Write the sum of \(0.\bar{3}\) and \(0.\bar{4}\)

If f(x) be a polynomial such that \(f\left( -\frac { 1 }{ 3 } \right) \)=0, then calculate one factor of f(x).

The graph of the linear equation 4x - 3y = 12 cuts y-axis at _____

Write the number of dimension(s) of a surface.

In \(\triangle ABC,\angle A=\angle B/2=\angle C/6,\) then what will be the measurement of \(\angle A?\)

Write ASA congruence rule for two triangles.

In an equilateral triangle ABC, D and E are the mid-points of sides AB and AC respectively, then length of DE is....

Bisector of an angle divides it in to_______equal parts

Find the amount of water displaced by a solid spherical ball of diameter 4.2 cm, when it is completely immersed in water.

The class-mark of the class 130-150 is

If \(a=\frac { \sqrt { 3 } +1 }{ \sqrt { 3 } -1 } \) and \(b=\frac { 1 }{ a } \) , find the value of \({ a }^{ 2 }+ab+{ b }^{ 2 }\)

Factorise: \(16x^3-2y^3\)

In which quadrant do the given point lie? (2,-1)

Draw a graph of the line x - 2y = 3. From the graph, find the coordinates of the point when
(i) x =-5
(ii) y = 0.

l,m and n are parallel lines intersected by transversal 't' at A, B, and C respectively. Find the measure of \(\angle 1,\angle 2and\angle 3\) Give reasons

D is any point on side BC of ΔABC, such that AD = AC. Show that AB > AD.

How will you complete an arc of a circle?

Find the area of an equilateral triangle of side 10 cm.

The radius and height of a right circular cone are in the ratio 4 : 3. If the area of the base of the cone is 154 cm², find the area of its curved surface. \(\left[ Use\ \pi =\frac { 22 }{ 7 } \right] \)

In a particular section of Class IX, 40 students were asked about the month of their birth, the following was prepared for the data so obtained.

Observe the bar graph given above and answer the following question:
(i) How many students were born in the month of November?
(ii) In which month were the maximum number of students born?

Classify the following numbers as rational or irrational: 0.3796

If \(x=\frac { \sqrt { 3 } +\sqrt { 2 } }{ \sqrt { 3 } -\sqrt { 2 } } \quad and\quad y=\frac { \sqrt { 3 } -\sqrt { 2 } }{ \sqrt { 3 } +\sqrt { 2 } } \) find the value of x²-y²+xy, if \(\sqrt { 6 } \)=2.4.

If the point (-1,-5) lies on the graph of 3x=ay+7, then find the value of 'a'.

In the figure, \(\angle BAC=50^o, \angle GBD=70^o\) and l and m are parallel lines. Find x,y, and z.

Example 4. AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see figure). Show that ㄥA > ㄥC and ㄥB > ㄥD

In \(\Delta\)GHK; D, E and F are the mid-point of sides HK, KG and GH respectively. show that EFHK is trapezium and ar(EFHK) = \(\frac { 3 }{ 4 } ar(\Delta GHK)\)

Prove that an isosceles trapezium is cyclic

the length, breadth and height of a room are 6 m, 4 m and 3 m respectively. Find the cost of white washing the four walls of the room at the rate of Rs 12 per m². The room has an entrance door mearuring 2.5 m \(\times\) 1 m which is not to be white washed.

The following data on the number of girls (to the nearest ten) per thousand boys in different sections of the Indian society is given below:

(i) Represent the information above by a bar graph.
(ii) In the classroom discuss what conclusion can be arrived at from the graph.

Evaluate:\(\frac { 40 }{ 2\sqrt { 10 } +\sqrt { 20 } +\sqrt { 40 } -2\sqrt { 5 } } \) when it is given that \(\sqrt { 10 } =3.162\)

Find the value of the polynomial \(p(z)={ 3z }^{ 2 }=4z+\sqrt { 17 } \)  when z=3.

In the given figure, \(\angle ACD=\angle ABC\) CP bisects \(\angle BCD.\) Prove that \(\angle APC=\angle ACP.\)

Show that each angle of a rectangle is a right angle.

Find the angle marked as x in each of following figures where O is the centre of the circle:
(i) 

(ii)

(iii)

(iv)

(v)

Find the length of the longest rod that can be placed in a room 12 m \(\times\) 9 m \(\times\) 8 m.

Geetha told her classmate Radha that "\(\sqrt { \frac { \left( \sqrt { 2 } -1 \right) }{ \left( \sqrt { 2 } +1 \right) } } \) is an irrational number." Radha replied that "you are wrong" and further claimed that "If there is a number 'x' such that x³ is an irrational number, then x⁵ is also irrational". Geetha said, "No Radha, you are wrong". Radha took some time and after verification accepted her mistakes and thanked Geetha for pointing out these mistakes. 
(i) Justify both the statements.
(ii) What value is depicted from this question?

In figure, PQ = PR. Show that PS > PQ.