Let A = {1, 2, 3} and B = {x | x is a prime number less than 10}. Find A × B and B × A

Concept: Ordered Pair

If B × A = {(-2, 3), (-2, 4), (0, 3), (0, 4), (3, 3), (3, 4)} find A and B

Concept: Ordered Pair

Multiple Choice Question :

If the ordered pairs (a + 2, 4) and (5, 2a + b) are equal then (a, b) is

Concept: Ordered Pair

If the ordered pairs (x^{2} – 3x, y^{2} + 4y) and (– 2, 5) are equal, then find x and y

Concept: Ordered Pair

Find all positive integers, when divided by 3 leaves remainder 2

Concept: Euclid’s Division Lemma

Prove that the product of two consecutive positive integers is divisible by 2

Concept: Euclid’s Division Lemma

When the positive integers a, b and c are divided by 13, the respective remainders are 9, 7 and 10. Show that a + b + c is divisible by 13

Concept: Euclid’s Division Lemma

Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4

Concept: Euclid’s Division Lemma

If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y

Concept: Euclid’s Division Lemma

A positive integer, when divided by 88, gives the remainder 61. What will be the remainder when the same number is divided by 11?

Concept: Euclid’s Division Lemma

Prove that two consecutive positive integers are always co-prime

Concept: Euclid’s Division Lemma

Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy

Concept: Euclid’s Division Lemma

Using Euclid’s division lemma, if the cube of any positive integer is divided by 9 then the possible remainders are

Concept: Euclid’s Division Lemma

Prove that n^{2} – n divisible by 2 for every positive integer n

Concept: Euclid’s Division Lemma

When the positive integers a, b and c are divided by 13 the respective remainders is 9, 7 and 10. Find the remainder when a b + + 2 3c is divided by 13

Concept: Euclid’s Division Lemma

Show that 107 is of the form 4q +3 for any integer q

Concept: Euclid’s Division Lemma

Solve the following system of linear equations in three variables

x + y + z = 5; 2x – y + z = 9; x – 2y + 3z = 16

Concept: Simultaneous Linear Equations in Three Variables

Solve the following system of linear equations in three variables

`1/x - 2/y + 4 = 0; 1/y - 1/z + 1 = 0; 2/z + 3/x = 14`

Concept: Simultaneous Linear Equations in Three Variables

Solve the following system of linear equations in three variables

x + 20 = `(3y)/2 + 10` = 2z + 5 = 110 – (y + z)

Concept: Simultaneous Linear Equations in Three Variables

Discuss the nature of solutions of the following system of equations

x + 2y – z = 6; – 3x – 2y + 5z = – 12; x – 2z = 3

Concept: Simultaneous Linear Equations in Three Variables