1.A two-digit number has digits whose sum is 12 and whose difference is 6. What is the number?
2.A two-digit number has a tens digit that exceeds its units digit by 2. If the number equals seven times the sum of its digits, what is the units digit?
3.Find the value of x that satisfies the equation: 6x - 27 + 3x = 4 + 9 - x.
4.Find the value of x that satisfies the equation: 19(x + y) + 17 = 19(-x + y) - 21.
5.The combined price of 2 chairs and 3 tables is Rs.1300, while the total cost of 3 chairs and 2 tables is Rs.1200. By how much does the price of one table exceed the price of one chair?
6.A fraction has a denominator that is one less than twice its numerator. When both the numerator and denominator are increased by 1, the fraction equals 3/5. What is the original fraction?
7.The price of 10 kilograms of apples is the same as the price of 24 kilograms of rice. Additionally, the cost of 6 kilograms of flour is equal to the cost of 2 kilograms of rice. If the price per kilogram of flour is Rs. 20.50, what is the combined cost of purchasing 4 kilograms of apples, 3 kilograms of rice, and 5 kilograms of flour?
8.A question paper contains five problems, each with three internal options. In how many different ways can a candidate attempt at least one problem by choosing one option per problem?
9.There are 20 male students and 25 female students in a class. How many different pairs consisting of one boy and one girl can be formed?
10.How many different ways can you choose three consonants and two vowels from the letters in the word "TRIANGLE"?
11.A container holds 9 yellow balls, 3 white balls, and 4 red balls. How many different ways can you select two balls from this collection?
12.Using the digits {1, 2, 3, 5, 7, 9}, how many distinct four-digit even numbers can be created?
13.Using the digits {1, 3, 4, 5, 7, 9} without repeating any digit, how many unique four-digit numbers can be created?
14.In how many different ways can six boys and six girls be arranged in a single row for a photograph such that no two girls are seated next to each other?
15.A lock features three rotating rings, each displaying six unique letters. What is the maximum number of failed attempts possible before the lock opens?
16.A committee consists of 5 men and 6 women. How many different ways can a team of eight members be chosen from this committee?
17.How many different ways can you choose 3 men and 2 women if it is required that a specific man and a specific woman are included in the selection?
18.A group consists of 5 males and 6 females. How many different ways can you choose 2 males and 3 females from this group?
19.How many distinct arrangements can be formed using all the letters in the word 'MESMERISE'?
20.How many different arrangements can be made using the letters of the word MEADOWS such that all vowels are positioned only in the even-numbered slots?