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Which condition is used to prove that diagonals of a square are perpendicular biscetors?

If $G$ and $G^{\prime }$ be the centroids of the triangles $ABC$ and $A^{\prime }{B}^{\prime }{C}^{\prime }$ respectively, then $\overrightarrow{A{A}^{\prime }}+\overrightarrow{B{B}^{\prime }}+\overrightarrow{C{C}^{\prime }}=$

The angle between two diagonals of the parallelogram with vectors $2\hat{i}+\hat{j}$ and $\hat{k}-2\hat{j}$ as adjacent sides is:

The location of co-ordinates A and B in the form (x, y) are (___,___) and (___,___) respectively.

Find the circumference of the circle given in the figure below.
(Take $\pi$ as $\frac{22}{7}$)

According to a survey conducted in a city, 25% were doctors, 30% engineers, 15% businessmen and rest were illiterates. If the total population of the city is 5000, the number of illiterates is ___ .

Construct a triangle XYZ whose perimeter 15 cm and whose base angles are 60° and 70°.

Question 3

Radha made a picture of an aero plane with colored papers as shown in the given figure. Find the total area of the paper used.

Find the area of rhombus whose each side is equal to $15cm$ and one of its diagonal is $24cm$?

The following pie-chart sshows the monthly expenditure of Shikha on various items. If she spends Rs 16000 per month, answer the following questions:

(i) How much does she spend on rent?

(ii)How much does she spend on education?

(iii) What is the ratio of expenses on food and rent?

Find the cubes of:

(i) $\frac{3}{7}$ (ii) $\frac{8}{9}$ (iii) $\frac{10}{13}$

(iv) $1\frac{2}{7}$ (v) $2\frac{1}{2}$

If ABCD is a rectangle AC and BD are its diagonals which intersect at point 'O' as shown in the figure, then AC = ___ $\times$ OB.

Match the given shapes with their corresponding lateral surface area.

If top, front and side view is shown on the figure. Identify the solid figure.

Match the following numbers with the correct product of prime factors.

1. 1008

2. 784

3. 240

The length of a rectangle is $4a$ metres and its area is $72a^2$ sq m, the breadth of the rectangle is :

A coin is thrown and it lands on a chess board. Find the probability of it landing on a white square if it falls exactly inside a square.

1. 6

$997\times 998=$ ___

Question 1(i)
State whether the number given below is a perfect cube or not.
216

Use the given model to multiply the following:





$\frac{1}{5}\times \frac{1}{4}=$

Question 2 (viii)

Write the coordinates of the point M.

Show that if a straight line is perpendicular to one of the two or more parallel lines, then it is also perpendicular to the remaining lines.

The exterior angle measure of regular polygon having three sides is.

In triangle ABC, D is a point on AB and E is a point on AC such that DE || BC. If $\frac{AD}{AB}$ = $\frac{AE}{x}$, Then $x$ is

Question 5 (iv)

For the following number, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also, find the square root of the square number so obtained:

2028

Find the median for the distribution given below.

$$\begin{array}{cccccc}Class& 200-300& 300-400& 400-500& 500-600& 600-700\\ Numberofstudents& 3& 5& 20& 10& 6\end{array}$$

$(4\times {10}^3+3\times 1+1\times {10}^{-1}+6\times {10}^0)=$

Diagonals in a rhombus