Correct Answer: The disparity in access to digital technologies 

Solution : The digital divide refers to the disparity in access to digital technologies, such as computers and the internet, between different groups of people, often based on socioeconomic status, geography, or demographics.

Correct Answer: Imperial Bank of India

Solution : The correct option is Imperial Bank of India.

The Imperial Bank of India operated from 1921 to 1955. It came into existence through the merger of three presidency banks: the Bank of Calcutta, the Bank of Bombay, and the Bank of Madras.

Correct Answer: $\sqrt{2}+1$

Solution : $\sin\theta+\cos\theta=\sqrt{2}\cos\theta$
⇒ $\sin \theta = (\sqrt{2}-1)\cos\theta$
⇒ $\frac{\sin \theta}{(\sqrt{2}-1)}=\cos\theta$
⇒ $\frac{\sin \theta(\sqrt{2}+1)}{2-1}=\cos\theta$
⇒ $\frac{\sin \theta(\sqrt{2}+1)}{2-1}=\cos\theta$
⇒ $\frac{\cos \theta}{\sin \theta}=\sqrt{2}+1$
$\therefore\cot \theta=\sqrt{2}+1$
Hence, the correct answer is $\sqrt{2}+1$.

Correct Answer: $4-2 \sqrt{2}$

Solution : This is a telescoping series, where each term cancels out a part of the next term. 
$\frac{1}{4-\sqrt{15}}-\frac{1}{\sqrt{15}-\sqrt{14}}+\frac{1}{\sqrt{14}-\sqrt{13}}-\frac{1}{\sqrt{13}-\sqrt{12}}+\frac{1}{\sqrt{12}-\sqrt{11}}-\frac{1}{\sqrt{11}-\sqrt{10}}+\frac{1}{\sqrt{10}-3}-\frac{1}{3-\sqrt{8}}$
Rationalising the denominator and use the formula $a^2 - b^2 = (a+b)(a-b)$, we get,
$=\frac{\sqrt{15}+4}{1}-\frac{\sqrt{15}+\sqrt{14}}{1}+\frac{\sqrt{14}+\sqrt{13}}{1}-\frac{\sqrt{13}+\sqrt{12}}{1}+\frac{\sqrt{12}+\sqrt{11}}{1}-\frac{\sqrt{11}+\sqrt{10}}{1}+\frac{\sqrt{10}+3}{1}-\frac{3+\sqrt{8}}{1}$
$=\sqrt{15}+4-\sqrt{15}-\sqrt{14}+\sqrt{14}+\sqrt{13}-\sqrt{13}-\sqrt{12}+\sqrt{12}+\sqrt{11}-\sqrt{11}-\sqrt{10}+\sqrt{10}+3-3-\sqrt{8}$
$=4-\sqrt{8}$
$=4-2\sqrt{2}$
Hence, the correct answer is $4-2\sqrt{2}$.

Correct Answer: The hospital has been rebuilt by the villagers.

Solution : The correct choice is the second option.

Passive voice is the voice in which the object experiences an action rather than the person who performs the action. Hence, the object in the active sentence becomes the subject in

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