Update
Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है • Muft Shiksha™ एक 100% Free Education Portal है 🇮🇳, जिसका उद्देश्य Class 9–12 के हर विद्यार्थी तक High-Quality Education को पूरी तरह मुफ्त पहुँचाना है। 🇮🇳 हम मानते हैं कि अच्छी शिक्षा किसी student की आर्थिक स्थिति पर निर्भर नहीं होनी चाहिए। 🇮🇳 हर विद्यार्थी को वही Quality Study Material, MCQs, Quizzes, Exam Preparation, Concept-Based Learning और Bilingual Support मिलना चाहिए, जो आमतौर पर महंगी Coaching या Premium Platforms में मिलता है। Muft Shiksha™ 🇮🇳 इसी सोच के साथ बनाया गया है
Subjects
Topic Wise MCQ

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

Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.

Back to Chapter Subject Page
Share

Start Derivations of formulas and their connections Topic Quiz

Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.

Easy Test 150 Questions Medium Test 150 Questions Hard Test 150 Questions Expert Test 150 Questions
Topic Navigation

Continue Chapter Revision

Leaderboard

Derivations of formulas and their connections Practice Questions

Showing 331-340 of 600 questions.

Search
Question 331/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि necklace में clockwise और anticlockwise arrangements same मानी जाएं तो ((n-1)!) से आगे किससे divide किया जाता है?

If clockwise and anticlockwise arrangements are considered the same in a necklace, by what is ((n-1)!) further divided?

Explanation opens after your attempt
Correct Answer

B. (2)

Explanation

Simple Explanation

Reflection भी same होने पर हर circular arrangement दो बार गिनी जाती है। परीक्षा में necklace type में (\frac{(n-1)!}{2}) याद रखें। / When reflection is also same each circular arrangement is counted twice. In exams remember (\frac{(n-1)!}{2}) for necklace type.

Open Question Page
Ask Friends
Question 332/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

किस स्थिति में \(n^r\) formula \(^{n}P_r\) की जगह आता है?

In which situation does the formula \(n^r\) replace \(^{n}P_r\)?

Explanation opens after your attempt
Correct Answer

A. जब repetition allowed हो और order important होWhen repetition is allowed and order is important

Explanation

Simple Explanation

हर (r) स्थान पर (n) choices स्वतंत्र रूप से रहती हैं। परीक्षा में repetition allowed हो तो decreasing product नहीं लिखें। / Each of the (r) positions has (n) independent choices. In exams do not write a decreasing product when repetition is allowed.

Open Question Page
Ask Friends
Question 333/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{n}P_r\) के derivation में choices घटती क्यों हैं?

Why do choices decrease in the derivation of \(^{n}P_r\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि चुनी गई वस्तु दोबारा नहीं चुनी जातीBecause a chosen object is not selected again

Explanation

Simple Explanation

Without repetition में एक choice use होने के बाद available count कम होता है। परीक्षा में no repetition को falling product से जोड़ें। / Without repetition the available count decreases after one choice is used. In exams connect no repetition with a falling product.

Open Question Page
Ask Friends
Question 334/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{n}C_r\) के formula में ((n-r)!) denominator क्यों आता है?

Why does ((n-r)!) appear in the denominator of the formula for \(^{n}C_r\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि factorial (n!) में चुनी न गई वस्तुओं की arrangements भी शामिल होती हैंBecause (n!) includes arrangements of unselected objects too

Explanation

Simple Explanation

Formula में (n!) से unwanted tail ((n-r)!) और order (r!) दोनों हटते हैं। परीक्षा में combination denominator के दोनों भाग समझें। / In the formula (n!) loses both unwanted tail ((n-r)!) and order (r!). In exams understand both parts of the combination denominator.

Open Question Page
Ask Friends
Question 335/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि \(^{n}C_r\) maximum के आसपास होता है तो consecutive ratio किससे तुलना की जाती है?

If \(^{n}C_r\) is near maximum, the consecutive ratio is compared with what?

Explanation opens after your attempt
Correct Answer

A. (1)

Explanation

Simple Explanation

Maximum के पास \(\frac{^{n}C_{r+1}}{^{n}C_r}\) (1) के आसपास होता है। परीक्षा में increasing से decreasing transition ratio से पहचानें। / Near the maximum \(\frac{^{n}C_{r+1}}{^{n}C_r}\) is around (1). In exams use the ratio to identify transition from increasing to decreasing.

Open Question Page
Ask Friends
Question 336/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{16}C_7\) और \(^{16}C_9\) के बराबर होने का कारण क्या है?

What is the reason \(^{16}C_7\) and \(^{16}C_9\) are equal?

Explanation opens after your attempt
Correct Answer

A. (7+9=16) इसलिए complementary selection है(7+9=16), so it is complementary selection

Explanation

Simple Explanation

Indices का sum (n) होने पर \(^{n}C_r=^{n}C_{n-r}\)। परीक्षा में sum check सबसे तेज तरीका है। / When indices sum to (n), \(^{n}C_r=^{n}C_{n-r}\). In exams checking the sum is the fastest method.

Open Question Page
Ask Friends
Question 337/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि \(^{9}P_4=9\cdot8\cdot7\cdot6\), तो यह product किस formula से connected है?

If \(^{9}P_4=9\cdot8\cdot7\cdot6\), this product is connected with which formula?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9!}{5!}\)

Explanation

Simple Explanation

Falling product \(9\cdot8\cdot7\cdot6\) में बाकी tail (5!) हटता है। परीक्षा में last chosen factor के बाद denominator tail लिखें। / In the falling product \(9\cdot8\cdot7\cdot6\), the remaining tail (5!) is removed. In exams write the denominator tail after the last chosen factor.

Open Question Page
Ask Friends
Question 338/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(^{10}C_4\) को \(^{10}P_4\) से derive करते समय कौन-सा operation सही है?

Which operation is correct while deriving \(^{10}C_4\) from \(^{10}P_4\)?

Explanation opens after your attempt
Correct Answer

B. (4!) से भागDivide by (4!)

Explanation

Simple Explanation

\(^{10}P_4\) ordered count है और \(^{10}C_4\) unordered count है। परीक्षा में order हटाने के लिए (r!) से divide करें। / \(^{10}P_4\) is an ordered count and \(^{10}C_4\) is unordered. In exams divide by (r!) to remove order.

Open Question Page
Ask Friends
Question 339/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

कौन-सी expression \(^{n}C_2\) को \(^{n}P_2\) से सही जोड़ती है?

Which expression correctly connects \(^{n}C_2\) with \(^{n}P_2\)?

Explanation opens after your attempt
Correct Answer

B. \(^{n}C_2=\frac{^{n}P_2}{2!}\)

Explanation

Simple Explanation

Ordered pair से unordered pair पाने के लिए (2!) orders हटते हैं। परीक्षा में pair selection में यह connection बहुत उपयोगी है। / To get unordered pairs from ordered pairs (2!) orders are removed. This connection is very useful in pair selection exams.

Open Question Page
Ask Friends
Question 340/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

यदि (n) different objects को (p) और (q) groups में बांटा जाए जहां (p+q=n), तो count किस formula से जुड़ा है?

If (n) different objects are divided into groups of (p) and (q) where (p+q=n), the count is connected with which formula?

Explanation opens after your attempt
Correct Answer

A. \(\frac{n!}{p!q!}\)

Explanation

Simple Explanation

पहले (p) चुनने पर बाकी (q) तय हो जाते हैं, इसलिए \(\frac{n!}{p!q!}\)। परीक्षा में group sizes fixed हों तो factorial division सोचें। / After choosing (p), the remaining (q) are fixed, so \(\frac{n!}{p!q!}\). In exams use factorial division for fixed group sizes.

Open Question Page
Ask Friends

Derivations of formulas and their connections Learning Links

Permutations and Combinations Chapter

All chapter topics and quizzes

Easy Derivations of formulas and their connections Test

Topic-wise timed quiz

Mathematics Subject

All chapters and levels

Search Derivations of formulas and their connections

Find related MCQs