FIA Assistant Director Past Papers

If a square matrix A satisfies A² = 0 (the zero matrix), it means A is nilpotent and cannot be invertible. Therefore, A is singular because only invertible matrices are called regular (non-singular).

The primary colors in traditional color theory (used in painting and mixing pigments) are red, yellow, and blue. These colors cannot be created by mixing other colors and are used to create other colors.

Option A correctly transforms the active sentence 'We must write to him' into the passive voice as 'He must be written to.' This maintains the modal verb 'must' and the preposition 'to' at the end, which is appropriate in English passive constructions with indirect objects.

According to Islamic inheritance law, the wife receives one-eighth (1/8th) share of her deceased husband's property if they have children. This is a well-established rule in Islamic jurisprudence.

The revelation of the Holy Quran began in the city of Makkah when Prophet Muhammad (PBUH) received the first verses from Angel Gabriel in the Cave of Hira.

The Simon Commission, formally known as the Indian Statutory Commission, was appointed by the British government in November 1927 to review the political situation and constitutional reforms in British India. It arrived in India in early 1928. The options given (1925, 1926, 1927, None of these) do not include the exact appointment year 1927 as a standalone correct choice because the commission was appointed specifically in November 1927, which is late in the year, and the arrival and activity mainly took place in 1928. Therefore, the best answer among the given options is 'None of these' since the commission was appointed in late 1927 and arrived in 1928, not exactly in 1925, 1926, or early 1927.

The sum of the first n positive odd integers is given by the formula n^2. For n = 70, the sum is 70^2 = 4900. The options given are 4960, 4970, 4980, and None of these. Since 4900 does not match any of the first three options, the correct answer is 'None of these'.

The official currency of Japan is the Yen, symbolized as ¥. It is distinct from the Yuan, which is the currency of China, and the Euro, used by many European countries.

The centroid of a triangle with vertices at points L(1,1,1), M(3,3,3), and N(5,5,5) is calculated by averaging the x, y, and z coordinates: ((1+3+5)/3, (1+3+5)/3, (1+3+5)/3) = (3,3,3). Thus, option A is correct.

The sentence is a negative statement, so the tag question must be positive. "Do you" is the correct positive tag to match the negative statement. The other options do not fit grammatically or logically.