List of top Questions asked in CBSE Class VIII

How many numbers lie between squares of the following numbers? 

1. \(12\) and \(13\) 
2.  \(25\) and \(26\) 
3.  \(99\) and \(100\)

Using the given pattern, find the missing numbers. 
\(1^ 2 + 2^2 + 2^2 = 3^2\)
\(2^ 2 + 3^2 + 6^2 = 7^2 \)
\(3^ 2 + 4^2 + 12^2 = 13^2 \)
\(4 ^2 + 5^2 + ....^2 = 21^2 \)
\(5^ 2 +....^2 + 30^2 = 31^2\) 
\(6^ 2 + 7^2 + ....^2 = ....^2\)

Observe the following pattern and supply the missing number. 
\(11^2 = 121\) 
\(101^2 = 10201\) 
\(10101^2 = 102030201\) 
\(1010101^2 = …\) 
\(...^2= 10203040504030201\)

Observe the following pattern and find the missing digits. 
\(11^2\) = \(121\) 
\(101^2\) = \(10201\) 
\(1001^2 = 1002001\) 
\(100001^2 = 1…2…1 \)
\(10000001^2 = …\)

The squares of which of the following would be odd numbers? 

1. 431 
2. 2826 
3. 7779 
4. 82004

What will be the unit digit of the squares of the following numbers? 

1. 81 
2. 272 
3.  799 
4.  3853 
5.  1234 
6.  26387 
7.  52698 
8.  99880 
9.  12796
10.  55555

Multiply the binomials.
(i) (2x + 5) and (4x – 3)
(ii) (y – 8) and (3y – 4)
(iii) (2.5l – 0.5m) and (2.5l + 0.5m)
(iv) (a + 3b) and (x + 5)
(v) (2pq + 3q²) and (3pq – 2q²)
(vi) (\(\frac{3}{4}\) a² + 3b²) and 4(a² – \(\frac{2}{3}\) b²)

(a) Add: p ( p – q), q ( q – r) and r ( r – p) 
(b) Add: 2x (z – x – y) and 2y (z – y – x) 
(c) Subtract: 3l (l – 4 m + 5 n) from 4l (10 n – 3 m + 2 l) 
(d) Subtract: 3a (a + b + c) – 2 b (a – b + c) from 4c (– a + b + c)

(a) Simplify 3x (4x – 5) + 3 and find its values for (i) x = 3 (ii) x =\(\frac{1}{2}\)
(b) Simplify a (a²+ a + 1) + 5 and find its value for (i) a = 0, (ii) a = 1 (iii) a = – 1.

Find the product.
(i) a² \(\times\) (2a²²) \(\times\) (4a²⁶)
(ii) (\(\frac{2}{3}\) xy) \(\times\)(\(\frac{-9}{10}\) x²y²)
(iii) (\(\frac{-10}{3}\) pq³) × (\(\frac{6}{5}\) p³q)
(iv) (x) \(\times\) (x²) \(\times\) (x³) \(\times\) (x⁴)

Find the probability of the events given in Question 2 [ (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5.].

If you have a spinning wheel with \(3\) green sectors, \(1\) blue sector and \(1\) red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?

Complete the table.

	First expression	Second expression	Product
(i)	a	b + c + d	…
(ii)	x + y – 5	5xy	…
(iii)	p	6p 2 – 7p + 5	…
(iv)	4p 2q 2	p 2 – q 2	…
(v)	a + b + c	abc	…

Numbers \(1\) to \(10\) are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of . 

1. getting a number \(6\)? 
2. getting a number less than \(6\)? 
3. getting a number greater than \(6\)? 
4. getting a \(1\)-digit number?

Find the.

1. Probability of the pointer stopping on D in (Question 1-(a))?
2. Probability of getting an ace from a well shuffled deck of \(52\) playing cards?
3. Probability of getting a red apple. (See figure below)

When a die is thrown, list the outcomes of an event of getting 

1. (a) a prime number (b) not a prime number. 
2. (a) a number greater than 5 (b) a number not greater than 5.

List the outcomes you can see in these experiments. 

1. Spinning a wheel 
2. Tossing two coins together

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.
 

Language	Hindi	English	Marathi	Tamil	Bengali	Total
Number of students	40	12	9	7	4	72

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions: 

1. In which subject did the student score 105 marks? (Hint: for 540 marks, the central angle = 360°. So, for 105 marks, what is the central angle?) 
2. How many more marks were obtained by the student in Mathematics than in Hindi? 
3. Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi. (Hint: Just study the central angles).

Draw a pie chart showing the following information. The table shows the colours preferred by a group of people.
 

Colours	Number of people
Blue	18
Green	9
Red	6
Yellow	3
Total	36

Obtain the product of
(i) xy, yz, zx
(ii) a, – a² , a³
(iii) 2, 4y, 8y² , 16y³
(iv) a, 2b, 3c, 6abc
(v) m, – mn, mnp

A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey.

From this pie chart answer the following: 

1. If 20 people liked classical music, how many young people were surveyed? 
2. Which type of music is liked by the maximum number of people? 
3. If a cassette company were to make 1000 CD’s, how many of each type would they make?

Obtain the volume of rectangular boxes with the following length, breadth and height, respectively.
(i) 5a, 3a², 7a⁴
(ii) 2p, 4q, 8r
(iii) xy, 2x²y, 2xy²
(iv) a, 2b, 3c

\(ABC\) is a right-angled triangle and \(O\) is the mid point of the side opposite to the right angle. Explain why \(O\) is equidistant from \(A, B\) and \(C\). (The dotted lines are drawn additionally to help you).