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State, the number of faces, number of vertices and number of edges of :
(i) a pentagonal pyramid
(ii) a hexagonal prism

In a model of a ship, the mast is 9 cm high, while the mast of the actual ship is 12 m high. If the length of the ship is 28 m, how long is the model ship?

Which of the following cannot be the angle of rotational symmetry of a regular polygon?

Factorise the following:

Is
it possible to have a polyhedron with any given number of faces?
(Hint:
Think of a pyramid).

An expression having 5 terms is called:

The adjacent angles of a parallelogram are___.

Question 10
Find the values of the letters in the following and give reasons for the steps involved.
$12A$
$\underset{–}{+6AB}$
$\underset{–}{A09}$

In the given figure if O is the centre of the circle, then $\angle CAB$ equals

Define a parallelogram.

Perimeter of a rectangle is 240cm. If it's length is decreased by 10% and it's breadth is increased by 20% we get the same perimeter. Find original length and breadth of rectangle.

A man borrows $Rs.10,000$ at $5\%$ per annum compound interest. He repays $35\%$ of the sum borrowed at the end of the first year and $42\%$ of the sum borrowed at the end of the second year. How much must he pay at the end of the third year in order to clear the debt ?

Try to draw quadrilateral ABCD of these specifications:

(i) AB = 7 cm, BC =5 cm, CD = 4 cm, ∠B = 60°, ∠C = 140°.

(ii) AB = 8 cm, BC = 6 cm, CD = 5.5 cm, DA = 3 cm, ∠B = 50°.

(iii) AB = 8.5 cm, BC = 4.5 cm, CD = 5 cm, DA = 6 cm, BD = 7.5 cm.

Draw the nets of the following:

i) Triangular prism

ii) Tetrahedron

iii) Cuboid

The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?

What is the cube root of $36\times 48$?

Find the equation of a line which is parallel to $y$-axis and has $x$-intercept as 5.

I bought a second-hand car for ₹50,000, had it transported for ₹5,000 and sold it for ₹59,400. What is my profit %?

Twice a number increase by 5 is the same as 3 times the number decreased by 8, find the number

A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.

(i) Which season got the most votes?

(ii) Find the central angle of each sector.

(iii) Draw a pie chart to show this information.

Season	Number of votes
Summer	90
Rainy	120
Winter	150

Express 70 as the product of its prime factors.

Find the surface area of the given below figure having dimension in cm as shown.

Question 28

The solution of the equation 3x +7 = - 20 is ___ .

The diameter of Earth is $1,27,56,000m$. Express the number in the standard form.

There are 1800 students in a school. 800 selected football, 750 selected basketball and the remaining selected cricket. Find the ratio of the total number of students to the number of students who selected cricket.

Recognise the type of angles in the following figures:

(i)

(ii)

(iii)

In a triangle ABC, ∠B = 28° and∠C = 56°. Find the largest and the smallest sides.

Four alternative options are given for each of the following statements. Select the correct option.

What is the product (x + 2) (x − 3)?

A. 2x − 6

B. 3x − 2

C. x² − x − 6

D. x² − 6x

Given ab = 4096, find the difference between the maximum and minimum value of (a + b).

Question 174

A particular star is at a distance of about $8.1\times {10}^{13}km$ from the Earth.

Assuring that light travels at $3\times {10}^{8}m$ per second, find how long does light takes from that star to reach the Earth?

A steamer goes downstream from one port to another in 9 hours. It covers the same distance upstream in 10 hours. If the speed of the stream be 1 km/h, find the speed of the streamer in still water and the distance between the ports.

If three angles of a quadrilateral are 50^o, 70^o and 120^o, then the fourth angle of the quadrilateral is: