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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 521/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(n) distinct people को row में arrange करना है और (A) तथा (B) के बीच exactly (k) people हों। Count कौन-सी है?

(n) distinct people are arranged in a row and exactly (k) people are between (A) and (B). Which count is correct?

Explanation opens after your attempt
Correct Answer

A. (2(n-k-1)(n-2)!)

Explanation

Simple Explanation

(A,B) की positions distance (k+1) पर होती हैं और order के (2) choices हैं। परीक्षा में fixed gap problems में positions first count करें। / The positions of (A,B) are at distance (k+1), and there are (2) choices for order. In exams count positions first in fixed-gap problems.

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Question 522/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(10) people की line में (A) और (B) के बीच exactly (3) people हों, तो count क्या है?

In a line of (10) people, if exactly (3) people are between (A) and (B), what is the count?

Explanation opens after your attempt
Correct Answer

A. \(2\cdot6\cdot8!\)

Explanation

Simple Explanation

Positions के (10-3-1=6) choices और (A,B) order के (2) choices हैं। परीक्षा में between condition में position pairs गिनें। / There are (10-3-1=6) position choices and (2) choices for the order of (A,B). In exams count position pairs for between conditions.

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Question 523/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(9) distinct books को shelf पर रखना है और (3) specified books का relative order fixed हो। Count क्या है?

(9) distinct books are arranged on a shelf and the relative order of (3) specified books is fixed. What is the count?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9!}{3!}\)

Explanation

Simple Explanation

उन (3) books के (3!) relative orders में केवल (1) allowed है। परीक्षा में fixed relative order में total को (k!) से divide करें। / Only (1) of the (3!) relative orders of those (3) books is allowed. In exams divide total by (k!) for fixed relative order.

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Question 524/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(12) people की line में (A) before (B), (C) before (D), और (E) before (F) हो, तो count क्या होगा?

In a line of (12) people, if (A) is before (B), (C) is before (D), and (E) is before (F), what is the count?

Explanation opens after your attempt
Correct Answer

A. \(\frac{12!}{8}\)

Explanation

Simple Explanation

तीन स्वतंत्र before-after restrictions count को \(2^3\) से divide करती हैं। परीक्षा में independent pairs पर (2) की power से divide करें। / Three independent before-after restrictions divide the count by \(2^3\). In exams divide by a power of (2) for independent pairs.

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Question 525/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(n) people की circular seating में (A) और (B) के बीच exactly (k) people one direction में हों, तो core counting idea क्या है?

In circular seating of (n) people, if exactly (k) people lie between (A) and (B) in one direction, what is the core counting idea?

Explanation opens after your attempt
Correct Answer

A. (A) को fix करके (B) की two possible circular positions देखेंFix (A) and check the two possible circular positions of (B)

Explanation

Simple Explanation

Circular rotation हटाने के बाद fixed distance वाली positions गिनी जाती हैं। परीक्षा में circular distance में पहले one object fix करें। / After removing circular rotation, positions with fixed distance are counted. In exams fix one object first for circular distance.

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Question 526/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(8) people को round table पर बैठाना है और (A) तथा (B) adjacent न हों। Count कौन-सी है?

(8) people are seated around a round table and (A) and (B) are not adjacent. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. \(7!-2\cdot6!\)

Explanation

Simple Explanation

Total circular arrangements (7!) हैं और adjacent block \(2\cdot6!\) ways में आता है। परीक्षा में circular not adjacent को complement से करें। / Total circular arrangements are (7!), and the adjacent block occurs in \(2\cdot6!\) ways. In exams handle circular not-adjacent by complement.

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Question 527/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(7) couples को round table पर बैठाना है और हर couple साथ रहे। Count क्या होगा?

(7) couples are seated around a round table and every couple stays together. What is the count?

Explanation opens after your attempt
Correct Answer

A. \(6!\cdot2^7\)

Explanation

Simple Explanation

(7) couple-blocks की circular arrangement (6!) है और हर block में (2) internal orders हैं। परीक्षा में circular block count में blocks minus one factorial लें। / The circular arrangement of (7) couple-blocks is (6!), and each block has (2) internal orders. In exams use blocks minus one factorial for circular block count.

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Question 528/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(6) men और (6) women को round table पर alternate बैठाने की count क्या है?

What is the count for seating (6) men and (6) women alternately around a round table?

Explanation opens after your attempt
Correct Answer

A. \(5!\cdot6!\)

Explanation

Simple Explanation

पहले men को circle में (5!) ways से बैठाएं, फिर (6) gaps में women को (6!) ways से रखें। परीक्षा में circular alternate में starting factor (2) न लगाएं। / Seat the men in a circle in (5!) ways, then place the women in the (6) gaps in (6!) ways. In exams do not add a starting factor (2) in circular alternation.

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Question 529/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(9) distinct beads को bracelet में arrange करने पर count क्या होगा?

What is the count for arranging (9) distinct beads in a bracelet?

Explanation opens after your attempt
Correct Answer

A. \(\frac{8!}{2}\)

Explanation

Simple Explanation

Bracelet में rotations और reflections same माने जाते हैं। परीक्षा में bracelet count के लिए (\frac{(n-1)!}{2}) लगाएं। / In a bracelet, rotations and reflections are considered the same. In exams use (\frac{(n-1)!}{2}) for bracelet count.

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Question 530/600 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(0,1,2,3,4,5,6,7,8) से repetition बिना (5)-digit even numbers बनाते समय (0) last digit case में count क्या होगा?

Using (0,1,2,3,4,5,6,7,8) without repetition, what is the count for (5)-digit even numbers when (0) is the last digit?

Explanation opens after your attempt
Correct Answer

A. \(^{8}P_4\)

Explanation

Simple Explanation

Last digit (0) fix होने पर बाकी (4) places में (8) non-zero digits से ordered selection होता है। परीक्षा में zero-last case leading restriction हटाता है। / When the last digit is fixed as (0), the remaining (4) places use ordered selection from (8) non-zero digits. In exams the zero-last case removes the leading restriction.

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