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.

Select the best matching option. Chose the correct option.
i. If $3\,\,^nP_3=^nP_4$ then value of $n$ is:

• (a) $5$
  
• (b) $6$
  
• (c) $7$
  
• (d) $8$
  See Answer

  (b): $6$

ii. Numbers of ways of arrangement of the word “GARDEN”

• (a) $ 480$
  
• (b) $600$
  
• (c) $720$
  
• (d) $840$
  See Answer

  ©: $720$

iii. The product of $r$ consective positive numbers is divisible by

• (a) $r!$
  
• (b)$(r+1)!$
  
• (c) $r!+1$
  
• (d) $ 2r!$
  See Answer

  (a): $r!$

iv. The total number of $6$-digit number in which all the odd and only odd digits appear is:

• (a) $\dfrac{5}{2}\,\,6!$
  
• (b) $6!$
  
• (c) $\dfrac{1}{2}\,\,6!$
  
• (d) $\dfrac{3}{2}\,\,6!$
  See Answer

  (a): $\dfrac{5}{2}\,\,6!$

v. Let $A=\{1,2,3,4,...,20\}. $ Find the number of ways that the integer chosen a prime number is:

• (a) $3$
• (b) $5$
• (c) $7$
• (d) $8$
  See Answer

  (d): $8$

vi. From $A=\{1,3,5,7,9\}$ and $B=\{2,4,6,8\}$ if a cartisan product $A\times B$ is chosen, then the number of ways that $a+b=9$ is :

• (a) $0$
  
• (b) $2$
  
• (c) $3$
  
• (d) $4$
  See Answer

  ©: $3$

vii. A student has to answer $10$ out of $12$ question in an examination such that he must choose at least $4$ from first five questions. The number of choices is:

• (a) $30$
• (b) $35$
• (c) $40$
• (d) $45$
  See Answer

  (b): $35$

viii. If $^nC_4=^nC_{10}$, then value of $n$ is:

• (a) $10$
• (b) $12$
• (c) $13$
• (d) $14$
  See Answer

  (d): $14$

ix. If $^{15}C_{3r}=^{15}C_{r+3}$, then value of $r$ is:

• (a) $1$
• (b) $2$
• (c) $3$
• (d) $4$
  See Answer

  (c): $3$

x. The numbers of ways in which $r$ latters can be posted in $n$ letter boxes in a town is:

• (a) $^nC_r$
• (b) $^nP_r$
• (c) $r^n$
• (d) $n^r$
  See Answer

  (c): $r^n$

Question 2 & 3>