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Arithmetic mean of a given data from a frequency table is given by

Question 85 (xi)

Expand the following, using suitable identities.

$(\frac{2a}{3}+\frac{b}{3})(\frac{2a}{3}-\frac{b}{3})$

Statement 1: Square numbers can never end with 2, 3, 7 or 8.

Statement 2: If a number ends with 0, 1, 4, 5, 6 or 9, it must be a square number.

Which of these statement(s) is/are right?

Question 63 (ii)



How many faces does the following solid have?



Hexahedron

Without adding the numbers, find the sum of successive odd numbers 1, 3, 5, 7, 9, 11, 13 and 15.

In which of the following situations, an angle bisector construction cannot be used to bisect the angle created between two given lines?

If no diagonal are 44. Then the number of sides in the polygon is

Question 8 (i)

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:

$\begin{array}{cccccccccc}1& 6& 2& 3& 5& 12& 5& 8& 4& 8\\ 10& 3& 4& 12& 2& 8& 15& 1& 17& 6\\ 3& 2& 8& 5& 9& 6& 8& 7& 14& 12\end{array}$

(i) Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5- 10.

An isosceles trapezium has an area of 36 cm², the parallel sides are 12 cm and 6 cm respectively. The perimeter of the trapezium should be

The area of a pizza of diameter of 14 inches is ______ sq inches. (Take pi = 22/7)

It is possible to have a regular polygon with measure of each exterior angle as 22 digree,how

Frequency of an entry ___.

Question 4 (i)

The heights of 50 students, measured to the nearest centimeters, have been found to be as follows:

$\begin{array}{cccccccccc}161& 150& 154& 165& 168& 161& 154& 162& 150& 151\\ 162& 164& 171& 165& 158& 154& 156& 172& 160& 170\\ 153& 159& 161& 170& 162& 165& 166& 168& 165& 164\\ 154& 152& 153& 156& 158& 162& 160& 161& 173& 166\\ 161& 159& 162& 167& 168& 159& 158& 153& 154& 159\end{array}$

(i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as 160 - 165, 165 - 170, etc.

Question 2

Both x and y vary inversely with each other. When x is 10, y is 6, which of the following is not a possible pair of corresponding values of x and y?
(a) 12 and 5
(b) 15 and 4
(c) 25 and 2.4
(d) 45 and 1.3

Question 85 (vii)

Expand the following, using suitable identities.

$(2x+9)(2x-7)$

Factorise:
$x^2+6ax+9a^2$

Using an identity expand :

$(2y+5)(2y+5)$

The cost of Maruti 800 in the year 1998 was ₹ 2,50,000. After the end of one year and four months, the price underwent depreciation by 10% per annum. Its new price is:

If $(150{)}^2$ is added to the cube of a number, the answer so obtained is 77372. What is the number?

Seema bought $1\frac{5}{7}$m cloth for her dress. If the designer uses $1\frac{1}{3}$m for making the dress , then the length of the remaining cloth is ___ m.

Find the solution for the following pair of equations

$4y-3x=-7$

$3x-2y=5$

How can -2 be used as a base to write 32?

$$\begin{array}{ccccc}X& 2& 4& 5& 50\\ Y& 4& 8& x& 100\end{array}$$

What is the constant that is used to find the missing values of the table?

Question 60

State whether the following statement is true or false:

There are five perfect cubes between 1 and 100.

Question 93 (ii)

The following expression is the area of a rectangle. Find the possible length and breadth of the rectangle.

$x^2-3x+2$

If a sequence follows the pattern $2.5n-10$, then find the ${10}^{th}$ term of the sequence.