Hi Dinesh,

Greetings to you!

Below is the sample code which I have tested in my org and it is working fine. Kindly modify the code as per your requirement.

Visualforce:

<apex:page standardController="Contact" extensions="HideSectionBasedOnPicklistC">
    <apex:form >
        <apex:pageBlock > 
            <apex:actionRegion >
                <apex:selectList value="{!pickchoice}" multiselect="false" size="1">
                    <apex:selectOptions value="{!items}"/>
                    <apex:actionSupport event="onchange" rerender="out1,out2"/>
                </apex:selectList>
            </apex:actionRegion>            
            <br/><br/>
            <apex:pageBlockSection id="out1" >
                <apex:outputPanel rendered="{!IF(pickchoice== 'NRI' && pickchoice!= 'None', true , false)}">                    
                    <apex:outputLabel value="First Name" /><br/>
                    <apex:inputField value="{!contact.FirstName}" /><br/><br/>
                    <apex:outputLabel value="Last Name" /><br/>
                    <apex:inputField value="{!contact.LastName}" />
                </apex:outputPanel>
            </apex:pageBlockSection>
            
            <apex:pageBlockSection id="out2" >
                <apex:outputPanel rendered="{!IF(pickchoice== 'Non-NRI' && pickchoice!= 'None', true , false)}">
                    <apex:outputLabel value="Email" /><br/>
                    <apex:inputField value="{!contact.Email}" /><br/><br/>
                    <apex:outputLabel value="Phone" /><br/>
                    <apex:inputField value="{!contact.Phone}" />
                </apex:outputPanel>
            </apex:pageBlockSection>        
        </apex:pageBlock>
    </apex:form>
</apex:page>

Controller:

public class HideSectionBasedOnPicklistC {
    
    public String Pickchoice {get;set;}
    
     public HideSectionBasedOnPicklistC(ApexPages.StandardController controller) {

    }
    
    public List<SelectOption> getItems() {
        List<SelectOption> options = new List<SelectOption>();
        options.add(new SelectOption('None','None'));
        options.add(new SelectOption('NRI','NRI'));
        options.add(new SelectOption('Non-NRI','Non-NRI'));
        return options;
    }
}

Or you can use below code also:
 

<apex:page standardController="Account">
    
    <apex:form id="theForm">
        
        <apex:pageBlock>
            <apex:pageblockSection>
                <apex:inputField value="{!Account.Rating}">
                    <apex:actionSupport event="onchange" reRender="theForm"/>
                </apex:inputField>
            </apex:pageblockSection>
        </apex:pageBlock>
        
        <apex:pageblock>
            <apex:pageblockSection rendered="{!Account.Rating = 'Hot'}">
                <apex:inputField value="{!Account.Name}"/>
            </apex:pageblockSection>
            
             <apex:pageblockSection rendered="{!Account.Rating = 'Warm'}">
                <apex:inputField value="{!Account.Phone}"/>
            </apex:pageblockSection>
            
            <apex:pageblockSection rendered="{!Account.Rating = 'Cold'}">
                <apex:inputField value="{!Account.Website}"/>
            </apex:pageblockSection>
        </apex:pageblock>
        
    </apex:form>
    
</apex:page>

I hope it helps you.

Kindly let me know if it helps you and close your query by marking it as solved so that it can help others in the future. It will help to keep this community clean.

Thanks and Regards,
Khan Anas