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The volume of a cylinder is $231c{m}^3$ and its height is 6 $cm$. A ball will fit inside the cylinder if its radius is ______.

Simplify
(i) $(\frac{81}{49}{)}^{\frac{-3}{2}}$
(ii) $(14641{)}^{0.25}$
(iii) $(\frac{32}{243}{)}^{\frac{-4}{5}}$
(iv) $(\frac{7776}{243}{)}^{\frac{-3}{5}}$

Which of the following is a non-terminating as well as non-repeating decimal?

Question 5 (a)

Express the following as kg using decimals:
2g

How many faces does a triangular prism has?

1. 4

Convert 1025 paise to rupees.

The bar graph below gives the calories consumed by three guys A, B and C after eating chocolate. What is the number of calories consumed by C if his share of chocolate is equal to $(\frac{3}{8}{)}^{\text{th}}$​​ of what A has eaten?

Question 131

Fill in the blank to make the statement true.

19 x 12 + 19 = 19 x (12 +........)

Question 93

Ms Anita has to drive from Jhareda to Ganwari. She measures a distance of 3.5 cm betweeen these village on the map. What is the actual distance between the villages, if the map scale is 1 cm= 10 km?

(a). Choose the largest and smallest integer among the following: [4 MARKS]

$32,-50,-75,120,-365,175$

(b). Simplify:
$(-3)+(-2)+(-5)+7$

(c). $-6÷3=?$

(d). $3\times 6\times 2\times (-40)=?$

Prime factorization of 18 is .

Question 49

Which points in the given figures appear to be mid-points of the line segments? When you locate a mid-point, then name the two equal line segments formed by it.

Question 4

If A, B, C are three points on a line such that AB = 5 cm, BC = 3 cm and AC = 8 cm, which one of them lies between the other two?

The perimeter of a square is 368 cms. Can you find the length of each side of the square?

A regular pentagon and a regular decagon have the same perimeter. Then the ratio of their areas are:

Sophie collected some flowers from her garden. There were $12.50\%$ roses, $10.50\%$ jasmine, and $7.00\%$ lilies. Express the percentage of jasmines as a fraction with the denominator $100$.

Question 36

If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is___cm.

The rainfall (in mm) in a city on 7 days of a certain week was recorded as follows:

$\begin{array}{cccccccc}Day& \text{Mon}& \text{Tue}& \text{Wed}& \text{Thurs}& \text{Fri}& \text{Sat}& \text{Sun}\\ \text{Rainfall}& 0.0& 12.2& 2.1& 0.0& 20.5& 5.5& 1.0\\ \left(\text{in mm}\right)& & & & & & & \end{array}$

(i) Find the range of the rainfall in the above data.

(ii) Find the mean rainfall for the week.

(iii) On how many days was the rainfall less than the mean rainfall? [4 MARKS]

30 acres of land were to be distributed among 45 farmers equally. Each farmer cultivates 3 different crops in equal areas, in his land. What is the area of cultivation available for one kind of crop for a farmer?

In the figure below, lines AB and CD intersect each other at point O. If the angle $\angle AOD={110}^{\circ }$ then, $\angle AOC$ is

Solve:

$\frac{12}{15}-\frac{7}{15}$

Find:(–15) – (–18)

Question 4 (i)

State whether the following statement is true or false. Give reasons for your answer.

Every natural number is a whole number.

In the figure below, a ray OC extends from a point O on a straight line AB. If $\angle$AOC = ${135}^{\circ }$, then $\left(\frac{\angle BOC}{3}\right)$ is equal to :

Question 198
Test the divisibility of the following numbers by 11.
(a) 5335
(b) 9020814

Consider the square plot given below with the green portion as garden. Express the part of plot used as garden in decimals.

'Any more doubts anybody?' you asked everybody there. After that, the council concluded that this design was good and they were all so happy after getting the knowledge of negative numbers and integers. They allowed you to leave to Earth. Everybody thanked you. At the time you were leaving, it was 2:00 pm. You asked Shubhlin that where you actually were. Then he assured that you will know shortly. When you came out of the tunnel, it was very chilling. You asked about the temperature to Shubhlin, he told it is 6 degrees below 0.

At this, you told Shubhlin to use integers and tell the temperature once again. This time Shubhlin understood the question and answered correctly. What was the answer given by Shubhlin?