Comprehension

निर्देश: निम्नलिखित वेंन आरेख पर विचार कीजिए, जहाँ X, Y और Z तीन समुच्चय हैं। मान लीजिए Z में तत्वों की संख्या को n(Z) द्वारा दर्शाया गया है जो 90 के बराबर है। 

F1 Aman.K 07-09-2020 Savita D1

यदि Y और Z में तत्वों की संख्या 4 : 5 के अनुपात में हैं तो b का मान क्या है?

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NDA (Held On: 6 Sep 2020) Maths Previous Year paper
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  1. 18
  2. 19
  3. 21
  4. 23

Answer (Detailed Solution Below)

Option 3 : 21
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Detailed Solution

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संकल्पना:

दिया गया है: n(Z) = 90 और Y और Z में तत्वों की संख्या 4 : 5 के अनुपात में हैं। 

निम्न का मान ज्ञात करने के लिए: b = ?

F1 Aman.K 07-09-2020 Savita D1

n(Y) = 16 + 18 + 17 + b

n(Z) = 12 + 18 + 17 + c = 90 

 

\(\rm \frac{n(y)}{n(z)}=\frac{16+18+17+b}{12+18+17+c}=\frac{4}{5}\\ \Rightarrow \frac{51+b}{90}=\frac{4}{5}\\ \Rightarrow (51+b)\times 5=360 \\\Rightarrow255+5b=360\\ \Rightarrow5b=105\\ \Rightarrow b=21\)

अतः विकल्प (3) सही है। 

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