Test by Bikram | Mock GATE | Test 1 | Question: 32

Question

Let $f\left ( n \right )$m  $g\left ( n \right )$ and $h\left ( n \right )$ be functions whose domain is a subset of positive integers such that $f\left ( n \right )= O\left (n^{2}\right), g\left ( n \right )= O\left(n^{3}\right), h\left ( n \right )= O\left(n^{4}\right).$ Then:

1. $f \left ( n \right ) +g \left ( n \right )= O \left(n^{3}\right)$   
2. $h \left ( n \right ) -g \left ( n \right )=O \left ( n \right )$    
3. $f \left ( n \right ).g \left ( n \right )=O\left( n^{4}\right)$   
4. $h \left ( n \right ) .g \left ( n \right ) =O\left(n^{7}\right)$

Which of the above is/are incorrect?

• A. $(d)$ $only$
• B. $(c)$ $only$
• C. $(b)$ $and$ $(d)$ $only$
• D. $(b)$ $and$ $(c)$ $only$

Answer 1

Here  (a) is correct because f(n) = O(n^2) and g(n) = O(n^3), and f(n) + g(n) = O(n^3) (Addition Rule asymptotic behavior)
Similarly item (d) is also correct according to the Multiplication Rule for asymptotic behavior. Hence the answer is (D).

Comments

oh no...question was asking which is incorrect.. sorry...i have to be more careful

---

@vineet

why not read question carefully !!

it says Which of the above is/are incorrect ? 

---

can someone explain option b why it is wrong.