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CUET PG 2021 — Mathematics PYQ

CUET PG | Mathematics | 2021

In a room containing 28 people, there are 18 people who speak English, 15 people who speak Hindi and 22 people who speak Kannada, 9 people speak both English and Hindi, 11 people speak both Hindi and Kannada whereas 13 people speak both Kannada and English. How many people speak all the three languages?

Choose the correct answer:

A.
6
(Correct Answer)
B.
7
C.
8
D.
9

Correct Answer:

Explanation

Formula:

Teeno sets ke liye formula hota hai:

n(E \cup H \cup K) = n(E) + n(H) + n(K) - [n(E \cap H) + n(H \cap K) + n(K \cap E)] + n(E \cap H \cap K)

Solution:

Ab values ko formula mein rakhte hain:

28 = 18 + 15 + 22 - (9 + 11 + 13) + n(E \cap H \cap K)

Pehle brackets aur addition ko solve karte hain:

28 = 55 - 33 + n(E \cap H \cap K)

28 = 22 + n(E \cap H \cap K)

Ab $n(E \cap H \cap K)$ nikalne ke liye:

n(E \cap H \cap K) = 28 - 22

n(E \cap H \cap K) = 6

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Explanation

Formula:

Teeno sets ke liye formula hota hai:

$n(E \cup H \cup K) = n(E) + n(H) + n(K) - [n(E \cap H) + n(H \cap K) + n(K \cap E)] + n(E \cap H \cap K)$

Solution:

Ab values ko formula mein rakhte hain:

$28 = 18 + 15 + 22 - (9 + 11 + 13) + n(E \cap H \cap K)$

Pehle brackets aur addition ko solve karte hain:

$28 = 55 - 33 + n(E \cap H \cap K)$

$28 = 22 + n(E \cap H \cap K)$

Ab $n(E \cap H \cap K)$ nikalne ke liye:

$n(E \cap H \cap K) = 28 - 22$

$n(E \cap H \cap K) = 6$