If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.

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

Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R₁ = {(3,7), (4,7), (7,10), (8,1)}

A Relation R is given by the set {(x, y) / y = x + 3, x \(\in \) {0, 1, 2, 3, 4, 5}}. Determine its domain and range.

A relation ‘f’ \(X \rightarrow Y\) is defined by f(x) = x² - 2 where x \(\in \) {-2, -1, 0, 3} and Y = R
(i) List the elements of f
(ii) Is f a function?

Let f{(x, y)| x, y \(\in \) N and y = 2x}. be a relation on ℕ. Find the domain, co-domain and range. Is this relation a function?

Let f(x) = 2x + 5. If x ≠ 0 then find \(\frac { f(x+2)-f(2) }{ x } \).

A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.

If A = {-2, -1, 0, 1, 2} and f: A ⟶ B is an onto function defined by f(x) = x² + x + 1 then find B.

For what values of natural number n, 4ⁿ can end with the digit 6? 

Determine the value of d such that 15 \(\equiv \) 3 (mod d).

Find the next three terms of the following sequence.
8, 24, 72, … 

Find the first term and common difference of the Arithmetic Progressions whose n^th terms are given below t_n = -3 + 2n

Find the sum of the following series
1 + 2 + 3 +...+ 60

Find the LCM and GCD for the following and verify that f(x) x g(x) = LCM x GCD
(x³ - 1)(x + 1), (x³ + 1)

QA and PB are perpendiculars to AB. If AO = 10 cm, BO = 6 cm and PB = 9 cm. Find AQ.

In the figure, AD is the bisector of \(\angle\)A. If BD = 4 cm, DC = 3 cm and AB = 6 cm, find AC.

Two circles with centres O and O' of radii 3 cm and 4 cm, respectively intersect at two points P and Q, such that OP and O'P are tangents to the two circles. Find the length of the common chord PQ.

Find the area of the triangle whose vertices are (-3, 5) , (5, 6) and (5, - 2)

Find the equation of a straight line whose Inclination is 45⁰ and y intercept is 11

If the base area of a hemispherical solid is 1386 sq. metres, then find its total surface area?

The standard deviation and mean of a data are 6.5 and 12.5 respectively. Find the coefficient of variation.

Two coins are tossed together. What is the probability of getting different faces on the coins?

What is the probability of drawing either a king or a queen in a single draw from a well shuffled pack of 52 cards?

Find the range and coefficient of range of the following data.
43.5, 13.6, 18.9, 38.4, 61.4, 29.8