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**Hint:**In this question, we have the number of students appeared and passed in specific years. We need to first calculate the number of students who passed in the examination. Then we will get the passing percentage of class \[X\] for both the years. Then we can easily find out the required solution.

**Complete step by step answer:**

It is given that, in \[2007 - 08\], the number of students appeared for class \[X\] examination was \[1,05,332\] and in \[2008 - 09\], the number was \[1,16,054\].

Also given that, \[88,151\] students pass the examination in \[2007 - 08\] and \[103804\] students in \[2008 - 09\].

We need to find out the increase or decrease in pass \[\% \] in class \[X\] result.

The number of students appearing for class \[X\] examination in \[2007 - 08\] was \[1,05,332\].

The number of students passing the examination in \[2007 - 08 = 88,151\].

The percentage of the students, who passed the examination \[ = \dfrac{{88151}}{{105332}} \times 100 = 83.68\% \]

The number of students appearing for class \[X\] examination in \[2008 - 09\] was \[1,16,054\].

The number of students passing the examination in \[2008 - 09 = 103804\].

The percentage of the students, who passed the examination \[ = \dfrac{{103804}}{{116054}} \times 100 = 89.44\% \]

Since the passing percentage in \[2008 - 09\] is more than the passing percentage in \[2007 - 08\], it has increased.

The increase in pass \[\% \] in class \[X\] result is \[ = \left( {89.44 - 83.68} \right)\% = 5.76\% \]

**$\therefore $ The increase in pass \[\% \] in class \[X\] result is \[5.76\% \]**

**Note:**

Here we use the given in the question, the values are large so we have to concentrate on calculations of this problem.

In mathematics, a percentage is a number or ratio that represents a fraction of \[100\]. It is often denoted by the symbol "\[\% \]"

The percentage of \[x\] is denoted by \[x\% \] and defined by, \[x\% = \dfrac{x}{{100}}\]

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