Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 18:01:41 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p11 Question 18 and 19, Exercise 6.2 Solutions of Question 18 and 19 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $10,000$$0,2,3,5,6$$4$$10000$$3$$5$$0$$3={ }^{3} P=6$$0$$5=3 p_{6}=6$$10000$$5$$=6+6=12$$3$$4$$5$$={ }^{4} P_{3}=2$$4$$5$$4$$5={ }^{4} P_{3}=24$$3$$3$$3$$5=$${ }^{4} P_{2}=12$$3$$5$$3$$5=$${ }^{4} P_{2}=12$$2$$3$$2$$5={ }^{4} … anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:48 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p4 Question 4 and 5, Exercise 6.2 Solutions of Question 4 and 5 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $3$$1,2,3,4,5,6,$$3$$6$$\mathrm{I}:$$2$$$\underline{ },\underline{ },\underline{2}$$$={ }^{5} P_{2}=20$$4$$$\underline{ },\underline{ },\underline{4}$$$={ }^{5} P_{2}=20$$6$$$\underline{ },\underline{ },\underline{6}$$$={ }^{5} P_… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:51 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/re-ex6-p1 Question 1, Review Exercise 6 Solutions of Question 1 of Review Exercise 6 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $3\,\,^nP_3=^nP_4$$n$$5$$6$$7$$8$$6$$ 480$$600$$720$$840$$720$$r$$r!$$(r+1)!$$r!+1$$ 2r!$$r!$$6$$\dfrac{5}{2}\,\,6!$$6!$$\dfrac{1}{2}\,\,6!$$\dfrac{3}{2}\,\,6!$$\dfrac{5}{2}\,\,6!$$A=\{1,2,3,4,...,20\}. $$3$$5$$7$$8$$8$$A=\{1,3,5,7,… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:36 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-1-p6 Question 6(vi-ix), Exercise 6.1 Solutions of Question 6(vi-ix) of Exercise 6.1 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n\in N$$\quad 33!$$2^{15}$$$33!=33.32.31\cdots4.3.2.1$$$2,4,8,16,32$$2^1,2^2,2^3,2^4,2^5$\begin{align*}33!&=2^5.2^4.2^3.2^2.2(33\times31\times\cdots6\times5\times3\times1)\\ &=2^{15}(33\times31\times\cdots\times3\times1)\end{al… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:34 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-3-p7 Question 7 and 8, Exercise 6.3 Solutions of Question 7 and 8 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $5$$6$$4$$2$$2$$3$$={ }^{4} C_{2} \times{ }^{6} C_{3}=6 \times 20=120$$5$$6$$4$$2$$2$$2$$2,3$$2$$120$$3$$2$$={ }^{4} C_{3} \cdot{ }^{6} C_{2}=4 \times 15=60$$4$$={ }^{4} C_{4} \times{ }^{6} C_{1}=1 \times 6=6$$=120+60+6=186$$5$$6$… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:29 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2 Exercise 6.2 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$n \in \mathbb{N}$${ }^n P_r=\frac{n!}{(n-r)!}$$\quad{ }^… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:59 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-3 Exercise 6.3 (Solutions) The solutions of the Exercise 6.3 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n \in \mathbb{N}$${ }^{n} C_{r}=\frac{n!}{r!(n-r)!}$$n,{ }^{n-1} C_{r-1}=(n-r+1){ }^{n} C_{r-1}$$r^{n} C_{r}=(n-r+1)^{n} C_{r-1}$${ }^{n-1} C_{r-1}+{ }^{n-1} C_{r}={ }^{n} C_{r}$${ }^{n} C_{r}+{ }^{n} C… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:35 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/re-ex6-p3 Question 4, 5 and 6, Review Exercise 6 Solutions of Question 4, 5 and 6 of Review Exercise 6 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $0,2,3,4,5,7$$6$$$=6!=720$$$0$$5$$$5!=120$$$6-$$$=720-120=600$$$7$$$(7-1)!=720$$$2$$$\dfrac{720}{2}=360$$$11!$$10!$$$=11!-10!=36288000$$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:38 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p12 Question 20 and 21, Exercise 6.2 Solutions of Question 20 and 21 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $6$$6$$5!$$6$$6!$$=5! \times 6!=86400$$= n = 4$$= {}^4P_4 = 24.$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:45 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-3-p8 Question 9 and 10, Exercise 6.3 Solutions of Question 9 and 10 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$n$$n$$n$$C_{2}$$n$$n$$={ }^{n} C_{2}-n$$=\frac{n!}{2!(n-2)!}-n$$10$$10$$3$$7$$10$${ }^{10} C_{7}$$7$$3$$7={ }^{10} C_{7}=120$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:33 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p10 Question 16 and 17, Exercise 6.2 Solutions of Question 16 and 17 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $1,2,3,4,5,6$$1, 3$$5$$=3 \times{ }^{5} P_{5}=360$$4$$1,2,3,4$$5$$1$$={ }^{4} P_{3}=24$$3$$24$$5$$24$$24+24+24=72$$4$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:43 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-3-p9 Question 11 and 12, Exercise 6.3 Solutions of Question 11 and 12 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $n$$35$$n$\begin{align*}{ }^{n} C_{2}-n&=35\\ \text{or} \quad \dfrac{n!}{2!(n-2)!}-n&=35\\ \dfrac{n(n-1)(n-2)!}{2(n-2)!}-n&=35\\ \dfrac{n(n-1)-2 n}{2}&=35\\ n^{2}-n-2 n&=70\\ n^{2}-3 n-70&=0\\ n^{2}+7 n-10 n-70 & =0 \\ n(n+7)-… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:31 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-1 Exercise 6.1 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$10!$$\dfrac{12!}{7! 3! 2!}$$\dfrac{4!-2!}{3!+5!}$$\dfrac… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:40 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-2-p5 Question 6 and 7, Exercise 6.2 Solutions of Question 6 and 7 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $4$$$1,2,3,4,5,6$$6$$6$$6$$6$$$\text{Total possibilities }6 \times 6 \times 6 \times 6=6^4=1296$$$1,1,2,2,3,3,4$$=7$$2^{\text {nd }}$$6^{\text {th }}$$1^{\text {st }}, 3^{\text {rd }}, 5^{\text {th }}$$7^{\text {th }}$$2,2,4$$1,1,… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 08:59:54 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/ex6-3-p6 Question 5 and 6, Exercise 6.3 Solutions of Question 5 and 6 of Exercise 6.3 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $11$$16$$11$$16$${ }^{16} C_{11}$$4368$$11$$11$$16$$10$$15$$$ { }^{15} C_{10}=3003 $$$5$$3$$3$$1$${ }^{5} C_{1}$$2$${ }^{3} C_{2}$$={ }^{5} C_{1} \times{ }^{3} C_{2}=5 \times 3=15$$2$$={ }^{5} C_{2} \times{ }^{3} C_{1}=10 \times 3… anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:29 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/re-ex6-p2 Question 2 and 3, Review Exercise 6 Solutions of Question 2 and 3 of Review Exercise 6 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $4$$26$$$^{26}P_4=358800$$$3$$0$$3$$100's$$9$$3$$$=10\times 10\times10=1000$$$0$$10$$3-$$0$$$=10\times 10=100$$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:43 +0000 https://www.mathcity.org/math-11-nbf/sol/unit06/rev-ex Review Exercise (Solutions) The solutions of the Review Exercise of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. Question 1.$4$$3$$0$$6$$0,2,3,4,5,7$$7$ anonymous@undisclosed.example.com (Anonymous) Sat, 08 Mar 2025 09:00:41 +0000