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 451-460 of 600 questions.

Search
Question 451/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

पहचान \(\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}={}^{m+n}C_r\) का सबसे सही संयोजनात्मक आधार क्या है?

What is the most correct combinatorial basis of the identity \(\sum_{k=0}^{r}{}^{m}C_k{}^{n}C_{r-k}={}^{m+n}C_r\)?

Explanation opens after your attempt
Correct Answer

A. दो अलग समूहों से कुल (r) वस्तुएं चुननाChoosing total (r) objects from two separate groups

Explanation

Simple Explanation

पहले समूह से (k) और दूसरे से (r-k) चुनकर सभी cases जुड़ते हैं। परीक्षा में दो समूहों वाली selection में वेंडरमोंड पहचानें। / Choose (k) from the first group and (r-k) from the second, then add all cases. In exams identify Vandermonde in two-group selection.

Open Question Page
Ask Friends
Question 452/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(\sum_{r=0}^{n}{}^{n}C_r^2={}^{2n}C_n\) को सिद्ध करने में कौन-सा विचार सबसे उपयुक्त है?

Which idea is most suitable to prove \(\sum_{r=0}^{n}{}^{n}C_r^2={}^{2n}C_n\)?

Explanation opens after your attempt
Correct Answer

B. दो (n)-आकार के समूहों से कुल (n) वस्तुएं चुननाChoosing total (n) objects from two groups of size (n)

Explanation

Simple Explanation

दूसरे समूह से (n-r) चुनना \({}^{n}C_{n-r}={}^{n}C_r\) के बराबर है। परीक्षा में square sum को दो समान समूहों से जोड़ें। / Choosing (n-r) from the second group equals \({}^{n}C_{n-r}={}^{n}C_r\). In exams connect square sums with two equal groups.

Open Question Page
Ask Friends
Question 453/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

({}^{n}C_r\cdot r!(n-r)!) हमेशा किसके बराबर होता है?

What is ({}^{n}C_r\cdot r!(n-r)!) always equal to?

Explanation opens after your attempt
Correct Answer

B. (n!)

Explanation

Simple Explanation

पहले (r) वस्तुएं चुनें, फिर चुनी और न चुनी दोनों सूचियों को क्रम में रखें। परीक्षा में factorial cancellation से भी यही तुरंत मिलता है। / Choose (r) objects first, then arrange both chosen and unchosen lists. In exams factorial cancellation also gives this quickly.

Open Question Page
Ask Friends
Question 454/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(r{}^{n}C_r=n{}^{n-1}C_{r-1}\) की double counting व्याख्या क्या है?

What is the double-counting interpretation of \(r{}^{n}C_r=n{}^{n-1}C_{r-1}\)?

Explanation opens after your attempt
Correct Answer

A. एक चुने हुए (r)-समूह में एक सदस्य को चिह्नित करनाMarking one member in a chosen (r)-group

Explanation

Simple Explanation

बाईं ओर समूह चुनकर mark करते हैं, दाईं ओर marked member पहले चुनते हैं। परीक्षा में (r) factor को marked choice मानें। / The left side chooses a group and marks one member, while the right side chooses the marked member first. In exams treat the factor (r) as a marked choice.

Open Question Page
Ask Friends
Question 455/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(r(r-1){}^{n}C_r=n(n-1){}^{n-2}C_{r-2}) में (r(r-1)) किसे गिनता है?

What does (r(r-1)) count in (r(r-1){}^{n}C_r=n(n-1){}^{n-2}C_{r-2})?

Explanation opens after your attempt
Correct Answer

A. चुने हुए समूह में ordered दो marked सदस्यOrdered two marked members in the selected group

Explanation

Simple Explanation

(r)-समूह में पहला और दूसरा marked member क्रम सहित चुने जाते हैं। परीक्षा में (r(r-1)) देखकर ordered marking सोचें। / In an (r)-group, the first and second marked members are chosen with order. In exams think of ordered marking when you see (r(r-1)).

Open Question Page
Ask Friends
Question 456/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(\sum_{r=0}^{n}r{}^{n}C_r=n2^{n-1}\) में दाईं ओर \(2^{n-1}\) क्यों आता है?

Why does \(2^{n-1}\) appear on the right side of \(\sum_{r=0}^{n}r{}^{n}C_r=n2^{n-1}\)?

Explanation opens after your attempt
Correct Answer

A. marked member चुनने के बाद बाकी (n-1) members स्वतंत्र रूप से चुने या छोड़े जाते हैंAfter choosing the marked member, the remaining (n-1) members are freely chosen or left

Explanation

Simple Explanation

पहले marked member के (n) choices हैं और बाकी पर two choices हैं। परीक्षा में binomial sum में extra (r) को marking से जोड़ें। / There are (n) choices for the marked member and two choices for each remaining member. In exams connect the extra (r) in binomial sums with marking.

Open Question Page
Ask Friends
Question 457/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(\sum_{r=0}^{n}r(r-1){}^{n}C_r) का सही सरल रूप कौन-सा है?

What is the correct simplified form of (\sum_{r=0}^{n}r(r-1){}^{n}C_r)?

Explanation opens after your attempt
Correct Answer

B. (n(n-1)2^{n-2})

Explanation

Simple Explanation

Ordered दो marked members चुनने के (n(n-1)) ways हैं और बाकी (n-2) freely चुने जाते हैं। परीक्षा में दो marks हों तो \(2^{n-2}\) आता है। / There are (n(n-1)) ways to choose two ordered marked members and the remaining (n-2) are chosen freely. In exams two marks lead to \(2^{n-2}\).

Open Question Page
Ask Friends
Question 458/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(\sum_{r=0}^{n}r^2{}^{n}C_r\) का सही रूप क्या है?

What is the correct form of \(\sum_{r=0}^{n}r^2{}^{n}C_r\)?

Explanation opens after your attempt
Correct Answer

C. (n(n+1)2^{n-2})

Explanation

Simple Explanation

(r-2=r(r-1)+r) लिखकर दो standard sums जोड़ते हैं। परीक्षा में \(r^2\) को split करना तेज तरीका है। / Write (r-2=r(r-1)+r) and add two standard sums. In exams splitting \(r^2\) is the fastest method.

Open Question Page
Ask Friends
Question 459/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\) का simplified form कौन-सा है?

What is the simplified form of \(\sum_{r=0}^{n}{}^{n}C_r{}^{r}C_k\)?

Explanation opens after your attempt
Correct Answer

A. \(^{n}C_k2^{n-k}\)

Explanation

Simple Explanation

पहले (k) marked members चुनें, फिर बाकी (n-k) members subset में आएं या न आएं। परीक्षा में nested selection में marked set पहले चुनें। / Choose the (k) marked members first, then each of the remaining (n-k) members may or may not enter the subset. In exams choose the marked set first in nested selection.

Open Question Page
Ask Friends
Question 460/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

\({}^{n}C_r{}^{r}C_s{}^{s}C_t\) को सही क्रम बदलकर किस रूप में लिखा जा सकता है?

By changing the order of selection, \({}^{n}C_r{}^{r}C_s{}^{s}C_t\) can be correctly written as which form?

Explanation opens after your attempt
Correct Answer

A. \(^{n}C_t{}^{n-t}C_{s-t}{}^{n-s}C_{r-s}\)

Explanation

Simple Explanation

पहले सबसे अंदर के (t) members चुनें, फिर (s-t), फिर (r-s) members जोड़ें। परीक्षा में nested choices को layers में उल्टा गिनें। / First choose the innermost (t) members, then add (s-t), then (r-s) members. In exams count nested choices backward by layers.

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