Explanation

Inverse proportion: y ∝ 1/x, so y × x = constant

Given: 10 × 2 = 20

So when x = 5 ⇒ y = 20 ÷ 5 = 4

Last verified on 23-06-2026

Explanation

Diameter = 12 cm ⇒ Radius = 6 cm

Formula: Surface area = 4πr²

= 4π × (6)² = 4π × 36 = 144π cm²

Last verified on 23-06-2026

Explanation

Let the 3-digit number be abc = 100a + 10b + c  

Reversed = cba = 100c + 10b + a  

Given: reversed - original = 297  

(100c + 10b + a) - (100a + 10b + c) = 297  

99c - 99a = 297 → 99(c - a) = 297 → c - a = 3  

Also given: a + c = 7  

Solve:  

a + c = 7  

c - a = 3  

Add both: 2c = 10 → c = 5  

Then a = 7 - 5 = 2  

Product of first and third digits = a × c = 2 × 5 = 10.

Last verified on 23-06-2026

Explanation

Use identity: (a + 1)(a - 1) = a² - 1  

Here 201 × 199 = (200 + 1)(200 - 1) = 200² - 1²  

= 40000 - 1  

= 39999  

Last verified on 23-06-2026

Explanation

2x² + 5x − 12 = 0

Factor form: (2x − 3)(x + 4) = 0

So, x = 3/2 or x = −4

Last verified on 22-06-2026

Explanation

(100)¹·⁵ = (100)³/² = √(100³) 

100³ = 1,000,000  

√1,000,000 = 1000

Last verified on 22-06-2026

Explanation

Diameter = 8 cm → radius r = 8 ÷ 2 = 4 cm  

Height = half of radius → h = 4 ÷ 2 = 2 cm  

Volume = πr²h = π × 4² × 2 = π × 16 × 2 = 32π cm³

Last verified on 21-06-2026

Explanation

Odd function: F(-x) = -F(x) → F(x) + F(-x) = 0

Even function: F(-x) = F(x) → F(x) + F(-x) = 2F(x)

Here we have F(x) + F(-x) = 6, a constant

That means the function is symmetric about y = 3

So we call it constant symmetric form.

Last verified on 21-06-2026

Explanation

When a value of x is given, we replace x in the polynomial and simplify to get the result.

This is called evaluation of a polynomial.

Last verified on 21-06-2026

Explanation

Greatest two-digit number = 99

First natural number = 1

Difference = 99 - 1 = 98

Last verified on 21-06-2026