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

Factorize: 6-x+x².

If \(\sqrt { 3 } x=\sqrt { 2 } x+1\) , then x is equal to _____

Explain when a system of axioms is called consistent.

What is the value of x in the figure given below?

Is it possible to construct a triangle, when its sides are 5.4 cm, 2.3 cm, 3.1 cm?

If in quadrilateral ABCD; ∠A=90° and AB=BC=CD=DA, then ABCD is a square.

If a 60^o angle is bisected twice,what will be measure of each that is constructed?

The radii of two right circular cylinders are in the ratio 2:3 and their heights are in the ratio 5:4, then the ratio of their volumes will be _______________

For the given data: 11,15, 17, y+1, 19, y-2, 3; if the mean is 14, find the value of y.

Simplify: 7³.9³

Write the coefficient of x³ of the following polynomials:
\(\frac { 2 }{ 3 } -\frac { 5 }{ 4 } x+{ x }^{ 3 }+\frac { 1 }{ 2 } { x }^{ 2 }\)

(a) Plot the following points in the coordinate plane.
A(-4,4), B(-6,0), C(-4,-4), D(-2,0)
(b) Name the figure formed by joining the points A, B, C and D is also find its area.

Solve for x: \(3x+11+{x\over2}=-{7\over2}+18.\)What will be the graph of this equation?

In the given figure, calculate the value of \(\angle PQR\)

PS is an altitude of an isosceles triangle PQR in which PQ = PR. Show that PS bisects \(\angle\)P.

In the figure, straight lines AB and CD pass through the centre O of the circle. If \(\angle OCE=40°\) and \(\angle AOD=75°\), find  \(\angle CDE\) and \(\angle OBE\).

Find the area of a triangle whose sides are 6.5 cm. 7 cm and 7.5 cm.

What is the volume of a cube whose total surface area is 864 m²?

The mean of 100 observations is 60. If one observation of 50 is replaced by 110, then what will be the new mean?

Simplify: \(\frac { \sqrt { 6 } }{ \sqrt { 2 } +\sqrt { 3 } } +\frac { 3\sqrt { 2 } }{ \sqrt { 6 } +\sqrt { 3 } } -\frac { 4\sqrt { 3 } }{ \sqrt { 6 } +\sqrt { 2 } } \)

Find the value of \((x-a)^3+(x-b)^3+(x-c)^3-3(x-a)(x-b)(x-c)\) where a+b+c=0

A rectangle field has to be cut out and its boundary marked with fencing with a given wire of length 100m.
(a)Represent the above situation using a linear equation
(b)Also plot its graph

In the given figure \(DE\bot AB.\) Find the value of x and y.

In \(\triangle ABC\) , AD is the perpendicular bisector of BC (see figure).Show that \(\triangle ABC\) is isosceles triangle in which AB = AC.

In figure, ABCD is a parallelogram, \(AE\bot DC\)and \(CF\bot AD\). If AB = 16cm, AE = 8 cm and CF = 10 cm, find AD.

Angle in a semicircle is a right angle. Prove it.

Find the surface area of a sphere of diameter:
(i) 14 cm                
(ii) 21 cm
(iii) 3.5 m.

The runs scored by two teams A and B on the first 74 balls in a cricket match are given below:

Construct the frequency polygon both teams on the same graph.