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- Exercise 6.1 (Solutions)
- Question 1, Exercise 6.1
- Question 2, Exercise 6.1
- Question 3 and 4, Exercise 6.1
- Question 5, Exercise 6.1
- Question 6(i-v), Exercise 6.1
- Question 6(vi-ix), Exercise 6.1
- Question 7(i-vi), Exercise 6.1
- Question 7(vii-xi), Exercise 6.1
- Exercise 6.2 (Solutions)
- Question 1, Exercise 6.2
- Question 2, Exercise 6.2
- Question 3, Exercise 6.2
- Question 4 and 5, Exercise 6.2
- Question 6 and 7, Exercise 6.2
- Question 8 and 9, Exercise 6.2
- Question 10 and 11, Exercise 6.2
- Question 12 and 13, Exercise 6.2
- Question 14 and 15, Exercise 6.2
- Question 16 and 17, Exercise 6.2
- Question 18 and 19, Exercise 6.2
- Question 20 and 21, Exercise 6.2
- Question 22 and 23, Exercise 6.2
- Exercise 6.3 (Solutions)
- Question 1(i-v), Exercise 6.3
- Question 1(vi-x), Exercise 6.3
- Question 2, Exercise 6.3
- Question 3, Exercise 6.3
- Question 4, Exercise 6.3
- Question 5 and 6, Exercise 6.3
- Question 7 and 8, Exercise 6.3
- Question 9 and 10, Exercise 6.3
- Question 11 and 12, Exercise 6.3
- Question 13 and 14, Exercise 6.3
- Question 1, Review Exercise 6
- Question 2 and 3, Review Exercise 6
- Question 4, 5 and 6, Review Exercise 6
- Review Exercise (Solutions)
Fulltext results:
- Exercise 6.2 (Solutions)
- ====== Exercise 6.2 (Solutions) ====== The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” p... ${ }^n P_n=2 \cdot{ }^n P_{n-2}$\\ [[math-11-nbf:sol:unit06:ex6-2-p1|Solution Question 1]] **Question 2.** Find $n$, if:\\ (i) $\quad n P_4=20^n P_2$ (ii)
- Exercise 6.3 (Solutions)
- ====== Exercise 6.3 (Solutions) ====== The solutions of the Exercise 6.3 of book “Model Textbook of Mathematics for Class XI” p... +{ }^{n} C_{r-1}={ }^{n+1} C_{r}$\\ [[math-11-nbf:sol:unit06:ex6-3-p1|Solution: Question 1(i-v)]] **Question 1(vi-x).** Prove the following for $n \in \mat
- Exercise 6.1 (Solutions)
- ====== Exercise 6.1 (Solutions) ====== The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” p... -2)!}$ (v) $\dfrac{8!}{(6!)^2}$ \\ [[math-11-nbf:sol:unit06:ex6-1-p1|Solution: Question 1]] **Question 2.** Write the following in factorial form:\\ (i) 1
- Review Exercise (Solutions)
- ====== Review Exercise (Solutions) ====== The solutions of the Review Exercise of book “Model Textbook of Mathematics for Class XI... tion. Choose the correct option. \\ [[math-11-nbf:sol:unit06:Re-ex6-p1|See MCQs: Question 1]] **Questi... by using $4$ distinct alphabets?\\ [[math-11-nbf:sol:unit06:Re-ex6-p2|Solution: Question 2 & 3 ]] **Q
- Question 2, Exercise 6.2
- ====== Question 2, Exercise 6.2 ====== Solutions of Question 2 of Exercise 6.2 of Unit 06: Permutation ... )===== Find $n$, if: $\quad ^nP_4=20\, ^nP_2$ ** Solution. ** \begin{align*} \dfrac{m}{(n-4)!}&=20 \c... = Find $n$, if: $\quad ^{2n}P_3=100 \, ^nP_2$ ** Solution. ** \begin{align*} \dfrac{(2 n)!}{(2 n-3)!}... ind $n$, if: $\quad16\, ^nP_3=13\, ^{n+1}P_3$ ** Solution. ** \begin{align*}16 \dfrac{n!}{(n-3)!}&=13
- Question 3, Exercise 6.2
- ====== Question 3, Exercise 6.2 ====== Solutions of Question 3 of Exercise 6.2 of Unit 06: Permutation ... ion 3(i)===== Find $r$, if: $^6P_{r-1}=^5P_4$ ** Solution. ** \begin{align*}{ }^{6} P_{r-1}&={ }^{5} ... (ii)===== Find $r$, if: $^{10}P_{r}=2\,^9P_r$ ** Solution. ** \begin{align*}{ }^{10} P_{r}&=2 \times{... on 3(iii)===== Find $r$, if: $^{15}P_{r}=210$ ** Solution. ** \begin{align*}^{15}P_{r}&=210\\ \dfrac{
- Question 7(i-vi), Exercise 6.1
- ====== Question 7(i-vi), Exercise 6.1 ====== Solutions of Question 7(i-vi) of Exercise 6.1 of Unit 06: ... $\quad \dfrac{n!}{(n-2)!}=930,\quad n \geq 2$ ** Solution. ** \begin{align*} \dfrac{n!}{(n-2)!}&=930\... }=20\cdot \dfrac{n!}{(n-3)!}, \quad n \geq 5$ ** Solution. ** \begin{align*} \dfrac{n!}{(n-5)!}&=20\c... == Find $n$, if $\quad (n+2)!= 60\cdot(n-1)!$ ** Solution. ** \begin{align*} (n+2)!&= 60(n-1)!\\ (n+2
- Question 2, Exercise 6.3
- ====== Question 2, Exercise 6.3 ====== Solutions of Question 2 of Exercise 6.3 of Unit 06: Permutation ... )===== Find $n$, if : $\,\, ^nC_5=\,\, ^nC_8$ ** Solution. ** \begin{align*}\dfrac{n!}{5!(n-5)!}=\dfr... === Find $n$, if : $\,\, ^nC_{15}=\,\, ^nC_7$ ** Solution. ** Since \begin{align*}{ }^{n} C_{r}&={ }^... === Find $n$, if : $\,\, ^nC_{50}=\,\, ^nC_1$ ** Solution. ** As we know \begin{align*}{ }^{n} C_{1}&
- Question 6(i-v), Exercise 6.1
- ====== Question 6(i-v), Exercise 6.1 ====== Solutions of Question 6(i-v) of Exercise 6.1 of Unit 06: Pe... d (2n)!=2^n(n!)[1\cdot3\cdot5 \cdots (2n-1)]$ ** Solution. ** \begin{align*} (2n)!&= (2n)(2n-1)(2n-2)... )!(n-1)]=(n+2)!$ FIXME problem in third term ** Solution. ** \begin{align*}L.H.S.&= (n+1)[n!n+(n-1)!(... c{n!}{r!(n-r+1)!}=\dfrac{(n+1)!}{r!(n-r+1)!}$ ** Solution. ** =====Question 6(iv)===== Prove for
- Question 1(vi-x), Exercise 6.3
- ====== Question 1(vi-x), Exercise 6.3 ====== Solutions of Question 1(vi-x) of Exercise 6.3 of Unit 06: ... ^{2n}C_n=\dfrac{2^n[1.3.5.\cdots(2n-1)]}{n!}$ ** Solution. ** \begin{align*}L.H.S &=\quad^{2n}C_n \\ ... $\quad^nC_p=^nC_q\implies p=q\,\,or\,\,p+q=n$ ** Solution. ** Let \begin{align*}{ }^{n} C_{p}&={ }^{n... $\,\,^nC_r+2^nC_{r-1}+^nC_{r-2}=\,^{n+2}C_r$ ** Solution. ** \begin{align*}L.H.S& ={ }^{n} C_{p}+2^{
- Question 4, Exercise 6.3
- ====== Question 4, Exercise 6.3 ====== Solutions of Question 4 of Exercise 6.3 of Unit 06: Permutation ... $\,\,^nC_{r-1}:\,^nC_{r}:\,^nC_{r+1}=6:14:21$ ** Solution. ** \begin{align*}\dfrac{n!}{(r-1)!(n-(r-1... xt{and}\\ 5r-2n+3&=0\quad \cdots(ii)\end{align*} Solving both equations simultaneously.\\ Multiply (ii... : $\,\,^nC_{r-1}:\,^nC_{r}:\,^nC_{r+1}=3:4:5$ ** Solution. ** \begin{align*}{ }^{n} C_{r-1}:{ }^{n} C
- Question 7 and 8, Exercise 6.3
- ====== Question 7 and 8, Exercise 6.3 ====== Solutions of Question 7 and 8 of Exercise 6.3 of Unit 06: ... can it be done if it has exactly $2$ women. ** Solution. ** (i) If there are exactly $2$ women then... can it be done if it has at least $2$ women. ** Solution. ** At least $2$ women means there could be... can it be done if it has at most $2$ women? ** Solution. ** At most to women mean either $1$ or $2$
- Question 1, Exercise 6.1
- ====== Question 1, Exercise 6.1 ====== Solutions of Question 1 of Exercise 6.1 of Unit 06: Permutation ... an. =====Question 1(i)===== Evaluate $10!$. ** Solution. ** \begin{align*} 10! &= 10 \times 9 \tim... 1(ii)===== Evaluate $\dfrac{12!}{7! 3! 2!}$. ** Solution. ** \begin{align*} \dfrac{12!}{7! \, 3! \, ... n 1(iii)===== Evaluate $\dfrac{4!-2!}{3!+5!}$ ** Solution. ** \begin{align*} \dfrac{4! - 2!}{3! + 5!}
- Question 2, Exercise 6.1
- ====== Question 2, Exercise 6.1 ====== Solutions of Question 2 of Exercise 6.1 of Unit 06: Permutation ... onal form: $\quad 14\cdot 13\cdot 12\cdot 11$ ** Solution. ** \begin{align*} &14\cdot 13\cdot 12\cdot ... form: $\quad 1\cdot 3\cdot 5 \cdot 7 \cdot 9$ ** Solution. ** $$1 \times 3\times 5\times 7 \times 9$$... rite in the fractional form: $\quad n(n^2-1)$ ** Solution. ** $$n(n^2-1)=n(n-1)(n+1)$$ Multiply and d
- Question 3 and 4, Exercise 6.1
- ====== Question 3 and 4, Exercise 6.1 ====== Solutions of Question 3 and 4 of Exercise 6.1 of Unit 06: ... }+\dfrac{3}{6!}+\dfrac{1}{7!}=\dfrac{4}{315}$ ** Solution. ** \begin{align*} LHS = & \dfrac{1}{5!}+\df... that: $\quad \dfrac{(n-1)!}{(n-3)!}=n^2-3n+2$ ** Solution. ** \begin{align*} LHS = & \dfrac{(n-1)!}{(n... ac{(2n)!}{n!}=2^n(1\cdot3\cdot5\cdots(2n-1))$ ** Solution. ** \begin{align*} L.H.S.&=\dfrac{(2n)!}{n!