Two pipes A and B work alternatively with a third pipe C to fill a swimming pool. Working alone, A, B and C require 10, 20 and 15 hours respectively. Find the total time required to fill the pool.
(A) 7 hours 14 minutes
(B) 6 hours 54 minutes
(C) 5 hours 14 minutes
(D) 8 hours 54 minutes

Two friends A and B decided to work together and fill a pool of capacity 1000 liters. Using a bucket each, A fills at the rate of 4 liters every 3 minutes and B fills at 3 liters every 4 minute. What would be the total time required to fill the pool, given that they take a break of 3 minutes each time both of them put a bucket into the pool at the same instant ?
(A) 6 hours
(B) 10 hours
(C) 8 hours
(D) 9 hours 57 minutes

Out of 7 boys and 4 girls, how many queues of 3 boys and 2 girls can be formed?
(A) 120
(B) 25200
(C) 24800
(D) 1440

What is the number of possible words that can be made using the word “EASYQUIZ” such that the vowels always come together?
(A) 120
(B) 720
(C) 2880
(D) 4320

The value of ⁷⁵C₂ is:

(A) 1215

(B) 2315

(C) 2775

(D) 1675

In how many different ways can the alphabets of the word ‘SCORING’ be arranged so that the vowels always come together?
(A) 120
(B) 720
(C) 240
(D) 1440

How many ways a 6 member team can be formed having 3 men and 3 ladies from a group of 6 men and 7 ladies?
(A) 700
(B) 720
(C) 120
(D) 500

How many 4-digit numbers can be formed from the digits 1, 2, 3, 4, 5, 6 and 7 which are divisible by 5 when none of the digits are repeated?
(A) 120
(B) 35
(C) 24
(D) 720

In how many ways can 20 boys and 18 girls make a queue such that no two girls are together?
(A) 20!* ²⁰C₁₈
(B) 20!* ²⁰P₁₈
(C) 20!* ²¹C₁₈
(D) 20!* ²¹P₁₈

In how many ways can an interview panel of 3 members be formed from 3 engineers, 2 psychologists and 3 managers if at least 1 engineer must be included?
(A) 30
(B) 15
(C) 46
(D) 45