প্রবাসী কল্যাণ ব্যাংকে লিখিত পরীক্ষার প্রশ্ন সমাধান ‘অফিসার ক্যাশ’ পদের, প্রবাসী কল্যাণ ব্যাংক (পিকেবি) অফিসার (ক্যাশ) পদের নিয়োগ পরীক্ষার প্রশ্ন ও সমাধান,প্রবাসী কল্যাণ ব্যাংক অফিসার (ক্যাশ) পদের পরীক্ষার প্রশ্ন সমাধান,

প্রবাসী কল্যাণ ব্যাংকে ‘অফিসার (ক্যাশ)’ পদের [২০১৯ সাল ভিত্তিক] লিখিত পরীক্ষার প্রশ্ন সমাধান

শুধুমাত্র গণিত অংশের সমাধান দেয়া হল বাকিটা নিচ থেকে প্রশ্ন দেখে নিন।

PKB (Cash)
2-11-2021
Written Math
Solved By: Shuvo Sarker Slokh

Q-1■.A sum of money becomes eight times in 3 years, if the rate is compounded annually. In how much time will the same amount at the same compound rate become sixteen times?
———-
Let , Capital be Tk 1 .
Now , P : (P+I) = 1 : 8 = 1 : 2^3
P : (P+I) = 1 : 16 = 1 : 2^4
So , In 4 years it will be 16 Times (Ans)
Q-2■M =7-4√3 হলে √M+1/√M=?
—————-
Here , m = 7-4√3
So , 1/m = 7+4√3 [ By Subtraction & Addition]
ie , m + 1/m = 14 —(1)
Now ,
(√M+1/√M)^2 = m + 1/m + 2 = 14+2 = 16
=> √M+1/√M = 4 (Ans)

Q-3■In a cricket match, Team A scored 232 runs without losing a wicket. The score consisted of byes, wides and runs scored by two opening batsmen: Ram and Shyam. The runs scored by the two batsmen are 26 times wides. There are 8 more byes than wides. If the ratio of the runs scored by Ram and Shyam is 6:7, then the runs scored by Ram is
——————–
Let , Byes = X , Wides = Y & Run = Z
Run (Z) = 26Y
Byes (X) = Y+8
Now , 26Y + Y + Y+8 = 232
=> 28Y = 224
=> Y = 8
Run = 26×8 = 208
So , Run scored by Ram = 208×6/13 = 96 (Ans).

Q-4■Q.After travelling 108 km, a cyclist observed that he would have required 3 hours less if he could have traveled at a speed 3 km/hr more. At what speed did he travel?
————-
Let , His speed be X km/hr
New , Speed = (X+3)km/hr
A/Q ,
108/X+3 – 108/X = 3
=>3X^2 + 9X- 324 = 0
=> X^2 + 3X – 108 = 0
=> (X+12)(X-9) = 0
=> X = 9
So , Speed 9 km/hr (Ans).

Q-5■A hall is 15m long and 12m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of the 4 walls, what is the volume of the hall?
———–
Let , Length = L , Broad = B & Height = H
A/Q ,
Area of Hall + Area of ceilling = Area of four walls
=> LB + LB = 2 (L+B) H
=> 15×12 + 15×12 = 2 (15+12) H
=> 360 = 2×27×H
=> H = 360/54 = 20/3
So , Volume of the hall = LBH = 15 × 12 × 20/3 = 1200 m^2 (Ans)

Q-6■Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in 3 hours and the other in 4 hours. At what time should the candles be lit so that at 4 PM, one stub is twice the length of the other?
————-
Let , Height = 12 inches (LCM of 3&4)
and X the number of hours it takes the first candle, to be twice the height of the second candle.
A/Q ,
12 – 3X = 2(12 – 4X)
=> 12 – 3X = 24 – 8X
=> 5X = 12
=> X = 12/5 = 2.4 hours or 2 h 24 m
Time = 4-2h 24 m at 1.36 pm (Ans)

Q-7■Q.A group of students has hired a bus for tk 3000 for going to a picnic.They understanding that each participant would share the charge in equal amounts. But because of 10 Students not turning up, the charged per student increased by tk 10 over the initial estimates. what was the number of students who originally registered for the picnic?
————
Let , X student registered for the picnic .
So , Cost per head = 3000/X
Because of 10 students turning up , new cost = 3000/X-10
A/Q,
3000/X-10 – 3000/X = 10
=> X^2 – 10X – 3000 = 0
=> X^2 – 60X + 50X – 3000 = 0
=> (X-60)(X+50) = 0
=> X = 60
So , Registered for the picnic 60 students (Ans)

প্রবাসী কল্যাণ ব্যাংক এর অফিসার (ক্যাশ) পদের নিয়োগ পরীক্ষার প্রশ্ন ও সমাধান ২০২১
Probashi Kallyan Bank (PKB) Officer (Cash) Exam Question and Solution 2021
পদের নামঃ অফিসার (ক্যাশ)

বাংলা অংশের সমাধানঃ

১. কাজী নজরুল ইসলাম রচিত উপন্যাস নয় কোনটি? উত্তর: শিউলিমালা

২. ‘রেনেসাঁস’ শব্দটি কোন ভাষা থেকে বাংলায় এসেছে? উত্তর: ফরাসি (‘রেনেসাঁস’ অর্থ পুনর্জন্ম বা পুনর্জাগরণ বা নবজাগরণ)

৩. নিচের কোনটি মুক্তিযুদ্ধভিত্তিক উপন্যাস নয়? উত্তর: আরেক ফাল্গুন ( জহির রায়হান এর আরেক ফাল্গুন ভাষা আন্দোলনের উপরে রচিত। ১৯৫৫ সালের ২১শে ফেব্রুয়ারী পালনের গল্প )

৪. ‘Agora’ শব্দের বাংলা পরিভাষা- উত্তর: সঠিক উত্তর নেই (সঠিক উত্তর মুক্তাঞ্চল)

৫. ‘রোহিনী’ কোন উপন্যাসের নায়িকা? উত্তর:কৃষ্ণকান্তের উইল ( বঙ্কিমচন্দ্র চট্টোপাধ্যায় রচিত কৃষ্ণকান্তের উইল উপন্যাসের নায়িকা রোহিনী)

৬. বাংলা ভাষা নিচের কোন ভাষাগোষ্ঠীর অন্তর্ভুক্ত? উত্তর: ইন্দো-ইউরোপীয়

৭. নিচের কোনটি বিষমীভবনের উদাহরণ? উত্তর: লাল>নাল (পাশাপাশি একই ব্যঞ্জনধ্বনি দু’বার থাকলে তাদের একটি পরিবর্তন হলে তাকে বিষমীভবন বলে)

৮. ‘নবনবতিতম’ কোন সংখ্যার পূরণবাচক সংখ্যাশব্দ? উত্তরঃ ৯৯

৯. ‘যেমন কর্ম তেমন ফল’। – কোন পদের উদাহরণ? উত্তর: সাপেক্ষ সর্বনাম

১০. প্রতিশব্দ নয়? উত্তর: উদক

১১. ‘বীরাঙ্গনা কাব্য’ গ্রন্থে মোট কয়টি পত্র সংকলিত আছে? উত্তর: ১১

১২. বাংলা সাহিত্যে ‘ভোরের পাখি’ নামে পরিচিত? উত্তর: বিহারীলাল চক্রবর্তী

১৩. After meat comes musterd- এর সঠিক বঙ্গানুবাদ? উত্তর: নুন আনতে পান্তা ফুরায়

১৪. ‘অনতিবৃহৎ বনে মৃগ অনুসন্ধান ও সংহার করা সাতিশয় ‍দুঃসাধ্য কার্য’। উত্তর: আটটি

১৫. ‘ভার্যা’ র বিপরীত শব্দ কোনটি? উত্তর: দয়িত [দার অর্থ= পত্নী, স্ত্রী /দয়িত অর্থ=প্রিয়পাত্র, কমনীয়, ভালবাসার পাত্র /বনিতা অর্থ=ভার্যা, পত্নী/ ভার্যা শব্দের অর্থ জায়া, পত্নী]

১৬. নিচের কোনটি সমার্থক নয়? উত্তর: গোফ খেজুরে -কাছাঢিলা [‘কাছা-ঢিলা’ বাগধারার অর্থ = অসাবধান । আর ‘গোঁফ খেজুরে’ বাগধারার অর্থ= নিতান্ত অলস)]

ইংরেজি অংশের সমাধানঃ

১৭. What is the masculine gender of `filly’? উত্তর: colt

১৮. Choose the phrase that best retains the meaning of the selected phrase in the sentence. Despite being a brilliant professor, he does not seem to `get his ideas across.? উত্তর: make his ideas understood.

১৯. Identify the correct sentence- উত্তর: She had faith in and hopes for the future.

২০. `No man is an island’ What does the proverb means? উত্তর: your own home is the best comfortable place to live in.

২১. `The expression, `Time after twilight and before night.’ can be substituted by the word- উত্তর: dusk

২২. Identify similar relationship expressed in the pair: `conscious: careless’. উত্তর: careful : indifferent

২৩. A lyric poem mourning for the death of an individual is called____. উত্তর: elegy

২৪. ‘Frailty, thy name is woman’. Here ‘frailty’ is ___ . উত্তর: a noun

২৫. In English grammar,___ deals with formation of sentences. উত্তর: Noun

২৬. Give me to drink, ___ I shall die of thirst. উত্তর: syntax

২৭. Change the voice: ‘They are going to sell the market’. উত্তর: The market is going to be sol by them

২৮. Change the sentence into Compound: “To his eternal disgrace, he betrayed his country. উত্তর: He betrayed his country and it was his eternal disgrace.

২৯. I don’t like horror films, and you?___ I can’t sleep after seeing such films. I like fantastic films. ___ I’ve got some at home. উত্তর: Neither do I/ So do I

৩০. We arrived Lisbon 6 p.m. a foggy November day. উত্তর: in/at/on

৩১. We didn’t know that he ___ from the University in 2010 and then ___ abroad. উত্তর: had graduated/worked

৩২. Identify the indirect form of the sentence: He said. “You had better see a doctor”- উত্তর: He advised him to see a doctor.

গণিত অংশের সমাধানঃ

[Q-33] Rani can walk a certain distance in 40 days when he take rests 9 hours a day. How long will he take to walk twice the distance, twice as fast and rest twice as long each day?
#Solution:
Let
Speed = 1km/hr
Rest 9 hr a day mean walk per day =(24-9)= 15 hr
So, Distance Cover = 15 km
Total Distance= 40×15= 600 km
Twice the distance means = 600×2= 1200 km
Speed = 2 km/hr
Rest = 9×2= 18 hr
So per day walk = (24-18)×2= 12 km
Time Req. = 1200/12 = 100 day[Answer.]

[Q-34] A takes 2 hours more than B to walk d km. If A doubles his speed, then he can make it in 1 hour less than B. How much time does B require for walking d km?
#Solution:
Speed Ration of A:A1= 1:2
Time Ration = 2:1
Now (2-1)==3
=> 1= 3
=> 2= 6
So Time Req for B = 6-2= 4 hr[Ans]

[Q-35] A computer Take 50 nano seconds to do an addition. How many addition can it do in
1 seconds?
#Solution:
50 Nanosecond = 50×10^(-9) Sec
In 1 Sec = 1/(50×10^(-9)
= 1/(5×10×10^-9)
= 1/(5×10^-8)
= 10^8×1/5= 0.2×10^8= 2×10^7= 2 billon[Ans]

[Q-36] A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of june beginning with a Sunday is:
#Solution:
There is Five sundays and 25 other days= 5×510 + 240×25[ June month consist of 30 days]
= 8550 Visitor
Avg. No of Visitors per day= 8550/30= 285[Ans]

[Q-37] A gardener has to plant trees in rows containing equal number of trees. If he plants in rows of 6, 8, 10 or 12 then five trees are left unplanted. But if he plants in rows of 13 trees each, then no tree is left. What is the number of trees that the gardener plants ?
#Solution:
LCM of 6,8,10,12= 120
The number Is = (120M+5)/13
When M = 7; Then (120M+5) is divisible by 13
Alternative:
Option Test : 845/13= 65; Divisible by 13

[Q-38] In a simultaneous throw of two dice what is the probability of getting a doublet ?
#Solution:
Total Number of Events = 6×6= 36
Getting Doublet = (6,6),(5,5),(4,4),(3,3),(2,2),(1,1)
So Probability of getting Doublet = 6/36= 1/6[Ans]

[Q-39] Two numbers are in the ratio 3:4. The LCM is 84. What is the greater number?
#Solution:
Ration of Two number = 3:4
So The Greater Number is = 84×4/12= 28[Ans]

[Q-40] If the selling price is double the profit is treble. Find the profit percent?
#Solution:
Let CP = CP
ATQ,
2SP-CP= 3P
And, SP-CP= P
=>3SP-3CP=3P
So, 3SP-3CP= 2SP-CP
=> 2CP=SP
=> CP:SP= 1:2
So Profit percent =100/1=100%[Ans]

[Q-41] what will be the difference of SI & CI at 10% on sum of TK 5000 after 5 years?
#Solution:
Diff. = 5000×(11/10)^5-5000×(1/10)×5-5000= 552[Ans]

[Q-42] If one star equals four circles and three circles equal four diamonds, then what is the ratio of star:diamond?
#Solution:
Star= 4×Circle
=> Star:Circle=4:1=16:4
And
3×Circle= 4×Diamond
=>Circle:Diamond= 4:3=4:3
Ration of Star:Diamond=16:3[Ans.]

[Q-43] If Q/P= 3/4; what is the value of (P+Q)/(P-Q)
#Solution:
Here, Q/P=1/4
=> P=4Q
Now, (4Q+Q)/(4Q-Q) = (5/3)[Ans.]

[Q-44] What is the sum of two consecutive even numbers, the difference of whose squares is 84?
#Solution:
Let The number be x & y
Here, x^2-y^2= 84
=> (y+2)^2-y^2=84
=> y^2+4y+4-y^2= 84
=> 4y= 80
=> y= 20
So, another number is =20+2= 22
So, Sum of two number = 22+20= 42[Ans]

[Q-45] One-fifth of a number is equal to 5/8th of another number. If 35 is added to the first number, it becomes four times of the second number. What is the second number?
#Solution:
A/5= 5B/8
=> 8A= 25B
=> A:B= 25:8
ATQ,
25x+35= 4×8x
=> 7x= 35
=> x= 5
So, The 2nd Num. Is = 8×5=40[Ans.]
Alternative:
A/5= 5B/8
=> 8A= 25B
=> A:B= 25:8
Now, (25-8)=35
=> 7= 35
=> 8= 40=Ans.

Q-46] Which is the correct Factor analysis x^2-2xy-z^2+ 2yz
#Solution:
x^2-2xy+y^2-(y^2+z^2+2yz)
= (x-y)^2-(y-z)^2
= (x-y+y-z)(x-y-y+z)
=(x-z)(x-2y+z)
[Q-47]x^3-0.001= 0, then Find x^2=?
#Solution:
x^-3= 0.001
=> x= 10
x^2= 100[Ans.]

[Q-48]If P is a point lying on line segment AB. Which of the following is true for all of the Time?
Ans. AB>AP

[Q-49] How many degrees does a minute hand move of 20 min?
#Solution: 1min= 6°
=> 20 min= 120°[Ans.]

[Q-50] If a, b, c are the length of a side of triangle then which of the following is true?
Ans. Option C ; A-B (1/5)^3y= (1/5)^3
=> y=1
Then (1/4)^1= 1/4 [Ans.]

Q-54] what is the value of 0.001/0.1×0.1
#Solution:
0.001/(0.1×0.1)= (1/1000)/(1/100)= 100/1000=1/10[Ans.]

[Q-55] If x-y= 3 then what is the value of x^3-y^3-9xy
#Solution:
x^3-y^3-9xy= (x-y)^3-3xy(x-y)-9xy= (3)^3
= 27[Ans.]

[Q-56] After getting two successive discounts a shirt with a list price of Rs. 150 is available at Rs. 105. If the second discount is 12.5%, find the first discount.
#Solution:
150×(100-x)%×87.5%= 105
=> 150×(100-x)%×7/8= 105
=> (15000-150x)×7= 84000
=> 105000-1050x= 84000
=> x= 20%[Ans.]

GK and Computer Part Solution:

৫৭. Which is the largest Rohingya refugee camp in Bangladesh? উত্তরঃ Kutupalong [কক্সবাজার]

৫৮. Who were known as ‘Bargi’ in Bengal history? উত্তরঃ Marathas [মারাঠা

৫৯. Which is the most risky zone of earthquake is Bangladesh? উত্তরঃ North-east zone [সিলেট এলাকা]

৬০. Who is the current Vice President of the USA? উত্তরঃ Kamala Harris [মহিলা হিসেবে ১ম আর ৪৯ তম ভাইস প্রেসিডেন্ট]

৬১. As per the latest changes in the Bengali Calendar, leap year is calculated in months. উত্তরঃ Falgun [Generally Falgun 29 days but 30 days in a leap year]

৬২.‘CEDAW’ id an UN convention related to the? – উত্তরঃ Rights of women

৬৩. When was the first case of COVID-19 confirmed in Bangladesh? উত্তরঃ 8 March 2020 [First dead in Bangladesh 18 March 2020]

৬৪. The Padma Bridge Stretches from- উত্তরঃ Munshiganj to Shariatpur [,মাওয়া থেকে জাজিরা]

৬৫. St. Martin Island is a-উত্তরঃ Union [সেন্টমার্টিন বাংলাদেশের কক্সবাজার জেলার অন্তর্গত টেকনাফ উপজেলার একটি ইউনিয়ন]

৬৬. Who has designed the logo of Mujib Year? উত্তরঃ Sabyasachi Hazra

৬৭. Which ethnic people constitute the world’s largest population? উত্তরঃ Han (চীন) [বিশ্ব জনসংখ্যার প্রায় ২০%]

৬৮. Which country has the longest national anthem in the world? উত্তরঃ Greece [গ্রীস]

৬৯. The length of Dhaka Metro Rail will be-উত্তরঃ 20.10 km [প্রায় ১২.৫ মাইল]

৭০. Which is the largest Muslim ethnic group in China? উত্তরঃ Hui [২য় উইঘুর]

৭১. Which desert is the driest in the world? উত্তরঃ Atacama Desert [আতাকামা মরুভূমি, এটি দক্ষিণ আমেরিকায় অবস্থিত]

৭২. Which country will host ‘World Cup U-19’ in 2022? উত্তরঃ সঠিক উত্তর নাই [সঠিক উত্তর West Indies]

৭৩. Ctrl, Shift and Alt are called ____keys. উত্তরঃ Modifier keys

৭৪. Which one of the following is a loop construct that will always be executed once? উত্তরঃ do while

৭৫. Which input values will cause an AND logic gate to produce a HIGH output? উত্তরঃ All inputs are HIGH

৭৬. Which of the following is not a valid IPV4 Address? উত্তরঃ 10.145.17.256 [256 is not a valid number in an IPv4 address]

৭৭. Consider that 5 computers are connected through mesh topology in a computer network. What are the number of connection lines needed if we want to add 2 more computers in the network? উত্তরঃ 11 [Formula n(n-1)/2] তাহলে ৭(৭-১)/২ = ২১, আগের ৫ টার জন্য ১০ টা আর নতুন ২ টার জন্য ১১ টা]

৭৮. Which of the following operating systems is an open-source software? উত্তরঃ Fedora 20

৭৯. What is the correct HTML tag for columns in a table? উত্তরঃ

৮০. USB is —– storage device. উত্তরঃ Secondary