Use this PowerShell script to install MongoDB

Install MongoDB 3.2.7 as a Windows Service using Windows PowerShell

$mongoDbPath = "$env:SystemDrive\MongoDB" 
$mongoDbConfigPath = "$mongoDbPath\mongod.cfg"
$url = "https://fastdl.mongodb.org/win32/mongodb-win32-x86_64-2008plus-3.2.7.zip" 
$zipFile = "$mongoDbPath\mongo.zip" 
$unzippedFolderContent ="$mongoDbPath\mongodb-win32-x86_64-2008plus-3.2.7"
 
if ((Test-Path -path $mongoDbPath) -eq $True) 
{ 
  write-host "Seems you already installed MongoDB"
    exit 
}

Write-Host "Setting up directories..."
$temp = md $mongoDbPath 
$temp = md "$mongoDbPath\log" 
$temp = md "$mongoDbPath\data" 
$temp = md "$mongoDbPath\data\db"

Write-Host "Setting up mongod.cfg..."
[System.IO.File]::AppendAllText("$mongoDbConfigPath", "dbpath=$mongoDbPath\data\db`r`n")
[System.IO.File]::AppendAllText("$mongoDbConfigPath", "logpath=$mongoDbPath\log\mongo.log`r`n")
[System.IO.File]::AppendAllText("$mongoDbConfigPath", "smallfiles=true`r`n")

Write-Host "Downloading MongoDB..."
$webClient = New-Object System.Net.WebClient 
$webClient.DownloadFile($url,$zipFile)

Write-Host "Unblock zip file..."
Get-ChildItem -Path $mongoDbPath -Recurse | Unblock-File

Write-Host "Unzipping Mongo files..."
$shellApp = New-Object -com shell.application 
$destination = $shellApp.namespace($mongoDbPath) 
$destination.Copyhere($shellApp.namespace($zipFile).items())
 
Copy-Item "$unzippedFolderContent\*" $mongoDbPath -recurse

Write-Host "Cleaning up..."
Remove-Item $unzippedFolderContent -recurse -force 
Remove-Item $zipFile -recurse -force

Write-Host "Installing Mongod as a service..."
& $mongoDBPath\bin\mongod.exe --config $mongoDbConfigPath --install

Write-Host "Starting Mongod..."
& net start mongodb

Also because of MongoDB driver 1.10 in Sitecore 8.1 we are only limited to MongoDB 3.0.0 so modify the above scripts to 3.0.0.

https://docs.mongodb.com/ecosystem/drivers/csharp/#compatibility

Akshay, I am getting the below error. I tried to change policy for current user still not able to install. If you have any idea about this error, please let me know.
net.exe : The service name is invalid.
At D:\Sitecore\Sitecore_MongoDB_Install.ps1:47 char:1

• & net start mongodb

• - CategoryInfo          : NotSpecified: (The service name is invalid.:String) [], RemoteException
  - FullyQualifiedErrorId : NativeCommandError
  
  

More help is available by typing NET HELPMSG 2185.

Hey you can add bellow before download mongodb file on line 25 to avoid SSL/TLS error.

[Net.ServicePointManager]::SecurityProtocol = [Net.SecurityProtocolType]::Tls12

Fixed excepetion:
Exception calling "DownloadFile" with "2" argument(s): "The request was aborted: Could not create SSL/TLS secure
channel."