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Sets — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSSets4 Marks
Question
In a library, 25 students read physics, chemistry and mathematics books. It was found that 15 students read mathematics, 12 students read physics while 11 students read chemistry. 5 students read both mathematics and chemistry, 9 students read physics and mathematics. 4 students read physics and chemistry and 3 students read all three subject books.

Based on the above information, answer the following questions.

  1. The number of students who reading only chemistry is:
  1. 5
  2. 4
  3. 2
  4. 1
  1. The number of students who reading only mathematics is:
  1. 4
  2. 3
  3. 5
  4. 11
  1. The number of students who reading only one of the subjects is:
  1. 5
  2. 11
  3. 8
  4. 6
  1. The number of students who reading atleast one of the subject is:
  1. 20
  2. 22
  3. 23
  4. 21
  1. The number of students who reading none of the subject is:
  1. 2
  2. 4
  3. 3
  4. 5
✓

Answer

Let M denotes set of student who reading mathematics books, P denotes who reading Physics books and C denotes who reading chemistry books.

we have,

$\text{n}(\text{U})=25,\text{n}(\text{M})=15,\text{n}(\text{P})=12,\text{n}(\text{C})=11,$ $\text{n}(\text{M}\cap\text{C})=5,\text{n}(\text{M}\cap\text{P})=9,\text{n}(\text{P}\cap\text{C})=4,\text{n}(\text{M}\cap\text{P}\cap\text{C})=3$

  1. (a) 5

Solution:

The number of students who reading only Chemistry is 5.

  1. (a) 4

Solution:

The number of students who reading only Mathematics is 4.

  1. (c) 8

Solution:

The number of students who reading only one of the subject is 4 + 5 + 2 i.e. 11.

  1. (c) 23

Solution:

The number of students who reading atleast one of the subject is 4 + 6 + 3 + 2 + 5 + 1 + 2 i.e. 23.

  1. (a) 2

Solution:

The number of students who reading none of the subject is 25 - 23 i.e. 2.

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