Directions(1-5): Permutation and Combinations
1. In how many ways can the letters of the word 'APPLE' be arranged ?

A. 720 B. 120 C. 60 D. 180

Answer : Option C
Explanation: The word 'APPLE' contains 5 letters, 1A, 2P, 1L.and 1E. ∴ Required number of ways = [latex]\frac{5!}{(1!)(2!)(1!)(1!)}[/latex] = 60
2. The value of [latex]{75}_{{P}_{2}}[/latex] is :

A. 2775 B. 150 C. 5550 D. None of these

Answer : Option C
Explanation: [latex]{75}_{{P}_{2}}[/latex] = [latex]\frac{75!}{75-2!}[/latex] = [latex]\frac{75!}{73!}[/latex] = [latex]\frac{75*74*(73!)}{73!}[/latex] = (75 * 74) = 5550.
3. In how many ways can the letters of the word 'LEADER' be arranged ?

A. 72 B. 144 C. 360 D. 720

Answer : Option C
Explanation: In the word 'MATHEMATICS', we treat the vowels AEAI as one letter. The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R. ∴ Required number of ways = [latex]\frac{6!}{(1!)(2!)(1!)(1!)(2!)}[/latex] = 360
4. How many words with or without meaning, can be formed by using all the letters of the word, 'DELHI', using each letter exactly once ?

A. 10 B. 25 C. 60 D. 120

Answer : Option D
Explanation: The word 'DELHI' contains 5 different letters. Required number of words = Number of arrangements of 5 letters, taken all at a time = [latex]{5}_{{P}_{5}}[/latex] = 5 ! = (5 *4 *3 *2 *1) = 120.
5. In how many different ways can the letters of the word 'RUMOUR' be arranged ?

A. 180 B. 90 C. 30 D. 720

Answer : Option A
Explanation: The word 'RUMOUR' contains 6 letters, namely 2R, 2U, 1M and 1U. ∴ Required number of ways = [latex]\frac{6!}{(2!)(2!)(1!)(1!)}[/latex] = 180

Directions(1-5): Averages 1. 3 years ago, the average of a family of 5 members was 17 years. A baby having been born, the average age of the family is the same today. The present age of the baby is:

A. 5 years B. 2 years C. 1 year D. 4 years

Answer : Option B
Explanation: Total age of 5 members, 3 years ago = (17 x 5) years = 85 years Total age of 5 members now = (85 + 3 x 5) years = 100 years Total age of 6 members now = (17 x 6) years = 102 years Age of the baby = (102 – 100) years = 2 years
2. The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years. The ratio of the number of boys to the number of girls in the class is:

A. 1 : 4 B. 2 : 3 C. 3 : 4 D. 4 : 2

Answer : Option B
Explanation: Let the ratio be k:1 Then, k x 16.4 + 1 x 15.4 = (k + 1) x 15.8 (16.4 – 15.8) k = (15.8 – 15.4) k = [latex]\frac{2}{3}[/latex]
3. The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what is the price of each of these two books?

A. Rs 10 and Rs 16 B. Rs 12 and Rs 24 C. Rs 24 and Rs 18 D. Rs 28 and Rs 12

Answer : Option A
Explanation: Total price of the two books = Rs. [(12 x 10) – (11.75 x 8)] = Rs. (120 – 94) = Rs. 26 Let the price of one book be Rs.x Then, the price of other book = Rs. (x + 60% of x ) = x + [latex]\frac{3}{5}[/latex]x = ([latex]\frac{8}{5}[/latex])x so, x + [latex]\frac{8}{5}[/latex]x = 26 , x = 10 The prices of the two books are Rs. 10 and Rs. 16
4. The average age of 30 boys of a class is equal to 14 years. When the age of the class teacher is included the average becomes 15 years. Find the age of the class teacher?

A. 50 B. 44 C. 45 D. 42

Answer : Option C
Explanation: Total ages of 30 boys = 14 x 30 = 420 years Total age when class teacher is included = 15 x 31 = 465 years Age of class teacher = 465 – 420 = 45 years
5. The Average of marks obtained by 120 candidates in a certain examination is 35. If the average marks of passed candidates is 39 and that of failed candidates is 15, what is the number of candidates who passed the examination?

A. 90 B. 100 C. 108 D. 115

Answer : Option B
Explanation: Let the number of passed candidates be a Then total marks =>120 x 35 = 39 a + (120 – a) x 15 4200 = 39 a + 1800 – 15 a a = 100

Directions(1-5): The following series are based on a specific pattern. In these series one number is wrong, find that odd one. 1. 6, 22, 34, 78, 146, 305, 594

A. 32 B. 22 C. 305 D. 146

Answer : Option C
Explanation: 6*2 + 10 = 22 22*2 – 10 = 34 34*2 + 10 = 78 78*2 – 10 = 146 146*2 + 10 = 302 302*2 – 10 = 594
2. 4, 4, 15, 74, 524, 4724, 51974

A. 51974 B. 15 C. 74 D. 524

Answer : Option B
Explanation: 4*1 + 0 = 4 4*3 + 2 = 14 14*5 + 4 = 74 74*7 + 6 = 524 524*9 + 8 = 4724 4724*11 + 10 = 51974
3. 3, 5, 13, 39, 177, 891

A. 177 B. 13 C. 5 D. 39

Answer : Option D
Explanation: 3*1 + 2 = 5 5*2 + 3 = 13 13*3 + 4 = 43 43*4 + 5 = 177 177*5 + 6 = 891
4. 3, 7, 12, 32, 57, 93, 142

A. 7 B. 12 C. 32 D. 57

Answer : Option B
Explanation: 3 + [latex]{2}^{2}[/latex] = 7 7 + [latex]{3}^{2}[/latex] = 16 16 + [latex]{4}^{2}[/latex] = 32 32 + [latex]{5}^{2}[/latex] = 57 16 + [latex]{4}^{2}[/latex] = 32 32 + [latex]{5}^{2}[/latex] = 57 57 + [latex]{6}^{2}[/latex] = 93 93 + [latex]{7}^{2}[/latex] = 142
5. 2, 13, 38, 130, 522, 2625

A. 2625 B. 522 C. 38 D. 130

Answer : Option D
Explanation: 2*1 + 11 = 13 11*2 + 12 = 38 38*3 + 13 = 127 127*4 + 14 = 522 522*5 = 2625