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

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Question 411/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(n) अलग वस्तुओं में से अधिकतम (3) वस्तुएं चुनने की संख्या कौन-सी है?

What is the number of ways to select at most (3) objects from (n) distinct objects?

Explanation opens after your attempt
Correct Answer

B. \(1+n+{}^{n}C_2+{}^{n}C_3\)

Explanation

Simple Explanation

At most (3) में (0), (1), (2), और (3) selections शामिल होते हैं। परीक्षा में upper limit हो तो सभी allowed cases जोड़ें। / At most (3) includes selections of (0), (1), (2), and (3). In exams add all allowed cases when there is an upper limit.

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Question 412/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(x_1+x_2+x_3+x_4=18\) के अऋणात्मक पूर्णांक हलों की संख्या क्या है?

What is the number of non-negative integer solutions of \(x_1+x_2+x_3+x_4=18\)?

Explanation opens after your attempt
Correct Answer

B. \(^{21}C_3\)

Explanation

Simple Explanation

Stars and bars में (18) stars और (3) bars arrange होते हैं। परीक्षा में अऋणात्मक हलों के लिए \(^{n+r-1}C_{r-1}\) लगाएं। / In stars and bars, (18) stars and (3) bars are arranged. In exams use \(^{n+r-1}C_{r-1}\) for non-negative solutions.

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Question 413/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(x_1+x_2+x_3=21\) और \(x_i\geq3\) हो, तो हलों की संख्या क्या होगी?

If \(x_1+x_2+x_3=21\) and \(x_i\geq3\), what is the number of solutions?

Explanation opens after your attempt
Correct Answer

A. \(^{14}C_2\)

Explanation

Simple Explanation

हर variable को पहले (3) देने पर (12) बचता है, फिर अऋणात्मक हल गिनते हैं। परीक्षा में minimum condition को shift करें। / Giving (3) first to each variable leaves (12), then count non-negative solutions. In exams shift the minimum condition.

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Question 414/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(9) identical pens को (4) students में बांटना है और खाली हिस्सा allowed है। Count कौन-सी है?

(9) identical pens are to be distributed among (4) students and zero share is allowed. Which count is correct?

Explanation opens after your attempt
Correct Answer

B. \(^{12}C_3\)

Explanation

Simple Explanation

Identical pens और distinct students के लिए (9) stars तथा (3) bars लगते हैं। परीक्षा में zero allowed distribution में stars and bars याद रखें। / For identical pens and distinct students, use (9) stars and (3) bars. In exams remember stars and bars for zero-allowed distribution.

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Question 415/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(11) identical balls को (5) boxes में रखना है और हर box में कम से कम (1) ball हो। Count कौन-सी है?

(11) identical balls are placed in (5) boxes and each box has at least (1) ball. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. \(^{10}C_4\)

Explanation

Simple Explanation

हर box को (1) ball देने के बाद (6) balls बचती हैं। परीक्षा में positive distribution में पहले minimum allot करें। / After giving (1) ball to each box, (6) balls remain. In exams allot the minimum first in positive distribution.

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Question 416/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(14) identical coins को (4) persons में बांटना है और exactly (1) person को कुछ न मिले। Count क्या है?

(14) identical coins are distributed among (4) persons and exactly (1) person gets nothing. What is the count?

Explanation opens after your attempt
Correct Answer

A. \(^{4}C_1\cdot{}^{13}C_2\)

Explanation

Simple Explanation

पहले empty person चुनें, फिर बाकी (3) persons में positive distribution करें। परीक्षा में exactly empty condition में choose empty plus positive stars-bars लगाएं। / First choose the empty person, then distribute positively among the remaining (3) persons. In exams use choose empty plus positive stars and bars for exactly empty conditions.

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Question 417/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(n) distinct objects को (r) distinct boxes में रखने पर count \(r^n\) कब होता है?

When is the count \(r^n\) for placing (n) distinct objects into (r) distinct boxes?

Explanation opens after your attempt
Correct Answer

A. जब हर object independently किसी भी box में जा सकता हैWhen each object can independently go to any box

Explanation

Simple Explanation

हर distinct object के पास (r) independent choices होते हैं। परीक्षा में distinct objects और unrestricted boxes में power rule लगाएं। / Each distinct object has (r) independent choices. In exams use the power rule for distinct objects and unrestricted boxes.

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Question 418/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(6) अलग prizes (10) students को देने हैं और एक student कई prizes पा सकता है। Count कौन-सी है?

(6) distinct prizes are given to (10) students and one student may receive several prizes. Which count is correct?

Explanation opens after your attempt
Correct Answer

B. \(10^6\)

Explanation

Simple Explanation

हर prize के लिए (10) independent choices हैं। परीक्षा में distinct prizes और repeated recipients allowed हों तो power formula लें। / Each prize has (10) independent choices. In exams use the power formula when distinct prizes and repeated recipients are allowed.

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Question 419/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(6) अलग prizes (10) students को देने हैं और कोई student एक से अधिक prize नहीं पा सकता। Count कौन-सी है?

(6) distinct prizes are given to (10) students and no student can receive more than one prize. Which count is correct?

Explanation opens after your attempt
Correct Answer

C. \(^{10}P_6\)

Explanation

Simple Explanation

Prizes अलग हैं और recipients repeat नहीं हो सकते, इसलिए ordered assignment बनता है। परीक्षा में distinct prizes without repetition को permutation समझें। / Prizes are distinct and recipients cannot repeat, so it becomes an ordered assignment. In exams treat distinct prizes without repetition as permutation.

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Question 420/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(6) identical prizes (10) students में बांटने हैं और एक student कई prizes पा सकता है। Count कौन-सी है?

(6) identical prizes are distributed among (10) students and one student may receive several prizes. Which count is correct?

Explanation opens after your attempt
Correct Answer

B. \(^{15}C_9\)

Explanation

Simple Explanation

Identical prizes distribution में (6) stars और (9) bars लगते हैं। परीक्षा में identical items और distinct receivers में stars and bars लगाएं। / In identical prize distribution, use (6) stars and (9) bars. In exams apply stars and bars for identical items and distinct receivers.

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