Let A =  {1,2, 3, 4} and B = {-1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Let R = {(1, 3), (2, 6), (3, 10), (4, 9)} \(\subseteq \) A x B bea relation. Show that R is a function and find its domain, co-domain and the range of R.

State whether the graph represent a function. Use vertical line test.

Let A = {0, 1, 2, 3} and B = {1, 3, 5, 7, 9} be two sets. Let f : A \(\rightarrow\)B be a function given by  f(x) = 2x + 1. Represent this function as an arrow .

Use Euclid's algorithm to find the HCF of 4052 and 12756.

Find the LCM and HCF of 6 and 20 by the prime factorisation method.

Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + Sz = 22

Using quadratic formula solve the following equations.9x²-9(a+b)x+(2a²+5ab+2b²)=0

Prove that the equation x²(a²+b²)+2x(ac+bd)+(c²+ d²) = 0 has no real root if ad≠bc.

In figure OA· OB = OC·OD
Show that \(\angle A=\angle C\ and\ \angle B=\angle D\)

Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

If A (-5, 7), B (-4, -5), C (-1, -6) and D (4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD.

Prove that \(\frac { sin\theta -cos\theta +1 }{ sin\theta +cos\theta -1 } =\frac { 1 }{ sec\theta -tan\theta } \) using the identity sec²θ= 1+ tan²θ.

In a right triangle ABC, right-angled at B, if tan A = 1, then verify that 2 sin A cos A = 1.

\(\frac { tan\quad A }{ 1\quad sec\quad A } ​​​​\frac { tan\quad A }{ 1\quad sec\quad A } ​​​​2cosec\quad A\)

(sin ∝+cos ∝)(tan ∝+cot ∝)=sec ∝+cosec ∝

\(1+\frac { { cot }^{ 2 }\alpha }{ 1+cosex\alpha } =cosec\alpha\)

Find the angle of elevation of the sun when the shadow of a pole h metres high is \(\sqrt3\) h metres long.

A ladder 15 metres long just reaches the top of a vertical wall. If the ladder makes an angle of 60^o with the wall, finf the height of the wall.

If 2sin²θ-cos2θ=2, then find the value θ.

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