If the mode of the following data is 7, the value of k is :

2, 4, 6, 7, 5, 6, 10, 6, 7, 2k + 1, 9, 7, 13

1. 2

2. 3

3. 4

4. 7

Given, mode = 7

From above set of numbers : 6 and 7 occurs most of the time (3 times each). For 7 to be the mode, its frequency must be greater than that of 6.

Therefore, the unknown expression 2k + 1 must be equal to 7.

⇒ 2k + 1 = 7

⇒ 2k = 7 - 1

⇒ 2k = 6

⇒ k = $\dfrac{6}{2}$

⇒ k = 3.

Hence, Option 2 is the correct option.