Question: In a class, 30 students play basketball, 20 students play volleyball, and 8 students play both. 12 students play neither basketball nor volleyball. What is the total number of students in the class?

​​Solution:

Number of students who play basketball, n(B) = 30

Number of students who play volleyball, n(V) = 20

Number of students who play both basketball and volleyball, n(B ∩ V) = 8

Number of students who play neither = 12

n(B ∪ V) = n(B) + n(V) - n(B ∩ V)

= 30 + 20 - 8 = 42

Total students in the class = students who play basketball or volleyball + students who play neither

n(U) = n(B ∪ V) + neither = 42 + 12 = 54

∴ Total 54 students in the class.

প্রশ্ন: f(x) = x3 + kx2 - 4x - 8 হয়, তাহলে k-এর কোন মানের জন্য f(- 2) = 0?

সমাধান: 
দেওয়া আছে, 
f(x) = x3 + kx2 - 4x - 8
∴ f(- 2) = (- 2)3 + k (- 2)2 - 4(- 2) - 8 
⇒ f(- 2) = - 8 + 4k + 8 - 8 
 ⇒ f(- 2) = 4k - 8 

যেহেতু, 
f(- 2) = 0 
 ⇒ 4k - 8 = 0
 ⇒ 4k = 8
 ⇒ k = 8 /4
 ⇒ k = 2

প্রশ্ন: 16{n - (1/2)} = 64 হলে, n এর মান কত?

সমাধান:
16{n - (1/2)} = 64
⇒ (24){n - (1/2)} = 26
⇒ 2{4n - (4/2)} = 26
⇒ 2(4n - 2) = 26
⇒ 4n - 2 = 6
⇒ 4n = 6 + 2
⇒ 4n = 8
⇒ n = 8/4
⇒ n = 2