Which of the following is the greatest? \[ 0.6, \ 0.666, \ \frac{5}{6}, \ \frac{2}{3} \]
Which of the following is the greatest? \[ 0.6, \ 0.666, \ \frac{5}{6}, \ \frac{2}{3} \]
Show Hint
To compare repeating and terminating decimals, convert them to fractions and compare their values.
0.6
0.666
\( \frac{5}{6} \)
\( \frac{2}{3} \)
The Correct Option is B
Solution and Explanation
Step 1: Convert the decimals to fractions
- 0.6 is equivalent to \( \frac{2}{3} \).
- 0.666 is already a terminating decimal and equals \( \frac{2}{3} \).
- \( \frac{5}{6} \) is in its simplest fractional form.
- \( \frac{2}{3} \) is also in its simplest form.
Step 2: Comparison
- \( 0.6 = \frac{2}{3} \), which is less than 0.666.
- 0.666 is slightly greater than \( \frac{2}{3} \), and is the greatest among the values listed.
Thus, the correct answer is (B).
Top GATE CS Programming and Data Structures Questions
- Which of the following sequences when stored in an array at locations A[1],..., A[10] forms a max-heap?
- Given N distinct elements in an array, determine the number of comparisons required to find the element which is not the largest:
Consider the following code:
main() { int x = 126, y = 105; { if (x > y) x = x - y; else y = y - x; } while (x != y) printf("%d", x); }- In a binary search tree with the following elements: \( 10, -4, 15, 13, 20, 5, 16, 19 \), the number of edges from node 19 to the root is?
Consider the following code:
int a; int arr[] = {30, 50, 10}; int *ptr = arr[10] + 1; a = *ptr; (*ptr)++; ptr = ptr + 1; printf("%d", a + arr[1] + *ptr);
Top GATE CS Trees Questions
- In a binary search tree with the following elements: \( 10, -4, 15, 13, 20, 5, 16, 19 \), the number of edges from node 19 to the root is?
Consider the following code:
int a; int arr[] = {30, 50, 10}; int *ptr = arr[10] + 1; a = *ptr; (*ptr)++; ptr = ptr + 1; printf("%d", a + arr[1] + *ptr);Consider the following hierarchical cache system with the following access times:
\[ \begin{array}{|c|c|c|} \hline \textbf{Cache Level} & \textbf{Hit Rate} & \textbf{Access Time} \\ \hline L1 & 90\% & 1 \text{ ns} \\ L2 & 80\% & 10 \text{ ns} \\ L3 & 100\% & 100 \text{ ns} \\ \hline \end{array} \]Find \( T_{avg} \) for hierarchical or simultaneous access.
- Consider a binary tree in which every node has either 0 or 2 children. Let \( N>0 \) be the number of nodes in the tree. The number of nodes that have exactly 2 children is:
What is the output of the following C code?
void foo(int *p, int x) { *p = x; } void main() { int *z; int a = 20, b = 25; z = a; // Incorrect: Should be z = a; foo(z, b); printf("%d", a); }Issue: The statement
z = a;is invalid becauseais an integer, andzis a pointer.
Top GATE CS Questions
- Which of the following sequences when stored in an array at locations A[1],..., A[10] forms a max-heap?
- The Lucas sequence Ln is defined by the recurrence relation: Ln = Ln−1 + Ln−2, for n ≥ 3, with L1 = 1 and L2 = 3. Which one of the options given is TRUE?
- Which of the following fields of IP header is/are always modified by any router before it forwards to IP Packet ?
- Which one of the following CIDR profix exactly represent the range of IP addresses 10.12.2.0 to 10.12.3.255?
- Consider an ethernet segment whose transmission is \(10^8\) bits per second. Maximum segment length \(500\ m\), speed of the provocation media velocity is \(2 × 10^8\) meter per second. What is the minimum frame size in bits ?