Ajax form no validation

I have a site http://nisanththulasi.com and on the top there is a login modal. I have added the code do_action(‘login_form’); and the captcha is displayed but its not validating.
I can able to login without captcha.

credentials are
admin/nisanth123!@#

https://ww.wp.xz.cn/plugins/wp-recaptcha-integration/