Mathematical Applications | MCQs

Explanation

To check if a number is exactly divisible by 4, we can check if the last two digits form a number that is divisible by 4.

2000: Last two digits are 00, which is divisible by 4.

Since 2000 ends in 00, it is exactly divisible by 4.

Explanation

A number is exactly divisible by 5 if it ends in 0 or 5.

230590 ends in 0, so it is divisible by 5.

Explanation

Given equation: x^2 - 3kx + 4k^2 = 0.

Sum of roots = 3k, Product of roots = 4k^2.

Sum of squares of roots = (sum of roots)^2 - 2(product of roots)

= (3k)^2 - 2(4k^2)

= 9k^2 - 8k^2

= k^2.

Given sum of squares = one of the options.

If sum of squares = 1, then k^2 = 1, so k = ±1

Explanation

Given equation:

x² - 5x + 6 = 0

Factor the quadratic equation:

(x - 2)(x - 3) = 0

This gives us:

x - 2 = 0 or x - 3 = 0

x = 2 or x = 3

The roots of the equation are x = 2 and x = 3.

Explanation

 1 + 2 + 3 + ... + n = 15  

This is an arithmetic series. Use the formula:

n(n + 1)/2 = 15  

→ Multiply both sides by 2:  

n(n + 1) = 30  

Try n = 5:  

5(6) = 30 

So, n = 5

Now calculate:  

1³ + 2³ + 3³ + ... + n³  

Use formula:  

[n(n + 1)/2]² = [5×6/2]² = (15)² = 225