The number of constant functions from a set containing m elements to a set containing n elements is

The function f:[0,2π]➝[-1,1] defined by f(x) = sin x is

If the function f:[-3,3]➝S defined by f(x) = x² is onto, then S is

Given A = {5,6,7,8}. Which one of the following is incorrect?

The shaded region in the adjoining diagram represents.

Write the following in roster form {x\(\in \)N : 4x + 9 < 52}

Write the following in roster form.
\(\left\{ x:\frac { x-4 }{ x+2 } =3,x\in R-\{ -2\} \right\} \)

The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S functions of the mileage m; C(m) = 0.4m + 50 and S(m) = 0.03m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles.

Check whether the following sets are disjoint where p = {x : x is a prime < 15} and Q = {x : x is a multiple of 2 and x < 16}

If U = {x : 1 ≤ x ≤ 10, x ∈ N}, A = {1, 3, 5, 7, 9} and B = {2, 3, 5, 9, 10} then find A'UB'.

Graph the function f(x) = x³ and \(g(x)=\sqrt[3]x\) on the same co-ordinate plane. Find f o g and graph it on the plane as well. Explain your results.

Write the steps to obtain the graph of the function y = 3(x-1)²+5 from the graph y = x²

By taking suitable sets A, B, C, verify the following results:
A \(\times\) (B\(\cap \)C) = (A\(\times\)B) \(\cap \) (A\(\times\)C)

Find the pairs of equal sets from the following sets. A = {0}, B = {x : x > 15 and x < 5}, C = {x : x - 5 = 0}, D = {x : x² = 25}, E = {x : x is an integral positive root of the equation x² - 2x - 15 = 0}.

Which of the following sets are finite and which are infinite?
Set of concentric circles in a plane.

The formula for converting from Fahrenheit to Celsius temperatures is \(y={5x\over 9}-{160\over 9}\). Find the inverse of this function and determine whether the inverse is also a function.

A simple cipher takes a number and codes it, using the function f(x) = 3x - 4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x(by drawing the lines)

The cartesian product A \(\times\) A has 9 elements among which are found (-1, 0) and (0, 1).Find the set A and the remaining elements of A \(\times\)A.

Show that the relation R on the set R of all real numbers defined as R = {(a, b): a < b²} is neither reflexive, nor symmetric nor transitive.