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Mathematics Derivations of formulas and their connections MCQ Questions for Class 11 General

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Question 271/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (7) लड़कों और (6) लड़कियों में से (3) लड़के तथा (2) लड़कियाँ चुननी हों, तो formula कौन-सा है?

If (3) boys and (2) girls are selected from (7) boys and (6) girls, which formula is correct?

Explanation opens after your attempt
Correct Answer

D. \(^{7}C_3\times{}^{6}C_2\)

Explanation

Simple Explanation

दो categories में बिना क्रम selection हो रहा है, इसलिए combinations multiply होंगे। परीक्षा में category-wise selection को अलग-अलग गिनें। / There is unordered selection in two categories, so combinations are multiplied. In exams count category-wise selections separately.

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Question 272/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(7) लड़कों और (6) लड़कियों से (5) सदस्यों की समिति में ठीक (3) लड़के हों, तो expression क्या है?

What is the expression for a (5)-member committee with exactly (3) boys from (7) boys and (6) girls?

Explanation opens after your attempt
Correct Answer

A. \(^{7}C_3\times{}^{6}C_2\)

Explanation

Simple Explanation

ठीक (3) लड़के और (2) लड़कियाँ चुननी हैं। परीक्षा में exact condition में केवल वही case लें। / Exactly (3) boys and (2) girls must be selected. In exams take only that case for exact conditions.

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Question 273/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(7) लड़कों और (6) लड़कियों से (5) सदस्यों की समिति में कम से कम (3) लड़कियाँ हों, तो सही sum कौन-सा है?

Which sum is correct for a (5)-member committee with at least (3) girls from (7) boys and (6) girls?

Explanation opens after your attempt
Correct Answer

C. \(^{6}C_3{}^{7}C_2+^{6}C_4{}^{7}C_1+^{6}C_5{}^{7}C_0\)

Explanation

Simple Explanation

लड़कियों की संख्या (3), (4) या (5) हो सकती है। परीक्षा में at least condition में सभी valid cases जोड़ें। / The number of girls can be (3), (4), or (5). In exams add all valid cases in at least conditions.

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Question 274/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (9) distinct letters से (6)-letter word बनाना हो और repetition allowed न हो, तो count को \(^{9}C_6\) से कैसे जोड़ेंगे?

If a (6)-letter word is made from (9) distinct letters without repetition, how is the count connected with \(^{9}C_6\)?

Explanation opens after your attempt
Correct Answer

A. \(^{9}C_6\times6!\)

Explanation

Simple Explanation

पहले (6) letters चुनते हैं और फिर उन्हें (6!) तरीकों से जमाते हैं। परीक्षा में word में order महत्वपूर्ण होता है। / First choose (6) letters and then arrange them in (6!) ways. In exams order is important in a word.

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Question 275/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (9) distinct letters से (6)-letter word बनाना हो और repetition allowed हो, तो count कौन-सा है?

If a (6)-letter word is made from (9) distinct letters with repetition allowed, what is the count?

Explanation opens after your attempt
Correct Answer

D. \(9^6\)

Explanation

Simple Explanation

हर स्थान पर (9) choices फिर से उपलब्ध हैं। परीक्षा में repetition allowed हो तो power rule \(n^r\) लगाएँ। / Each position has (9) choices available again. In exams use the power rule \(n^r\) when repetition is allowed.

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Question 276/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (8) digits में (0) शामिल है और repetition allowed है, तो (5)-digit numbers की count क्या होगी?

If (0) is included among (8) digits and repetition is allowed, what is the count of (5)-digit numbers?

Explanation opens after your attempt
Correct Answer

A. \(7\times8^4\)

Explanation

Simple Explanation

पहला digit (0) नहीं हो सकता, इसलिए (7) choices हैं और बाकी चार स्थानों पर (8) choices हैं। परीक्षा में leading zero को अलग देखें। / The first digit cannot be (0), so there are (7) choices and (8) choices for each of the remaining four places. In exams treat leading zero separately.

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Question 277/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (8) digits में (0) शामिल है और repetition allowed नहीं है, तो (5)-digit numbers की count क्या होगी?

If (0) is included among (8) digits and repetition is not allowed, what is the count of (5)-digit numbers?

Explanation opens after your attempt
Correct Answer

B. \(7\times{}^{7}P_4\)

Explanation

Simple Explanation

पहले स्थान के लिए (7) non-zero choices हैं और फिर बाकी (4) स्थान (7) बची digits से भरते हैं। परीक्षा में पहले स्थान को अलग handle करें। / There are (7) non-zero choices for the first place, and then (4) places are filled from the remaining (7) digits. In exams handle the first place separately.

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Question 278/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(^{n}C_r=^{n}C_{r-3}\) और lower indices अलग हैं, तो (n) के लिए सही relation कौन-सा है?

If \(^{n}C_r=^{n}C_{r-3}\) and the lower indices are different, which relation is correct for (n)?

Explanation opens after your attempt
Correct Answer

C. (n=2r-3)

Explanation

Simple Explanation

अलग lower indices पूरक होंगे, इसलिए (r+(r-3)=n) है। परीक्षा में equal combination को complement rule से हल करें। / Different lower indices are complementary, so (r+(r-3)=n). In exams solve equal combinations using the complement rule.

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Question 279/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(\frac{^{n}C_{r+1}}{^{n}C_r}=3\) हो, तो कौन-सा equation बनेगा?

If \(\frac{^{n}C_{r+1}}{^{n}C_r}=3\), which equation is formed?

Explanation opens after your attempt
Correct Answer

B. (n-r=3(r+1))

Explanation

Simple Explanation

अनुपात \(\frac{n-r}{r+1}\) है और उसे (3) के बराबर रखा गया है। परीक्षा में ratio formula से सीधे equation बनाएं। / The ratio is \(\frac{n-r}{r+1}\), and it is set equal to (3). In exams form the equation directly from the ratio formula.

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Question 280/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(\frac{^{n}C_r}{^{n}C_{r-1}}=4\) हो, तो कौन-सा equation सही है?

If \(\frac{^{n}C_r}{^{n}C_{r-1}}=4\), which equation is correct?

Explanation opens after your attempt
Correct Answer

A. (n-r+1=4r)

Explanation

Simple Explanation

अनुपात \(\frac{n-r+1}{r}\) होता है। इसे (4) के बराबर रखने पर (n-r+1=4r) मिलता है। / The ratio is \(\frac{n-r+1}{r}\). Setting it equal to (4) gives (n-r+1=4r).

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