q: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and repetition is allowed?
Options:
(A) 3441
(B) 3433
(C) 3333
(D) 3430
(E) 3773
a: Stream of consciousness: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 5 Ways ( As the question states that the last letter has to be a consonant)
Second letter can be filled in 7 Ways
Third letter can be filled in 7 Ways
Fourth letter can be filled in 7 Ways
So, Total number of ways = 2 Ways x 7 Ways x 7 ways x 7 ways x 5 ways = 3430 The answer is (D).

question: A train running at the speed of 60 km/hr crosses a pole in 9 seconds. Find the length of the train?
Options:
(A) 150
(B) 8827
(C) 166
(D) 199
(E) 121
answer: Stream of consciousness: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 9 = 150 meter The answer is (A).

q: A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 30 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 3/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
a: Stream of consciousness: The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 30/100 = 3/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) (1/5) (3/10) = 3/200 The answer is (A).

question: Which of the following is equal to the average (arithmetic mean) of (y+4)^2 and (y-4)^2?
Options:
(A) x^2
(B) x^2+2
(C) x^2 +12
(D) x^2+21
(E) y^2+16
answer: Stream of consciousness: Avg = [(y+4)^2 + (y-4)^2] / 2
Expanding and simplifying, (y^2 + 8y + 16 + y^2 - 8y + 16 ) / 2 = y^2 + 16 The answer is (E).

q: In an examination, 47% failed in English and 54% failed in Mathematics. Find the pass percentage in both the subjects if 31% failed in both the subjects?
Options:
(A) 70
(B) 50
(C) 40
(D) 20
(E) 30
a: Stream of consciousness: 16+31+23 = 70
100-70 = 30 The answer is (E).

q: Find the average of the first 41 natural numbers?
Options:
(A) 8
(B) 9
(C) 10
(D) 11
(E) 21
a:
Stream of consciousness: Average of the first 'n' natural numbers = (n + 1)/2
We get (41 + 1)/2 = 21 The answer is (E).