Q11. 
The letter of the word $LABOUR$ are permuted in all possible ways and the words thus formed are arranged as in a dictionary. What is the rank of the word $LABOUR$? 
A.  275 

B.  251 

C.  240 

D.  242 
Q12. 
There are fourteen juniors and twentythree seniors in the Service Club. The club is to send four representatives to the State Conference. (i) How many different ways are there to select a group of four students to attend the conference? (ii) If the members of the club decide to send two juniors and two seniors, how many different groupings are possible? 
A.  (i): ${^{37}C_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$ 

B.  (i): ${^{37}P_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$ 

C.  (i): ${^{37}P_4}$ , (ii): ${^{14}C_2}×{^{23}C_2}$ 

D.  (i): ${^{37}C_4}$ , (ii): ${^{14}P_2}×{^{23}P_2}$ 
Q13. 
A class photograph has to be taken. The front row consists of 6 girls who are sitting. 20 boys are standing behind. The two corner positions are reserved for the 2 tallest boys. In how many ways can the students be arranged? 
A.  6! × 1440 

B.  18! × 1440 

C.  18! ×2! × 1440 

D.  None of these 
Q14. 
If $5 × {^nP_3} = 4 × {^{n+1}P_3}$ find $n$? 
A.  10 

B.  12 

C.  11 

D.  14 
Q15. 
Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is: 
A.  69760 

B.  30240 

C.  99748 

D.  42386 