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

If (x - 6) is the HCF of x² - 2x - 24 and x² - kx - 6 then the value of k is

Graph of a linear equation is a ____________

If \(\triangle\)ABC is an isosceles triangle with \(\angle\)C = 90^o and AC = 5 cm, then AB is

The point of intersection of 3x − y = 4 and x + y = 8 is

If sin \(\theta \) + cos\(\theta \) = a and sec \(\theta \) + cosec \(\theta \) = b, then the value of b(a² - 1) is equal to 

Let X = {1, 2, 3, 4} and Y = {2, 4, 6, 8,10} and R = {(1, 2),(2, 4),(3, 6),(4, 8)} Show that R is a function and find its domain, co-domain and range?

Find k if f o f(k) = 5 where f(k) = 2k - 1.

Write an A.P. whose first term is 20 and common difference is 8.

Solve x + 2y - z = 5; x - y + z = -2; -5x - 4y + z = -11

If A = \(\left[ \begin{matrix} 2 & 1 \\ 1 & 3 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 2 & 0 \\ 1 & 3 \end{matrix} \right] \) find AB and BA. Check if AB = BA

Prove that tan²\(\theta \)-sin² \(\theta \) = tan² \(\theta \) sin² \(\theta \)

Simplify (1+tan²θ)(1-sinθ)(1+sinθ)

Find the depth of a cylindrical tank of radius 28 m, if its capacity is equal to that of a rectangular tank of size 28 m x 16 m x 11 m.

Find the standard deviation of 30, 80, 60, 70, 20, 40, 50 using the direct method.

The arrow diagram shows a relationship between the sets P and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.

The 13^th term of an A.P is 3 and the sum of the first 13 terms is 234.Find the common difference and the sum of first 21 terms.

If A = \(\left[ \begin{matrix} 1 & 3 & -2 \\ 5 & -4 & 6 \\ -3 & 2 & 9 \end{matrix} \right] \), B = \(\left[ \begin{matrix} 1 & 8 \\ 3 & 4 \\ 9 & 6 \end{matrix} \right] \), find A + B.

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

Let f: A ⟶ B be a function defined by f(x) = \(\frac{x}{2}\)-1, where A = {2, 4 , 6, 10, 12}, B = {0, 1, 2, 4, 5, 9}, Represent f by
(i) set of ordered pairs
(ii) a table
(iii) an arrow diagram
(iv) a graph

The sum of three consecutive terms that are in A.P. is 27 and their product is 288. Find the three terms.