1) 
x + y = 7
4 + y = 7
y = 3

The fraction = 3/4

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

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

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

∴ The required probability is 1/2

Question: If 20% of x is the same as the 10% of y, then x : y is equal to

Solution:
20% of x = 10% of y
⇒ (20/100) × x = (10/100) × y
⇒ 20 x = 10 y
⇒ x/b = 10/20
∴ x : y = 1 : 2

Question: If a + b = 11, a - b = 9, what is ab = ?

Solution: 
Given that
a + b = 13
a - b = 11

we know
4ab = (a + b)² - (a - b)²
4ab = 11² - 9²
4ab = 121 - 81
4ab = 40
ab = 40/4
ab = 10

Question: The difference between the length and breadth of a rectangle is 23 m. if its perimeter is 206 m, then its area is:

Solution: 
According to the question,
The difference between the length and breadth of a rectangle is 23 m
⇒ l - b = 23..............(1)
Its perimeter is 206 m
⇒ 2(l + b) = 206 m
⇒ l + b = 103 m.................(2)

Adding both equation (1) and (2)
⇒ 2l = 126
⇒ l = 63 m

Putting l = 63 in Equation (2)
⇒ b = 103 - 63
⇒ b = 40 m
Area of rectangle = Length(l) × Breadth(B)
                            ⇒ 63 × 40
                             ⇒ 2520 m²
∴ Its area is 2520 m².

- Anthology is called a collection of literary pieces.
- Numismatics is called a  collection of coins.
- Philately is called a collection of stumps. 
- Library is called a collection of books.

Source: britannica.com &  merriam-webster.com

- A brief and brilliant expression intended to produce surprise and pleasure is called Wit.
- A thing which stands for something else is Symbol.
- The central idea of literary work is Theme.
- A smaller unit of the structure of a poem is called Stanza.

Source: An ABC of English Literature by Dr. M Mofizar Rahman

- Because of is a preposition phrase and it is used before nouns or a noun phrase such as a  misunderstanding to express cause.
- Because is a conjunction and it introduces a clause with a subject and a verb.

For example:
She was absent because her cold was worse.
Or, She was absent because of her cold.

Source:  Barron’s TOEFL

- Subject + make/made + someone/something +verb word + extension.

For example:
She made the baby take a nap.
I can’t seem to make this dishwasher run.

Source:  Barron’s TOEFL.

- Burst into tears = কান্নায় ভেঙ্গে পড়া
- Burst into laughing = হাসিতে ফেটে পড়া

Source: Applied English Grammar & Composition by P.C. Das

- Preposition এর Object হিসাবে Noun/Noun Phrase/ Gerund/Pronoun  হয়। 
- Preposition এর পরে সাধারণত Noun/Noun Phrase/ Gerund/ Pronoun হয় ।

যেমন:
He is coming from school.
I have bought a book for you.

Source: Applied English Grammar & Composition by P.C. Das

In this sentence, that refers to radios (plural subjects) and takes the plural verb are not is.
অর্থাৎ,
That এর পূর্ববর্তী শব্দ অনুযায়ী পরবর্তী verb হবে।
উক্ত বাক্যটিতে that এর আগে radios শব্দটি plural, তাই verb is না হয়ে are হবে।

Source: Objective English for Competitive Examinations by Edgar Thorpe and Showick Thorpe.

- Mint is where coins are made.
- Stable is where horses live.
- Granary is a storage place for grains.
- Cage is an enclosure for domestic animals/birds.

Source: dictionary.cambridge.org

FEEBLE [ফীব্‌ল্‌] 
(adjective) দুর্বল; নিস্তেজ; ক্ষীণ।

Synonyms: Weak, Frail, Fragile, Infirm,
Antonyms: Mighty, Powerful, Rugged, Stalwart, Stout, Strong

other forms:
feeble minded (adjective) দুর্বলচিত্ত।
feebly (adverb) 
feebleness (noun)

Source: Accessible Dictionary by Bangla Academy

VIVACIOUS (adjective) 
- প্রাণবন্ত; প্রাণোচ্ছল; হাসিখুশি; জীবনীশক্তিপূর্ণ: a vivacious girl.

Synonyms: lively, animated, vivacious, sprightly. 
Antonyms: dead, inactive, inanimate, lackadaisical, languid, languishing.

other forms:
vivaciously (adverb) প্রাণবন্তভাবে।
vivacity [uncountable noun] প্রাণোচ্ছলতা; প্রাণচাঞ্চল্য।

Source: Accessible Dictionary by Bangla Academy

PENCHANT (noun) 
- রুচি; পছন্দ; ঝোঁক: penchant for classical music.

Synonyms: leaning, propensity,proclivity
Antonyms: aversion, disfavor, disinclination, dislike, disliking, disrelish, distaste

Source: Accessible Dictionary by Bangla Academy

He opened the door easily and he peeped in. The room was neat and clean. He waited for a minute or two and met a gentleman. After that,  he stepped into the room.

Source: Objective General English by Dr. R.S. Aggarwal and Vikas Aggarwal.

- Fleet is a collective noun. 
- A collective Noun is the name of a group or collection of persons or things of the same kind.
- For example: flock, band, cavalry, herd, jury, crowd, gang, team, party, infantry, fleet, navy, audience, committee, group etc.
- A proper noun is the name of a particular person, thing, place, or any other thing. For example: Rose, Rabindranath, Earth, Mars, etc.
- A common noun is one which is common to each member of a class of persons or things. for example:  Flower, Book, River etc.

Source: A Passage to the English Language by S.M. Zakir Hussain.

- So that, in order that- এর পরে may/might, shall/should বসে; can/could, বা will/would বসে না।
- He encouraged me so that/ in order that I might not lose heart.

Source: Applied English Grammar & Composition by P.C. DAS.

A foregone conclusion
English Meaning: a result that is obvious to everyone even before it happens.
Bangla Meaning: যে পরিণাম প্রথম থেকেই দেখা সম্ভব (ছিল); পূর্বগত পরিণাম। যে সিদ্ধান্ত আগেই স্থির হয়ে আছে বা স্থির হয়ে গেছে।

For example:
the victory was a foregone conclusion.

Source: Accessible Dictionary by Bangla Academy and Cambridge Dictionary

- Brown study means absent minded.
- Pay attention means to study, watch, listen to, or think about something .
- Beard-stroking means very serious thoughts or talk about complicated ideas.

Source: dictionary.cambridge.org

- Rise হলো intransitive verb এবং এর  past participle হলো risen. 
- আর raise হলো transitive verb. র  past participle হলো raised.
- বাক্যটি Present perfect tense এবং  intransitive verb. 
- তাই সঠিক উত্তর risen. 

Source: A Passage to the English Language by S.M. Zakir Hussain.

- Infinite (to+verb) কে passive voice এ রুপান্তর করতে হলে  to be এর পরে verb এর past participle হয়।

Active: There is no time to lose.
Passive: There is no time to be lost.

Active: You have to admit this.
Passive: This has to be admitted by you.

Source: Applied English Grammar & Composition by P.C. Das.

- যদি Reporting verb-টি  past tense-এ থাকে, তাহলে নিম্নলিখিত পরিবর্তন করতে হয় এবং yesterday থাকলে the day before হবে। 

Direct => Indirect
Present indefinite => Past indefinite
Present continuous => Past continuous
Present perfect => Past perfect
Past indefinite => Past perfect
Past perfect => Past perfect
Past continuous => Past perfect continuous
Future (shall/will) => Future (should/would)

She said that she had had a horrible experience on the road the day before. 
- এখানে past perfect হিসেবে একটি had এসেছে এবং মূল verb এর PP হিসেবে আরেকটি had ব্যবহৃত হয়েছে।

Source: Applied English Grammar & Composition by P.C. Das.

Noun: Progress, Progressist, Progression
Verb: Progress
Adjective: Progressive
Adverb: Progressively

Synonyms: advance, advancement, progression.
Antonyms: recess, recession, regress, regression.

Source: merriam-webster.com

The Correct spelling is: Buoyant (প্লবনশীল; উৎপতিষ্ণু; প্লবমান)

The correct spelling of other words:
- Apparent (স্পষ্টত প্রতীয়মান)
- Beginning (প্রারম্ভ; শুরু)
- Business (ব্যবসা)

Source: Accessible Dictionary by Bangla Academy