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What are the main concepts of algebraic expressions and identities

Draw an equilateral triangle of side 8 cm and its circumscribed circle. Find the radius of this circumscribed circle.

Two years ago, Dilip was three times as old as his son and two years hence, twice his age will be equal to five times that of his son. Then the present age of Dilip is what?

Solve :

2z - 1 = 14 - z

The possible expressions for the adjacent sides of the rectangle having

$35y^2+13y-12$ as its area are ____ and ____

a , b , c , d are four consecutive perfect squares. What is the number of odd numbers in between a and d?

The square root of 2.25 equals to

Question 1 (a)
Find the ratio of the following:
Speed of a cycle 15 km per hour to the speed of scooter 30 km per hour.

The parallel sides of a trapezium are 25 cm and 11 cm, the perpendicular distance between the parallel sides is 13 cm. Find the area of the trapezium.

A polygon is said to be a convex polygon if

The surface area of a cuboid of dimensions $10m\times 12m\times 8m$ is

A cuboid shaped bank locker has length, breadth and height as 50 cm, 50 cm and 2 m respectively. It has to be secured by a touch sensor system at the rate of ₹ 5 per 100 sq. cm. The total cost of security arrangement is ________.

If any point P(x,y) is in the II Quadrant then the value of x is ___ and the value of y is positive.

The triangle ABC is given.

If CO : OB = 2 : 5 and Area of Triangle AOC = $44c{m}^2$

Find Area of Triangle AOB.

The weekly pocket expenses (in rupees) of 30 students of a class are given below: 62 ,80 ,110 , 75 , 84 , 73 , 60 , 62, 100 , 87 , 78 , 94 ,117, 86, 65, 68, 90, 80,118 ,72, 95, 72, 103, 96, 64, 94, 87, 85, 105, 115. Construct a frequency table with class intervals 60 - 70 and so on. [3 MARKS]

The given triangle has Centroid at O.

If PC = 54 cm, Find the length of OC.

Find the number of edges in a match-box ___.

The total surface area of a cuboid with dimensions of $26m,14m$ and $6.5m$ is ___ $m^2$.

Match the following algebraic expressions with their factorised form.

Given below are the steps for the construction of a quadrilateral ABCD, where AB = 3.5 cm, BC = 6.5 cm, $\angle A={75}^{\circ },\angle B={105}^{\circ }$ and $\angle C={120}^{\circ }$. Which of the following is wrong?
1:- Draw AB = 3.5 cm.
2:- Construct $\angle DAB={75}^{\circ },\angle ABC={105}^{\circ }$ at B.
3:- Draw BC = 6.5 cm.
4:- At D construct $\angle ADC={120}^{\circ }$.

Four points A, B, C, D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by these points.

P = set of multiples of 3

Q = set of multiples of 5

P and Q are:

In a rhombus, if the measure of one angle is 60 degrees then the measure of its adjacent angle is:

The price of a computer was Rs 28,000. If the price is decreased by 10% then its new price will be:

The total number of non-square natural numbers between ${16}^2$ and ${17}^2$ $=a\times b=c$. What is the value of $a$, $b$ and $c$ respectively?

Find out the frequency of observation greater than or equal to 4.

$$\begin{array}{ccccccc}\text{Dice}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 10& 12& 6& 4& 8& 10\end{array}$$

40 workers working for 8 hours per day digs a hole of 1088$m^3$. If 45 workers work for 6 hours a day, then what volume of the hole they can dig?

Question 1 (ii)
What could be the possible ‘one’s’ digit of the square root of following number:

99856

The unit's digit in the cube of 2, 16, 20 is always _____.

The value of $(998{)}^2$ is equal to:

The smallest number by which 16384 must be divided so that quotient is a perfect cube is:

The medians of _____________ triangle are equal in length.

Employees of a company have been categorized according to their religious as given below:
$\begin{array}{ccccccc}\text{Religious}& \text{Hindu}& \text{Muslim}& \text{Sikh}& Christian& \text{Others}& \text{Total}\\ \text{Number of workers}& 420& 300& 225& 105& 30& 1080\end{array}$
Draw a pie - chart to represent the above information.

By using the formula, find the amount and compound interest on:

Rs 10240 for 3 years at $12\frac{1}{2}\%$ per annum compounded annually.

Without adding, find the sum:
(i) (1+3+5+7+9+11+13)
(ii) (1+3+5+7+9+11+13+15+17+19)
(iii) (1+3+5+7+9+11+13+15+17+19+21+23)

Find the product $24x^2(1-2x)\text{and evaluate its value for}x=3.$

Kamala borrowed from Ratan a certain rate for two years simple interest. She lent this sum at the same rate to Hari for two years compound interest. At the end of two years, she received Rs. 210 as compound interest, but paid Rs. 200 only as simple interest. Find the sum and the rate of interest.

What is the number of diagonals in a (i) heptagon (ii) octagon (iii) polygon of 12 sides ?