Let f = {(2, 7); (3, 4), (7, 9), (-1, 6), (0, 2), (5,3)} be a function from A = {-1,0, 2, 3, 5, 7} to B = {2, 3, 4, 6, 7, 9}. Is this
(i) an one-one function
(ii) an onto function,
(iii) both one and onto function?

f(x) = (1+ x)
g(x) = (2x - 1)
Show that fo(g(x)) = gof(x)

A function f: (1,6) \(\rightarrow\)R is defined as follows:

Find the value of f(5),

A function f: (1,6) \(\rightarrow\)R is defined as follows:

Find the value of f(2) - f( 4).

Which of the following list of numbers form an AP ? If they form an AP, write the next two terms:
1, 1, 1, 2, 2, 2, 3, 3,  3

In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?

How many terms of the AP: 24, 21, 18, ... must be taken so that their sum is 78?

The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

Seven years ago, Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

Find two consecutive natural numbers whose product is 20.

In \(AD\bot BC\) prove that AB² + CD² = BD² + AC². 

Prove that in a right triangle, the square of 8. the hypotenuse is equal to the sum of the squares of the others two sides.

In figure 0 is any point inside a rectangle ABCD. Prove that OB² + OD² = OA² + OC²

The perpendicular from A on side BC at a \(\triangle\)ABC intersects BC at D such that DB = 3 CD. Prove that 2AB² = 2AC² + BC².

If the points A(6, 1), B(8, 2), C(9, 4) and D(P, 3) are the vertices of a parallelogram, taken in order. Find the value of P.

Find a relation between x and y if the points (x, y) (1, 2) and (7, 0) are collinear.

Find the area of the triangle formed by the points P(-1, 5, 3), Q(6, -2) and R(-3, 4).

If sin (A - B) = \(\frac12\),  cos (A + B) = \(\frac12\), 0^o < A + ≤  90°, A > B, find A and B.

Evaluate \(\frac { tan{ 65 }^{ o } }{ tan{ 25 }^{ o } } \)

Express cot 85° + cos 75° in terms of trigonometric ratios of angles between 0° and 45°.

If 15tan² θ+4 sec² θ=23 then find the value of (secθ+cosecθ)² -sin² θ

If tanθ+sinθ=P; tanθ-sinθ=q P.T P²-q²=4\(\sqrt{pq}\)

Find the number of coins, 1.5 cm is diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.

A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in figure. If the height of the cylinder is 10 cm and its base is of radius 3.5 cm find the total surface area of the article.

S.D. of a data is 2102, mean is 36.6, then find its C.V.