Mathematics Quiz

What is the unit digit in the following product? 91×92×93×...........×99

• 2

• 1

• 4

• 0

Answer explanation

The product 91×92×93×...×99 includes the number 100, which contributes a unit digit of 0. Therefore, the unit digit of the entire product is 0.

Find the number of factors of 4200.

• 48

• 56

• 64

• 46

Answer explanation

To find the number of factors of 4200, we first find its prime factorization: 4200 = 2^3 × 3^1 × 5^2 × 7^1. The number of factors is calculated as (3+1)(1+1)(2+1)(1+1) = 4 × 2 × 3 × 2 = 48. Thus, the correct answer is 48.

How many factors does the number 12288 have?

• 24

• 26

• 28

• 22

Answer explanation

To find the number of factors of 12288, we first find its prime factorization: 12288 = 2^12 * 3^1. Using the formula (e1+1)(e2+1)... for the exponents, we get (12+1)(1+1) = 13*2 = 26. Thus, the correct answer is 26.

If a positive number N, when divided by 5 leaves a remainder 3, then the unit's place digit of N is?

• 0 or 5

• 0 or 2

• 3 or 8

• 1 or 5

Answer explanation

If N leaves a remainder of 3 when divided by 5, it can be expressed as N = 5k + 3 for some integer k. The unit's place of such numbers can only be 3 or 8, making '3 or 8' the correct choice.

The unit digit in 4 × 38 × 764 × 1256 is :

• 6

• 8

• 4

• 5

Answer explanation

To find the unit digit of 4 × 38 × 764 × 1256, we only need the unit digits: 4 (from 4), 8 (from 38), 4 (from 764), and 6 (from 1256). Multiplying these unit digits: 4 × 8 = 32 (unit digit 2), then 2 × 4 = 8, and finally 8 × 6 = 48 (unit digit 8). Thus, the answer is 8.

Calculate the sum of squares of number from 1 to 10.

• 384

• 285

• 385

• 380

Answer explanation

To find the sum of squares from 1 to 10, calculate 1^2 + 2^2 + ... + 10^2. This equals 1 + 4 + 9 + 16 + 25 + 36 + 49 + 64 + 81 + 100 = 385. Thus, the correct answer is 385.

Find the least number which should be added to 7864, to make it a perfect square.

• 61

• 57

• 71

• 79

Answer explanation

To find the least number to add to 7864 to make it a perfect square, calculate the square root of 7864, which is approximately 88.7. The next perfect square is 89^2 = 7921. Thus, 7921 - 7864 = 57. Therefore, the answer is 57.

The number 4050 becomes a perfect square when multiplying by a positive integer. Find the square root of the number.

• 95

• 80

• 90

• 85

Answer explanation

To make 4050 a perfect square, we find its prime factorization: 4050 = 2 × 3^4 × 5^2. To balance the exponents, we multiply by 2. Thus, 4050 × 2 = 8100, which is 90^2. Therefore, the square root is 90.

Which of the following numbers is a perfect square?

• 0.09

• 8.1

• 0.025

• All

Answer explanation

0.09 is a perfect square because it equals (0.3)². The other options, 8.1 and 0.025, are not perfect squares as they cannot be expressed as the square of a rational number.

Divide the number 137592 by the smallest number that leaves no remainder and quotient is a perfect cube. Find the cube root of the quotient.

• 8

• 2

• 4

• 6

Answer explanation

To find the smallest divisor of 137592 that results in a perfect cube, we divide by 6. The quotient is 22932, which is 6^3. The cube root of 6 is 6, making it the correct answer.