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

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Question 211/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{n}C_0+^{n}C_2+^{n}C_4+\cdots\) का योग \(2^{n-1}\) क्यों होता है?

Why is \(^{n}C_0+^{n}C_2+^{n}C_4+\cdots\) equal to \(2^{n-1}\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि even और odd indexed sums बराबर होते हैंBecause even and odd indexed sums are equal

Explanation

Simple Explanation

((1+1)^n) और ((1-1)^n) से even और odd sums बराबर मिलते हैं। परीक्षा में alternating sum identity याद रखें। / From ((1+1)^n) and ((1-1)^n), even and odd sums are equal. In exams remember the alternating sum identity.

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Question 212/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{n}P_r\) के product form में (r=5) हो तो अंतिम factor कौन-सा होगा?

In the product form of \(^{n}P_r\), if (r=5), what is the last factor?

Explanation opens after your attempt
Correct Answer

B. (n-4)

Explanation

Simple Explanation

अंतिम factor (n-r+1) होता है इसलिए (r=5) पर (n-4) मिलेगा। परीक्षा में (+1) को न भूलें। / The last factor is (n-r+1), so for (r=5) it is (n-4). In exams do not forget the (+1).

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Question 213/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{12}P_5\) में product form के कितने गुणनखंड होंगे?

How many factors will be in the product form of \(^{12}P_5\)?

Explanation opens after your attempt
Correct Answer

C. (5)

Explanation

Simple Explanation

(r=5) स्थान भरने हैं इसलिए (5) गुणनखंड होंगे। परीक्षा में factors की संख्या को selected positions से जोड़ें। / There are (r=5) positions to fill, so there will be (5) factors. In exams connect the number of factors with selected positions.

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Question 214/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{n}C_2=78\) हो तो (n) का मान क्या है?

If \(^{n}C_2=78\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

C. (13)

Explanation

Simple Explanation

(^{n}C_2=\frac{n(n-1)}{2}) और \(\frac{13\times12}{2}=78\) है। परीक्षा में pair formula से (n) पहचानें। / (^{n}C_2=\frac{n(n-1)}{2}) and \(\frac{13\times12}{2}=78\). In exams identify (n) using the pair formula.

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Question 215/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{n}P_2=156\) हो तो (n) का मान क्या होगा?

If \(^{n}P_2=156\), what will be the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (13)

Explanation

Simple Explanation

(^{n}P_2=n(n-1)) और \(13\times12=156\) है। परीक्षा में ordered pair count में division नहीं करें। / (^{n}P_2=n(n-1)) and \(13\times12=156\). In exams do not divide in ordered pair count.

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Question 216/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{n}C_4\) का simplified denominator कौन-सा factorial देता है?

Which factorial gives the simplified denominator of \(^{n}C_4\)?

Explanation opens after your attempt
Correct Answer

C. (4!)

Explanation

Simple Explanation

(^{n}C_4=\frac{n(n-1)(n-2)(n-3)}{4!}) होता है। परीक्षा में \(^{n}C_r\) के denominator में (r!) आता है। / (^{n}C_4=\frac{n(n-1)(n-2)(n-3)}{4!}). In exams (r!) appears in the denominator of \(^{n}C_r\).

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Question 217/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{n}C_4\) के numerator में कौन-सा product आता है?

Which product appears in the numerator of \(^{n}C_4\)?

Explanation opens after your attempt
Correct Answer

A. (n(n-1)(n-2)(n-3))

Explanation

Simple Explanation

((n-4)!) कटने के बाद चार factors (n) से (n-3) तक बचते हैं। परीक्षा में numerator factors की संख्या (r) होती है। / After cancelling ((n-4)!), four factors from (n) to (n-3) remain. In exams the number of numerator factors is (r).

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Question 218/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (9) लोगों में से (4) की committee और उसी committee से (1) leader चुनना हो तो expression क्या होगा?

If a committee of (4) is formed from (9) people and then (1) leader is chosen from the committee, what is the expression?

Explanation opens after your attempt
Correct Answer

A. \(^{9}C_4\times4\)

Explanation

Simple Explanation

पहले committee के \(^{9}C_4\) तरीके हैं और leader के (4) विकल्प हैं। परीक्षा में चयन के बाद role हो तो multiply करें। / First there are \(^{9}C_4\) ways for the committee and (4) choices for leader. In exams multiply when a role follows selection.

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Question 219/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

\(^{9}C_4\times4\) को permutation के रूप में कैसे लिख सकते हैं?

How can \(^{9}C_4\times4\) be written in permutation form?

Explanation opens after your attempt
Correct Answer

A. \(^{9}P_4\div3!\)

Explanation

Simple Explanation

एक leader अलग है और बाकी (3) सदस्यों का क्रम महत्वहीन है इसलिए \(^{9}P_4\) को (3!) से भाग देंगे। परीक्षा में roles और ordinary members अलग करें। / One leader is distinct and the order of the other (3) members is irrelevant, so divide \(^{9}P_4\) by (3!). In exams separate roles and ordinary members.

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Question 220/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (6) boys और (5) girls में से (3) boys तथा (2) girls चुनने हों तो formula कौन-सा है?

If (3) boys and (2) girls are selected from (6) boys and (5) girls, which is the formula?

Explanation opens after your attempt
Correct Answer

C. \(^{6}C_3\times{}^{5}C_2\)

Explanation

Simple Explanation

दो category 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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