Mean of three consecutive even numbers is 16. The numbers are 

Correct Answer - 4.25

Correct Answer - ` (i) 1/2 (ii) 3/4 `

Correct option is (D) 14, 16, 18 Let three consecutive even numbers are x - 2, x & x+2. \(\therefore\) Their mean \(=\frac{(x-2)+x+(x+2)}3\) \(=\frac{3x}3\) = x But given that mean of three consecutive even numbers is 16. \(\therefore\) x = 16 Thus,...

Correct option is (A) 6 Mean \(=\frac{\text{Sum of first five even natural numbers}}5\) \(=\frac{2+4+6+8+10}5\) \(=\frac{30}5=6\)

Correct option is  C) 4

(1) f(x) = \(\frac{x}{1-x^3}\)  f(-x) = \(\frac{-x}{1-(-x)^3}\)  = \(\frac{-x}{1+x^3}\) ≠ -f(x) or f(x) ∴ f(x) is neither even nor odd function. (2) f(x) = \(\frac{x^2}{1+x}\)  ∴ f(-x) = \(\frac{(-x^2)}{1+(-x)}\)  = \(\frac{x^2}{1-x}\) ≠ -f(x) or f(x). (3) f(x) = x-|x| ∴ f(-x) = -x-|-x| = -x-|x| = -(x+|x|) ≠ -f(x)...

B) x, x + 1, x + 2

Given that the first 10 even natural numbers be 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 Mean \(=\frac{Sum\, of \,all \,numbers}{Total\,numbers}\)  \(=\frac{2 + 4 + 6 + 8 + 10...

Let the consecutive even integers be ‘a’ and a + 2  ⇒ a2 + (a + 2)2 = 340  ⇒ 2a2 + 4a – 336 = 0  ⇒ a2 + 2a – 168...