List of practice Questions

Without doing any calculation, find the numbers which are surely not perfect squares. 

1. 153 
2. 257 
3. 408 
4. 441

What could be the possible 'one's' digits of the square root of each of the following numbers? 

1. 9801 
2. 99856 
3. 998001 
4. 657666025

Write a Pythagorean triplet whose one member is 

1. 6 
2. 14 
3.  16 
4.  18

Find the square of the following numbers 

1. 32 
2. 35 
3.  86 
4.  93 
5.  71 
6.  46

How many numbers lie between squares of the following numbers? 

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

How did Santosh begin to climb mountains?

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

Sharks are said to be ammonotelic animals Sharks can retain considerable amounts of ammonia in their blood

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)

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?

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

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