Queen Victoria was proclaimed Empress of India in 1877 — option 3.

Act and proclamation are two different steps, and the distinction is what the question turns on :

So 1876 is the year of the Act and 1877 the year she became Empress — which is what the question asks. Both years appear among the options for exactly that reason.

Why the title was created. The Crown had assumed direct rule of India in 1858 after the Revolt of 1857, but the sovereign still had no Indian title. An imperial title placed Victoria on a level with the Emperors of Germany and Russia, gave the princely states a single apex of allegiance, and was intended to bind the aristocracy of India to the Crown at a time when Russian influence in Central Asia was a live concern.

The Durbar of 1877 and its context. Lord Lytton’s Durbar was held with enormous ceremony — and in the middle of a famine in southern and western India in which millions died, a juxtaposition that Indian opinion did not forget. Lytton’s administration is also remembered for the Vernacular Press Act and the Arms Act, both of 1878, and for lowering the maximum age for the civil services examination from twenty-one to nineteen, which made it still harder for Indians to compete.

Two more Delhi Durbars followed: in 1903 for Edward VII, under Curzon, and in 1911 for George V — the one at which the transfer of the capital to Delhi was announced.

Hence, the answer is 1877.