Bank Math Master

Question: 


Solution: 

Question: What will come at the place of the question mark?
1, 9, 25, 49, 81,?

Solution: 
1 = 1²
9 = 3² 
25 = 5²
49 = 7²
81 = 9²
121 = 11²

Question: What is the solution of x² - 5x + 6 < 0? 
 
Solution: 
x² - 5x + 6 < 0
⇒ (x - 2)(x - 3) < 0

The inequality will be true if x - 2 > 0 and x - 3 < 0.
x - 2 > 0
⇒ x > 2

x - 3 < 0
⇒ x < 3

The inequality will be true if  2 < x < 3.
The solution of the inequality is 2 < x < 3

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

প্রশ্ন: If 2x + (2/x) = 3,then x² + (1/x²) =?

সমাধান:
2x + 2/x = 3
⇒ 2(x + 1/x) = 3
⇒ x + 1/x = 3/2

এখন
x² + 1/x² = (x)² + (1/x)²
= (x + 1/x)² - 2.x.1/x
= (3/2)² - 2
= (9/4) - 2
= (9 - 8)/4
= 1/4

Question: Dog : Bark :: Goat : ?

Solution: 
The relationship between "Dog" and "Bark" is that a dog typically produces the sound "bark." In a similar manner, a sound often associated with a goat is "bleat." So, the analogy would be:

Goat : Bleat

Also,
Bray is a sound commonly associated with Donkey
"Grunt" is a sound commonly associated with pigs
"Howl" is a sound typically associated with wolves

Question: Average of 60 numbers are 42. When 5 more numbers are included, the average of 65 numbers become 45. Find the average of 5 numbers.

Solution:
Total of 60 numbers = 60 × 42 = 2520
Now, total of 65 numbers = 65 × 45 = 2925

Hence, sum of 5 numbers = 2925 - 2520 = 405

∴ Average of five numbers = 405/5
 = 81

Question: The average of 6 numbers is 7. The average of three numbers of them is 5. What will be the average of the remaining numbers?

Solution:
Average of 6 numbers = 7
Sum of 6 numbers = 6 × 7 = 42
Average of three numbers = 5
Sum of three numbers = 5 × 3 = 15

∴ Sum of the remaining three numbers = 42 - 15 = 27

∴ Required average = 27/3 = 9

Question: What is the probability of getting 53 Tuesdays in a leap year?

Solution: 
1 year = 365 days . A leap year has 366 days
A year has 52 weeks. Hence there will be 52 Tuesdays for sure.
52 weeks = 52 x 7 = 364 days
366 – 364 = 2 days

In a leap year there will be 52 Tuesdays and 2 days will be left.

These 2 days can be:
1. Sunday, Monday
2. Monday, Tuesday
3. Tuesday, Wednesday
4. Wednesday, Thursday
5. Thursday, Friday
6. Friday, Saturday
7. Saturday, Sunday

Of these total 7 outcomes, the favourable outcomes are 2.

Hence, the probability of getting 53 days = 2/7

Question: If x : y = 15 : 4 then the value of (x - y)/(x + y) is- 

Solution: 
x : y = 15 : 4
⇒ x/y = 15/4
⇒ (x + y)/(x - y) = (4 + 15)/(15 - 4)
⇒ (x + y)/(x - y) = 19/11
⇒ (x - y)/(x + y) = 11/19

Question: 1 + 0.1 + 0.01 + 0.001 +......... =? 

Solution: 
1 + 0.1 + 0.01 + 0.001 +......... 
= 1 + (1/10) + (1/100) + (1/1000) +....

প্রথম পদ a = 1
সাধারণ অনুপাত r = 1/10

সমষ্টি = a/(1 - r)
= 1/{1 - (1/10)}
= 1/9/10
= 10/9

Question: A coin is tossed thrice. What is the probability of getting T zero number of times? 

Solution: 
Total ways = 2³ = 8
Ways getting T zero number of times = 1 (HHH)

∴ Probability = 1/8

Question: In an examination, 80% of candidates passed in English, and 85% of candidates passed in Mathematics. If 73% of candidates passed in both these subjects, then what percent of candidates failed in both subjects?

Solution: 
Students passed in English = 80%
Students passed in Math = 85%
Students passed in both subjects = 73%
Then, the number of students who passed in at least one subject
= (80 + 85) - 73
= 92%

Thus, students failed in both subjects = 100 - 92
= 8%

Question: If in a certain language, SISTER is coded as 535301, UNCLE is coded as 84670, and BOY as 129, how son is coded?

Solution: 
S → 5
O → 2
N → 4

Son is coded as 524 

Question: If a³ - b³ = 56 and a - b = 2, then the value of a² + b² =? 

Solution: 
a³ - b³ = 56
⇒ (a - b) (a² + ab + b²) = 56
⇒ a² + ab + b² = 56/2 = 28
⇒ (a - b)² + 3ab = 28 
⇒ 3ab = 28 - 4 = 24 
⇒ ab = 24/3 = 8

a² + ab + b² = 28
⇒ a² + b² = 28 - 8 = 20