If \(f(x)=\frac { 1 }{ x } \), and \(g(x)=\frac { 1 }{ { x }^{ 3 } } \) then f o g o(y), is ________

Given a₁ = -1, \(a=\frac { { a }_{ n } }{ n+2 } \), then a₄ is ____________

The square root of 4m² - 24m + 36 is ___________

In figure \(\angle OAB={ 60 }^{ o }\) and OA = 6cm then radius of the circle is ____________

Two concentric circles if radii a and b where a>b are given. The length of the chord of the circle which touches the smaller circle is ____________

The four vertices of a quadrilateral are (1, 2), (5, -6), (7, -4) and (k, -2) taken in order. If the area of quadrilateral is zero then find the value of k.

Sin(45^o+ θ ) - cos(45^o - θ) is equal to ___________

If S₁ denotes the total surface area at a sphere of radius ૪ and S₂ denotes the total surface area of a cylinder of base radius ૪ and height 2r, then ___________

Kamalam went to play a lucky draw contest 135 tickets of the lucky draw were sold. If the probability of Kamalam winning is \(\frac { 1 }{ 9 } \), then the number of tickets bought by kamalam is ____________

which of the following is true?

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 .

Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer.

Solve the following system of linear equations in three variables.
x + y + z = 6; 2x + 3y + 4z = 20;
3x + 2y + 5z = 22

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

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.

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 for the following data. 5, 10, 15, 20, 25. And also find the new S.D. if three is added to each value.

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?

Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
4,10,16, 22, ...

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

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

Find the coordinates at the points of trisection (i.e. points dividing in three equal parts) of the line segment joining the points A(2, -2) and B(-7, 4).

If ATB=90^o then prove that
\(\sqrt { \frac { tanA\quad tanB+tanA\quad cotB }{ sinA\quad secB } } -\frac { { Sin }^{ 2 }A }{ { Cos }^{ 2 }A } =tanA\)

What is the ratio of the volume of a cylinder, a cone, and a sphere. If each has the same diameter and same height?

Find the co-efficient of variation for the following data: 16, 13, 17,21, 18.

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

Find the value of f(3),

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

A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.

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

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

From a point on a bridge across a river, the angles of depression of the banks on opposite sides at the river are 30° and 45°, respectively. If the bridge is at a height at 3 m from the banks, find the width at the river.

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.