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

The shaded region in the adjoining diagram represents.

Find a so that the sum and product of the roots of the equation 2x²+ (a - 3) x + 3a - 5 = 0 are equal is

In a \(\triangle\) ABC, C = 90° then the value of sin A + sin B - 2\(\sqrt{2} cos{A\over2}cos {B\over 2}is\) _______________

If ⁿP_t = 720 nCr, then the value of r =  _________

Write the set {-1, 1} in set builder form.

If sec \(\theta\) + tan \(\theta\) = p, obtain the values of sec \(\theta\), tan \(\theta\) and sin \(\theta\) in terms of p

Find the value of \(\frac { 12! }{ 9!\times 3! } \)

In how many ways can the letters of the word PENCIL be arranged so that N is always next to E.

A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected, if the team has atleast one boy and one girl

A salesperson whose annual earnings can be represented by the function A(x) = 30,000 + 0.04x, where x is the rupee value of the merchandise he sells. His son also in sales and his earnings are represented by the function S(x) = 25,000 + 0.05x. Find (A+S) (x) and determine the total family income if they each sell Rs. 1,50,00,000 worth of merchandise.

Find the range of the following functions given by  \( f(x) = \frac { 1 }{ 2-sin\ 3x } .\)

If \(tan A=\frac{5}{6},tan B=\frac{1}{11}\)show that A + B = 45°.

If the letter of the word 'RACHIT' are arranged in all possible ways as listed in dictionary, then what is the rank of the word 'RACHIT'?

If \({1\over 7!}+{1\over9!}={x\over10!},\) find x.

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)

Show that the relation R on the set A = {x ∈ Z : 0 < x < 12} given by R = {(a, b) : la - b| is a multiple of 4} is an equivalence relation

A committee of 7 peoples has to be formed from 8 men and 4 women. In how many ways can this be done when the committee consists of
(i) exactly 3 women?
(ii) at least 3 women?
(iii) at most 3 women?

For any natural number n, 7ⁿ - 2ⁿ is divisible by 5.