List of top Mathematics Questions

The shape of the top surface of a table is a trapezium. Find its area if its parallel sides are 1 m and 1.2 m and perpendicular distance between them is 0.8 m.

These are \(500\) children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

Which of the following numbers are not perfect cubes: 

1. 216 
2. 128 
3.  1000 
4.  100 
5.  46656

Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube:

1. 243
2. 256
3.  72
4.  675
5.  100

Parikshit makes a cuboid of plasticine of sides \(5\) \(cm\), \(2\) \(cm\), \(5\) \(cm.\) How many such cuboids will he need to form a cube?

Find the square roots of the following numbers by the Prime Factorisation Method. 

1. 729 
2. 400 
3.  1764 
4.  4096 
5.  7744 
6.  9604 
7.  5929 
8.  9216 
9.  529 
10.  8100

Find the smallest square number that is divisible by each of the numbers \(8, 15\), and \(20\).

Find the smallest square number that is divisible by each of the numbers \(4, 9\), and \(10\).

\(2025\) plants are to be planted in a garden in such a way that each row contains as many plants as the number of rows. Find the number of rows and the number of plants in each row.

The students of Class VIII of a school donated Rs \(2401\) in all, for Prime Minister's National Relief Fund. Each student donated as many rupees as the number of students in the class. Find the number of students in the class.

Find the square roots of \(100\) and \(169\) by the method of repeated subtraction.

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 \(100\)

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)

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.].