ব্যাংক নিয়োগ প্রস্তুতি ⎯ লং কোর্স

Question: On dividing 15968 by a certain number, the quotient is 89 and the remainder is 37. The divisor is -

Solution: 
Divisor = (Dividend - Remainder)/ Quotient
= (15968 - 37)/89
= 15931/89
= 179

Question: Find the average of the first 20 natural numbers.

Solution:
প্রথম ২০ টি স্বাভাবিক সংখ্যার সমষ্টি = ২০(২০ + ১)/২
= ২১০

∴ গড় = ২১০/২০ = ১০.৫

Question: A man is 22 years older than his son. In three years, his age will be three times the age of his son. The present age of his son is -

Solution: 
ধরি,
পুত্রের বর্তমান বয়স = ক
পিতার বর্তমান বয়স = (ক + ২২)

প্রশ্নমতে,
(ক + ২২ + ৩) = ৩(ক + ৩)
ক + ২৫ = ৩ক + ৯
২ক = ১৬
ক = ৮

Question: If 7¹²⁶ is divided by 48, find the reminder.

Solution:
7¹²⁶ = (7²)⁶³ = 49⁶³
we know that, (xⁿ - aⁿ) is divisible by (x - a) for all values of n.
so,
(49⁶³ - 1) is divisible by (49 - 1) or, 48.

∴ remainder when divided by 48 is 1

Question: If x + 1/x = 6; find the value of 3x/(6x² - 5x + 6)?

Solution: 

Question: An amount of money was divided among 3 boys in such a way that the first boy was given twice the third boy and the second boy was given equal to third boy. If the average is 400 Taka. How much was the first boy given?

Solution: 
ধরি,
তৃতীয় বালক পায় = ক টাকা
∴ প্রথম বালক পায় = ২ক টাকা

প্রশ্নমতে,
(২ক + ক + ক)/৩ = ৪০০
৪ক/৩ = ৪০০
ক = ৩০০ টাকা

∴ প্রথম বালক পায় = ২ × ৩০০ = ৬০০ টাকা।

Question: The sum of the place values of 1 in the number 3510011 is -

Solution: 
সখ্যাটিতে ১ আছে ৩টি অবস্থানে।
৩৫১০০১১ এর স্থানীয় মান = ১
৩৫১০০১১ এর স্থানীয় মান = ১০
৩৫১০০১১ এর স্থানীয় মান = ১০০০০

∴ যোগফল = ১০০০০ + ১০ + ১
= ১০০১১

Question: The total age of two friends is 40. 5 years back their age ratio was 7 : 8. In 5 years what will be the ratio of their age?

Solution:
let, 5 years back their age was 7x and 8x
∴ 7x + 8x = 30
x = 2

after five years their age ratio will be (7 × 2 + 10) : (8 × 2 + 10)
= 24 : 26
= 12 : 13

Question: The average of 21 numbers is 16. The average of the first 10 of those is 14 and the average of last 10 numbers is 17. What is the 11th number?

Solution:
Total sum of result = (21 × 16) = 336
sum of first 10 results = (10 × 14) = 140
sum of last 10 results = (10 × 17) = 170

11th number= 336 - 140 - 170
= 26

Question: Which of the following is prime number?

Solution:
১৪৩ সংখ্যাটি ১১ দ্বারা বিভাজ্য।
২৮৯ সংখ্যাটি ১৭ দ্বারা বিভাজ্য।
১১৭ সংখ্যাটি ৩ দ্বারা বিভাজ্য।
৩৫৯ সংখ্যাটি ১ ও ৩৫৯ ছাড়া অন্য কোনো সংখ্যা দ্বারা বিভাজ্য নয়। তাই ৩৫৯ একটি মৌলিক সংখ্যা।

Question: Find the roots of 2x² - 18x = 180.

Solution: 
2x² - 18x = 180
2x² - 18x - 180 = 0
2x² - 30x + 12x - 180 = 0
2x(x - 15) + 12(x - 15) = 0
(x - 15)(2x + 12) = 0

either,
x - 15 =0
x = 15

or,
2x + 12
x = - 6

Question: If a + 9/a = 6; what is the value of (a² + 9/a²)?

Solution: 
(a + 9/a)² = (6)²
a² + 81/a² + 18 = 36
a² + 81/a² - 18 = 0
(a - 9/a)² = 0
a - 9/a = 0
a = 9/a
a² = 9

so, 
(a² + 9/a²) = 9 + 9/9 = 10

Question: Three numbers are in ratio 1 : 3 : 4 and HCF is 12. The numbers are -

Solution: 
ধরি,
সংখ্যা তিনটি x, 3x, 4x.
গ.সা.গু = x

∴ x = 12

সংখ্যাগুলো = 12, 36, 48.

Question: If x - 1/x = 4; what is the value of x + 1/x?

Solution: 
(x - 1/x)² = (4)²
x² + 1/x² - 2 = 16
x² + 1/x² = 18
x² + 1/x² + 2 = 18 + 2
(x + 1/x)² = 20
x + 1/x = √20
x + 1/x = 2√5

Question: If a/b = 2/3 and b/c = 4/5 what is the value of (a + b)/(b + c)?

Solution:
a/b = 2/3
b/c = 4/5

Question: Find the least number which will leave remainder 5 when divided by 8, 12, 16 and 20.

Solution: 
We have to find the Least number; therefore we find out the LCM of 8, 12, 16 and 20.
8 = 2 × 2 × 2;
12 = 2 × 2 × 3;
16 = 2 × 2 × 2 × 2;
20 = 2 × 2 × 5;
LCM = 2 × 2 × 2 × 2 × 3 × 5 = 240;
This is the least number which is exactly divisible by 8, 12, 16 and 20.
Thus,
Required number which leaves remainder 5 is,
240 + 5 = 245

Question: The product of two co-prime numbers is 442. Then their LCM is =?

Solution: 
HCF of co-prime number is always 1
∴ Let number are = x & y respectively
Product of number = xy
xy = 442 (given)
∴ Product of number = LCM × HCF
⇒ LCM × 1 = 442
⇒ LCM = 442

Question: If A591 is divisible by 11, find the value of the smallest natural number A?

Solution:
কোন সংখ্যা ১১ দ্বারা বিভাজ্য হবে যদি তার জোড় স্থানীয় অংক গুলোর সমষ্টি এবং বিজোড় স্থানীয় অংকগুলোর সমষ্টির পার্থক্য ০ হয় বা ১১ দ্বারা বিভাজ্য হয়।

অর্থাৎ,
(A + 9) - (5 + 1) = 0 বা, 11 দ্বারা বিভাজ্য হবে।
A এর মান 8 হলে, এটি 11 দ্বারা বিভাজ্য হবে।
A এর মান -3 হলে, সমষ্টি 0 আসবে তখনও 11 দ্বরা বিভাজ্য হবে।

কিন্তু -3 স্বাভাবিক সংখ্যা না তাই উত্তর 8 হবে।

∴ A এর মান 8 হলে সংখ্যটি 11 দ্বারা বিভাজ্য হবে।

Question: The average marks of four subjects is 120. If in one subject 33 was misread as 13 during the calculation, what would be the correct average?

Solution:
The average given is 120.
Difference of 33 and 13 is 20.
That means 20 must be added to the total.
Then the average of is and so must be added to average, i.e.
Correct average = 120 + 5 = 125

Question: 5 years ago, a man aged 28 got married. after 2 years, a baby child was born. What is the age ratio of the baby and father at present?

Solution:
the present age of the children is 3 years
the present age of the father is 33 years

so, the ratio is = 3 : 33
1 : 11

Question: Ten years ago, the average age of A, B, C and D was 40 yr. with E joining them now, the average of all the five is 49 yr. How old is E?

Soultion: 
Total present age of A, B, C and D
= (40 + 10) × 4
= 200 years
Total age present age of A, B, C, D and E
= 49 × 5
= 245 years
So, Age of E = 45 years

Question: Sum of three consecutive even integers is 60. Find the least integer among them.

Solution: 
x + (x + 2) + (x + 4) = 60
3x + 6 = 60
3x = 54
x = 18

Question: If (3x + 5y)/(3x - 5y) = 4; what is the value of x/y?

Solution: 
given,
(3x + 5y)/(3x - 5y) = 4
3x + 5y = 4(3x - 5y)
3x + 5y = 12x - 20y
5y + 20y = 12x - 3x
25y = 9x
x/y = 25/9

Question: The average of the first five multiples of 7 is- 

Solution:
the first five multiples of 7, 14, 21, 28, 35

the average is = (7 + 14 + 21 + 28 + 35)/5
= 21

Question: David obtained 76, 65, 82, 67 and 85 marks (out of 100) in English, Bangla, physics, chemistry and biology. What are his average marks in the subjects of science?

Solution:
Science Subjects are Physics, Chemistry, Biology.

the average of these subjects = (82 + 67 + 85)/3 = 78

Question: Find the quadratic polynomial if the roots are 4 and 5.

Solution: 
Hence the roots are 4 and 5. 
so, the quadratic polynomial is 
(x - 4)(x - 5)
= x² - 4x - 5x + 20
= x² - 9x + 20

Question: If x = 0.5 and y = 0.2, then the value of √0.8 × (4y)^x is equal to?

Solution: 
x = 0.5
y = 0.2

√0.8 × (4y)^x
= √0.8 × (4 × 0.2)^0.5
= √0.8 × √0.8
= 0.8

Question: The average run of a cricket player of 10 innings was 35. How many runs must be made in his next innings so as to increase his average of runs by 5?

Solution: 
Average after 11 innings = 35 + 5 = 40
Required number of runs,
= (40 × 11) - (35 × 10)
= 440 - 350
= 90

Question: If x * y = x² + y² - xy, then the value of 13*2 is?

Solution: 
 13*2 = (13)² + (2)² - (13 × 2)
= 169 + 4 - 26
= 147

Question: The average of 20 numbers is 35. If two numbers, 40 and 50 are discarded, then the average of the remaining numbers is nearly -

Solution:
Sum of 20 numbers = (20 × 35) = 700

after discarding 2 numbers of 40 and 50 the new average is = (700 - 40 - 50)/18
= 33.89

Question:  If f(x) = 3x² + bx + 4 and f(- 1) = 0; Then b = ?

Solution:
f(x) = 3x² + bx + 4 
∴ f(- 1) = 3(- 1)² + b(- 1) + 4
= 3 - b +4
= 7 - b 

A.T.Q,
7 - b = 0
∴ b = 7