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How to add single quote "'" to javascript string

So many related questions out there, but none satisfyingly answered using javascript (no jQuery).
I wish to add quotes around a variable in a string I'm building. My string itself should contain single quotes within it like so:
'{'a'}'
I can get:
'{a}'
When I try to add single quotes around the key a I get:
'{\'a\'}'
I've used both of the following syntax with the same result.
Any suggestions??
concat('\'','a','\'')
'\''+'a'+'\''
See line 39 of this code: https://repl.it/#mike_butak/LiveForHisPleasureHeReallyIsThere
Thanks!

Like this?
console.log("'{'a'}'")
To expand on this, when you are building the string, just use " around the string, and ' within the string.

Having a hard time replicating your issue! See:
var temp = '\'{\'a\'}\'';
console.log('s' + temp + 's');
I'd definitely recommend demonstrating the issue you are asking about in a console print or in a readily available editor online before posting a question!
As per your comment, updating to make it part of a variable assignment. Still unclear what the issue is!

Setting an element value using HTML entities

I'm having an issue trying to set an input field's value when using HTML entities in that they are coming out literally as " rather than ".
Here is the code I am using:
document.getElementById('inputSurname').setAttribute('value', 'test"""');
in which the output is test""" though I want the output to be test""".
It doesn't look like a double-encoding issue since in the source code I am seeing it the same way I have set it here.
I know I could decode the value from its HTML entity format though this is something I want to avoid if possible for security.
Any help would be much appreciated :)

Try this:
document.getElementById('inputSurname').value = 'test"""';
Or if you want to keep &quot:
function myFunction() {
document.getElementById('myText').value = replaceQuot('test&quot&quot&quot');
}
function replaceQuot(string){
return string.replace('&quot', '""');
}

Or you can use escape characters.
document.getElementById("inputSurname").setAttribute("value", "test\"\"\"\"");

Well you could just write the new value as 'test"""'.
For other characters however, I'm going to refer you to this answer: HTML Entity Decode

Trying to append html string fail with jQuery

I'm trying to append the following string to head with jQuery :
"<script type='text/javascript'> window['adrum-app-key'] = 'dummy';</script>"
But it always fails. Trying to do the same with 'Hello' string for example works as expected.
Following the code snippet I use to append the string :
var integrationScriptTag = handlebars.partials.integration(integrationData);
$(document).ready(function() {
$('head').append(integrationScriptTag.trim());
});
First string is the result of parsing integrationData.
Any help will really be appreciated.
Edit: I realize I misguided some of you with the first string. It is just a representation of what is produced by the first line of the second code snippet. So it doesn't really matter if it is some quote marks or not. The fact is I don't use a literal but rather a variable which is equal to the first string. I corrected the syntax so that there is no more confusion.
Here is the jsFiddle reproducing the problem.
jsFiddle

This should fix it:
'<script type=\'text/javascript\'> window[\'adrum-app-key\'] = \'dummy\';</script>'
or this would too:
'<script type="text/javascript"> window["adrum-app-key"] = "dummy";</script>'
Essentially you have quotes mismatch.

Use this, it will fix the issue
'<script type=\'text/javascript\'> window[\'adrum-app-key\'] =\'dummy\';<\/script>'

I finally found that you cannot append script tags to head with jQuery this way.
I found some solutions here and there (look at the first code snippet of the selected answer for the second link).

The head is parsed prior to the execution of javascript. So you probably have to perform the append outside the $(document).ready function.

show images using javascript and CSS

I have to create a javascript code which calls different images on the click of an image button. I have given names to the images as product1, product2, product3. I am new to JavaScript.
var count;
document.getElementById("divProduct").style.backgroundImage="url('images/product'+count)";
I am trying the above code, but it's not working

If you look at the syntax highlighting, + count is being treated as a string.
You put it outside of the single quotes (kind of), but you still need to put it outside of the double quotes, which are the quotes you're really using to delimit the string:
document.getElementById("divProduct").style.backgroundImage="url('images/product" + count + "')";

You are also missing the image extension. It should be .png or .jpg or something else depending on whatever type your image is.
Also I'd like to know if you are getting any errors on the console.
Edit : For those looking for answers to this question, please also check blender's reply below mine.

Your code should be like Blender said and still if it doesn't work add in you div
sample:
<div id="divProduct"> </div>

I think it must be like;
var count;
document.getElementById("divProduct").style.backgroundImage="url('images/product" + count + ".jpg')";

How to pass value to using external variable in javascript?

following code works properly
draw([['Rice',20,28,38],['Paddy',31,38,55],]);
but when i try using external variable like
var val1=20;
var val2=30;
var val3=40;
draw([['Rice',val1,val2,val3],['Paddy',31,38,55],]);
It wont work.

Just showing that your example code works fine using the Firebug console. Can you post more of your code? Your stripped-down example is probably missing something else that's causing a problem.
What is your draw() function doing? Could something in that function be breaking?
EDIT: Another problem could be the trailing comma after your second array. That will throw an error in Internet Explorer.
alert([['Rice',val1,val2,val3],['Paddy',31,38,55],]);
should be:
alert([['Rice',val1,val2,val3],['Paddy',31,38,55]]);
That may solve your issue (though you also have that in your 'working' example, but I thought it worth mentioning).

Your code snippets are not equivalent -- the second one has different values (['Rice',20,30,40] vs ['Rice',20,28,38]). Other than that, they are equivalent and should have the same effects.