ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

The correctly spelt word is Patience (ধৈর্য; সহিষ্ণুতা)

The correct spelling of other words: 
Embellish (সুন্দর করা; অলংকৃত করা)
Magazine (পত্রপত্রিকা)
Commission (কমিশন)

Source: Accessible Dictionary by Bangla Academy & Cambridge Dictionary

The correctly spelt word is Publication (প্রকাশ; প্রকাশনা।)

The correct spelling of other words: 
Diligent  (পরিশ্রমী)
Aggression  (হামলা)
Difference (পার্থক্য)

Source: Accessible Dictionary by Bangla Academy & Cambridge Dictionary

The correctly spelt word is Uncertain (পরিবর্তনশীল; অস্থির; অনিশ্চিত)

The correct spelling of other words: 
Stubborn (একগুঁয়ে)
Malleable (নমনীয়)
Decisive (চূড়ান্ত)

Source: Accessible Dictionary by Bangla Academy & Cambridge Dictionary

– কোনো কিছুর উদাহরণ দেওয়ার ক্ষেত্রে Such as ব্যবহার হয়।
উদাহরণঃ Magazines such as Time, Newsweek, and U.S. News provide the reader with a pictorial report of the week’s events.

– কোনো কারণ বা শর্ত বুঝাতে As ব্যবহার হয়।
উদাহরণঃ Had his meals delivered to him as he couldn't navigate the icy sidewalk with his walker.

Source: Barron’s TOEFL

– Sentence বা Clause-এ Contradiction বুঝাতে Despite/ In spite of ব্যবহার হয়।
– মনে রাখতে হবে যে, Despite  এর পরে Of হয় না এবং in spite এর of পরে হয়।

উদাহরণঃ 
 Despite the delay, they arrived on time.
 In spite of the delay, they arrived on time.

Source: Barron’s TOEFL

– যেমন কর্ম তেমন ফল = As you sow, so you reap.
– নানা মুনির নানা মত = Many men, many minds.
– ইচ্ছা থাকলে উপায় হয় = Where there is a will, there is a way.
– সবুরে মেওয়া ফলে = Patience has its reward.

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

- হাটে হাঁড়ি ভেঙ্গে দেয়া = The cat is out of the bag.
- জোর যার মুলুক তার = Might is right.
- বিড়ালের গলায় ঘন্টা বাঁধবে কে = Who will bell the cat.
- ঝোপ বুঝে কোপ মারা = Strike the iron while it is hot.

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

The rainy season has its demerits. But it is a blessing to the economy of our country. It helps nature to gain a new life. We always welcome this season and enjoy its beauty.

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

Agriculture is a main economic activity in Bangladesh. It recently employs about 50 percent of the country’s labour force. And, contributes about 20 percent of the country's gross domestic product (GDP). The development of  an emerging economy counts on the advancement of the agriculture sector.

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

– অনেক অর্থ প্রকাশে uncountable noun এর আগে Much বসে।
যেমনঃ He has much money.
– অনেক অর্থ প্রকাশে countable noun এর আগে Many বসে।
যেমনঃ Many Children are playing in the field.
– কিছু সংখ্যক বুঝাতে countable noun এর আগে A few বসে।
যেমনঃ A few man were present in the meeting
– সামান্য কিছু আছে এমন বুঝাতে countable noun এর আগে few বসে।
যেমনঃ there are few books on the table.

–  A noun which can be counted by the number is called Countable Noun.
–  Common Noun হলো Countable Noun.
– যেমনঃbook, pen, boy, girl etc

– A noun which cannot be counted by numbers but may be measured by some other units only is called Uncountable Noun.
–Material Noun, Proper Noun, Collective Noun, এবং Abstract Noun Uncountable Noun.
– যেমনঃ rice, water, milk,money, Nazrul, goodness etc.

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

– Had better একটি modal verb যা advice for future এর ক্ষেত্রে ব্যবহার হয়।
– Had better এর পরে Verb Base form বসে।
– Modal verbs হলো can, could, may, might, shall, should, will, would, may, might, ought to, had better, would rather etc.
– Modal verbs এর পরে Verb Base form বসে। 
যেমনঃ
You had better not go alone.
Greg would rather have a Pepsi than Fanta.

Source: Barron’s TOEFL

এখানে provided (that) হলো Conjunction.
এর অর্থ if, or only if:

More examples:
- We'll be there at about 7.30, provided that there's a suitable train.
- Provided that there are enough seats, anyone can come on the trip.
- Provided that the boat leaves on time, we should reach France by morning.

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"Provided" শব্দটির নিচে আন্ডারলাইন থাকার কথা ছিলো।
লাইভ প্রশ্নে আন্ডারলাইন না আসায় উত্তর তুলে দেওয়া হয়েছে।

–  Psychoanalysis  এ জন্য Sigmund Freud বিখ্যাত।
– Physics ও Mathematicsএর বিশ্ব বিখ্যাত বিজ্ঞানী Sir Isaac Newton.
–  Newton এর বিখ্যাত three laws of motion—the basic principles of modern physics-  এর result হলো  the law of universal gravitation.
– John Dalton হলো  একজন English meteorologist and chemist, ও pioneer in the development of modern atomic theory.
– Alan Turing হলো একজন British mathematician and logician.
– Bertrand Russell হলো একজন  British philosopher, logician, and social reformer।
– 1950 সালে সাহিত্যে  Nobel Prize এ ভূষিত হয়।

Source: britannica.com

Many men, many minds = নানার মুনির নানা মত
–  men শব্দটি plural তাই, minds শব্দটি plural.

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

– Principle = তত্ত্ব,সূত্র
– Prime = প্রধান, মুখ্য, মৌলিক
– Principal = অধ্যক্ষ, মালিক, কর্তা, প্রধান, মুখ্য, (বাণিজ্যে) পুঁজি, মূলধন

Source: প্রশাসনিক পরিভাষা, বাংলা একাডেমি।

– while এর পরে subject + verb বা noun phrase থাকতে পরে।
– কিন্তু When এর পরে অব্যশই subject + verb হবে।

যেমনঃ
While on vacation, she bought gifts for his family.
Or, while she was on vacation, she bought gifts for his family.
Or, when she was on vacation, she bought gifts for his family.

Source:  Barron’s TOEFL

- several days, a month, few month, two years etc অনির্দিষ্ট সময়ের জন্য For হয়। 
- Wednesday, July, 2003, etc নির্দিষ্ট সময়ের জন্য Since হয়।

যেমনঃ
Mannan has been on diet for last month.   
We have been living here since 2010.

Source:  Barron’s TOEFL

– If যুক্ত clauseটি past indefinite  হলে,
– অন্য clauseটির subjectএর পরে would/could/might+verbএর base form হবে। 
– বাক্যটির অর্থ: একটি গাড়ী থাকলে আমরা আমাদের নদীমাতৃক দেশের পর্যটন এলাকায় ভ্রমণ করতাম।

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

– In a fix অর্থ get into trouble বা কষ্ট পাত্তয়া।
– Get rid of  অর্থ মুক্তি পাওয়া, কাউকে ত্যাগ করা।
– In lieu of  অর্থ পরিবর্তে বা instead of.
– Be puzzled অর্থ be confuzed বা কি করবে বুঝতে না পারা।

Source: Cambridge Dictionary

– Oligarchy is a small group of people having control of a country or organization.
– Secular state is  a government not connected with religious or spiritual matters.
– Autocracy is a system of government by one person with absolute power.
– Plutocracy is a form of government by the wealthy. 
– Bureaucracy is  a system of government by officials.
– Aristocracy is a form of government in which power is held by the nobility.

Source: Cambridge Dictionary

– Drake হলো Duck এর masculine gender.
– Common Gender হলো পুংবাচক বা স্ত্রীবাচক উভয় Noun.
যেমনঃ parent, baby, friend, child, infant, people, servant, thief, enemy, cousin, Orphan, student, doctor, teacher, monarch etc হলো Common Gender.

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

Question: {(3.63)² - (2.37)²}/(3.63 + 2.37) is simplified to- 

Solution: 
{(3.63)² - (2.37)²}/(3.63 + 2.37)
= (3.63 + 2.37)(3.63 - 2.37)/(3.63 + 2.37)
= 3.63 - 2.37
= 1.26

Question: The radius of a sphere is 3 cm . What is the volume of the sphere?

Solution: 
Radius of a sphere (r)=  3 cm
Volume of sphere = (4/3) × πr³ 
                             =  (4/3) × π3³ 
                             = (4/3) × 27π   
                              = 36π cm³
∴ The volume of the sphere is 36π cm³

Question: What is the value of A if tan(3A) = √3?

Solution:
tan(3A) = √3
tan(3A) = tan60°
3A = 60°
A = 20°

Question : If the product of two numbers is 5 and one of the number is 3/2, then sum of two numbers is :

Solution: 
Let two numbers be a and b
Given that
ab = 5 and a = 3/2

ab= 5
b = 5/a
    = 5/(3/2)
    = 5 × (2/3)
   = 10/3


a + b = (3/2) + (10/3)
           = (9 + 20)/6
            = 29/6

Question: A shopkeeper marks the price of an article at TK. 120. What will be the selling price. if he allows two successive discounts of 5% each ?

Solution:
At 5% discount for the first time = (120 × 95)/100 = Tk.114
At 5% discount for second time = (114 × 95)/100 = Tk. 108.30

Question: In how may different ways can the letters of the word TUESDAY be arranged in such a way that the vowels always come together? 

Solution:
The word 'TUESDAY' contains 7 different letters.
When the vowels UEA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters TSDY(UEA).
Now, 5 letters can be arranged in 5! ways 
                                                   = 120 ways.
The vowels (UEA) can be arranged among themselves in 3! = 6 ways.

∴ Required number of ways = (120 × 6) = 720

Question: The ages of A and B are in the ratio 3 : 1. Fifteen years hence, the ratio will be 2 : 1. The present age of A is : 

Solution: 
Given that 
Ratio of age of A and B = 3 : 1 
Let
The ages of A and B be 3x and x, respectively.
Now
15 years hence,
Age of A = 3x + 15 and Age of B = x + 15. 

Now
(3x + 15)​/(x + 15) = 2/1 ​
3x + 15 = 2x + 30
3x - 2x = 30 - 15
x = 15
 ∴A's age =3 × 15 = 45 years

Question: Three unbiased coins are tossed. What is the probability of getting at most two heads ?

Solution: 
Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}

Let E = event of getting at most two heads 
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}

P(E) = n(E)/n(S)
     = 7/8

Question: What is the value of (log₁₀√7)/(log₁₀7)?

Solution: 
(log₁₀√7)/(log₁₀7) 
= log₁₀(7)^1/2/(log₁₀7)
= (1/2)log₁₀7/log₁₀7
= 1/2

Question: A man performs 3/5 of the total journey by rail , 7/20 by bus and the remaining 7.5 km on foot. His total journey should be- 

Solution:
Let the total journey be x km
Now 
(3x/5) + (7x/20) + 7.5 = x
7.5 = x - (3x/5) - (7x/20)
7.5 = (20x - 12x - 7x)/20
x/20 = 7.5
x = 7.5 × 20
x = 150

Question: If f(x) = (4x - 7)/(2x - 4) what is the value of f(-1/2)?

Solution: 
f(x) = (4x - 7)/(2x - 4)
 f(-1/2) = {4(-1/2) - 7}/{2(-1/2) - 4}
             = (- 2 - 7)/(- 1 - 4)
             = (- 9)/(- 5)
             = 9/5

Question: A sum of money at simple interest doubles in 7 years. It will becomes four times in: 

Solution: 
Case I
Let
Principal be x
Amount after 7 years = 2x
Simple interest = 2x - x = x
Interest = (x × r × 7)/100
⇒ r = 100/7 %
Case II
Amount = 4x
Interest = 4x - x = 3x

Time n₂ = (100 × 3x)/{x × (100/7)}
⇒ n₂ = 21 years

∴ The correct answer is 21 years.

Question: The least number which when divided by 12, 15, 20 and 54 leaves in each case a remainder of 7 is-

Solution: 
Required number 
=(L.C.M.of 12, 15, 20, 54) + 7 

12 = 2 × 2 × 3
15 = 3 × 5
20 = 2 × 2 × 5
54 = 2 × 3 × 3 × 3

L.C.M. =2 × 2 × 3 × 3 × 3 × 5 = 540
 
Required number 
= 540 + 7 
= 547

Question: The factors of 2a² + 3a- 2 are-

Solution: 
2a² + 3a - 2 
2a² + 4a - a - 2 
2a(a + 2) - 1(a - 2) 
(a + 2)(2a - 1)

Question: The diameter of a circle is equal to the perimeter of a square whose area is 484cm². What is the circumference of the circle?

Solution: 
Area of square = 484cm²
Side of squared = √484
                          = 22 cm
Perimeter of square :
= 4a
= (4 × 22) cm
= 88 cm
= diameter of circle

∴ Circumference of circle :
           =πd =88×π=88π cm

Question: If 4^{x - 3} = 16a^{x - 5} what is the value of x?

Solution: 
4^{x - 3} = 16a^{x - 5} 
⇒ 4^{x - 3}/16 = a^{x - 5}
⇒ 4^{x - 3}/4² = a^{x - 5}
⇒ 4^{x - 5} = a^{x - 5}
⇒ 4^{x - 5}/a^{x - 5}= 1
⇒ (4/a)^{x - 5} = (4/a)⁰
⇒ x - 5 = 0
∴ x = 5

Question: The average of first 40 natural number is -

Solution: 
We know that,
The sum of first n natural numbers is n(n+1)​/2

Sum of first 50 natural numbers is = 40(40 + 1)/2 = 820
Hence, the average of first 40 natural numbers is = 820/40 = 20.5

Question: The one- third of the Supplementary angle to 30° is - 

Solution:
We know that the sum of the supplementary angles is 180°
The Supplementary angle to 30° is = 180° - 30° = 150°
Now
150°/3 = 50°

Question: If a + b + c = 15 and a² + b² + c² = 83, what is the value of ab + bc + ca?

Solution: 
Given that 
a + b + c = 15 
a² + b² + c² = 83
We know
(a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
15² = 83 + 2(ab + bc + ca)
225 = 83 + 2(ab + bc + ca)
225 - 83 = 2(ab + bc + ca)
142 = 2(ab + bc + ca)
ab + bc + ca = 71

Question: A man can row at 5 kmph in still water. If the velocity of current is 1 kmph and it takes him 1 hour to row to a place and come back, how far is the place?

Solution: 
Speed downstream = (5 + 1) kmph = 6 kmph.

Speed upstream = (5 - 1) kmph = 4 kmph.

Let the required distance be x km.
Then,
(x/6) + (x/4) = 1
(2x + 3x)/12 = 1
5x/12 = 1
5x = 12
x = 2.4 km