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

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Derivations of formulas and their connections Practice Questions

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Question 161/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

पास्कल पहचान से \(^{9}C_5\) का सही split कौन-सा है?

Using Pascal's identity, which is the correct split of \(^{9}C_5\)?

Explanation opens after your attempt
Correct Answer

A. \(^{8}C_5+^{8}C_4\)

Explanation

Simple Explanation

\(^{n}C_r=^{n-1}C_r+^{n-1}C_{r-1}\) में (n=9) और (r=5) रखें। परीक्षा में दोनों terms का upper index (1) घटता है। / Put (n=9) and (r=5) in \(^{n}C_r=^{n-1}C_r+^{n-1}C_{r-1}\). In exams the upper index of both terms decreases by (1).

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Question 162/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{n}C_r=\frac{n}{n-r},^{n-1}C_r\) में कौन-सा निचला सूचक समान रहता है?

In \(^{n}C_r=\frac{n}{n-r},^{n-1}C_r\), which lower index remains the same?

Explanation opens after your attempt
Correct Answer

C. (r)

Explanation

Simple Explanation

दोनों संचयों में निचला सूचक (r) है। परीक्षा में ऊपरी और निचले सूचक अलग-अलग देखें। / The lower index is (r) in both combinations. In exams read upper and lower indices separately.

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Question 163/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{n}C_{r+1}\) को \(^{n}C_r\) से जोड़ने वाला गुणक कौन-सा है?

Which multiplier connects \(^{n}C_{r+1}\) with \(^{n}C_r\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{n-r}{r+1}\)

Explanation

Simple Explanation

फैक्टोरियल रूपों का अनुपात लेने पर \(^{n}C_{r+1}=^{n}C_r\frac{n-r}{r+1}\) मिलता है। परीक्षा में adjacent terms पर ratio method उपयोग करें। / Taking the ratio of factorial forms gives \(^{n}C_{r+1}=^{n}C_r\frac{n-r}{r+1}\). In exams use ratio method for adjacent terms.

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Question 164/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि \(\frac{^{n}P_4}{^{n}P_3}=7\) हो तो (n) का मान क्या होगा?

If \(\frac{^{n}P_4}{^{n}P_3}=7\), what is the value of (n)?

Explanation opens after your attempt
Correct Answer

B. (10)

Explanation

Simple Explanation

अनुपात (n-4+1=n-3) होता है और (n-3=7) से (n=10) है। परीक्षा में consecutive permutations का ratio last factor देता है। / The ratio is (n-4+1=n-3), and (n-3=7) gives (n=10). In exams the ratio of consecutive permutations gives the last factor.

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Question 165/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{8}C_3\) को \(^{8}P_3\) से प्राप्त करने के लिए किससे भाग देना होगा?

To obtain \(^{8}C_3\) from \(^{8}P_3\), by what should we divide?

Explanation opens after your attempt
Correct Answer

A. (3!)

Explanation

Simple Explanation

तीन चुनी वस्तुओं के (3!) orders permutation में extra गिने जाते हैं। परीक्षा में combination पाने के लिए (r!) से भाग दें। / The (3!) orders of three chosen objects are counted extra in permutation. In exams divide by (r!) to get combination.

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Question 166/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(6) अलग सिक्कों में से खाली चयन छोड़कर selections की संख्या किस expression से मिलेगी?

Which expression gives the number of selections from (6) distinct coins excluding the empty selection?

Explanation opens after your attempt
Correct Answer

C. \(2^6-1\)

Explanation

Simple Explanation

कुल selections \(2^6\) हैं और खाली selection हटता है। परीक्षा में non-empty selection के लिए (1) घटाएँ। / Total selections are \(2^6\) and the empty selection is removed. In exams subtract (1) for non-empty selections.

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Question 167/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{n}C_3\) का numerator सरल करने पर कौन-सा product आता है?

When the numerator of \(^{n}C_3\) is simplified, which product appears?

Explanation opens after your attempt
Correct Answer

B. (n(n-1)(n-2))

Explanation

Simple Explanation

(^{n}C_3=\frac{n!}{3!(n-3)!}) में ((n-3)!) कटने पर (n(n-1)(n-2)) बचता है। परीक्षा में cancellation step साफ लिखें। / In (^{n}C_3=\frac{n!}{3!(n-3)!}), cancelling ((n-3)!) leaves (n(n-1)(n-2)). In exams write the cancellation step clearly.

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Question 168/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(^{n}C_3=\frac{n(n-1)(n-2)}{6}) में (6) कहाँ से आता है?

Where does (6) come from in (^{n}C_3=\frac{n(n-1)(n-2)}{6})?

Explanation opens after your attempt
Correct Answer

B. (3!) सेFrom (3!)

Explanation

Simple Explanation

(3!=6) होता है और यह चुनी गई तीन वस्तुओं के internal orders हटाता है। परीक्षा में छोटे factorial values याद रखें। / (3!=6), and it removes internal orders of three chosen objects. In exams remember small factorial values.

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Question 169/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(10) points से triangles बनाने की maximum संख्या का formula connection कौन-सा है यदि कोई (3) collinear नहीं हैं?

What formula connection gives the maximum number of triangles from (10) points if no (3) are collinear?

Explanation opens after your attempt
Correct Answer

B. \(^{10}C_3\)

Explanation

Simple Explanation

Triangle बनाने के लिए (3) points का unordered selection चाहिए। परीक्षा में shape बनाने में points का order नहीं गिनें। / A triangle needs an unordered selection of (3) points. In exams do not count the order of points while forming a shape.

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Question 170/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि (7) candidates में से (3) posts अलग-अलग हैं तो choose-and-arrange expression कौन-सा है?

If there are (3) different posts among (7) candidates, what is the choose-and-arrange expression?

Explanation opens after your attempt
Correct Answer

B. \(^{7}C_3\times3!\)

Explanation

Simple Explanation

पहले (3) candidates चुनें और फिर उन्हें (3!) ways से posts दें। परीक्षा में अलग posts हों तो arrangement जोड़ें। / First choose (3) candidates and then assign the posts in (3!) ways. In exams add arrangement when posts are different.

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