All trigonometric functions are periodic. What is the period of cos x?
The period of a trigonometric function is the smallest positive value \(P\) for which the function repeats its values. For a function \(f(x)\), this means \(f(x+P) = f(x)\) for all \(x\) in the domain of \(f\). We need to find this value for \(\cos x\).
Therefore, the smallest positive value \(P\) for which \(\cos(x+P) = \cos x\) is \(2\pi\).
Correct Option: C) \(2\pi\) is the smallest positive value for which the cosine function repeats its values, making it the period of \(\cos x\).
This problem involves work and time. We can solve it by calculating the amount of work done per day (efficiency) by Giri alone and by Giri and her friend together. Then, we can find the friend's per-day work and, subsequently, the time taken by the friend alone.
Correct Option: A) 12
The friend can complete the work alone in 12 days.
The question asks for the full form of "IBM" in IBM Corporation. This is a general knowledge question related to common abbreviations of well-known companies.
IBM stands for International Business Machines. It is an American multinational technology and consulting company.
B) International Business Machines is the correct full form of IBM. IBM is a globally recognized technology company.
The question asks about the origin of Tanjore paintings in relation to various dynasties. To answer this, we need to recall the historical context and patronage of this art form.
C) Cholas — While Tanjore painting flourished significantly under the Nayakas and Marathas of Thanjavur (16th-19th centuries), its origins and the rich artistic tradition of the region are deeply rooted in the Chola period (9th-13th centuries). The Cholas were prolific patrons of art and architecture in the Thanjavur region, establishing a strong cultural foundation from which later art forms, including Tanjore painting, evolved. The question asks about the origin, pointing to the earliest significant dynastic influence.
The question asks for the full form of the acronym SEO in the context of web pages. This is a common term in digital marketing and web development.
Correct Option: A) Search Engine Optimisation is the correct full form of SEO. This term refers to the practice of increasing the quantity and quality of traffic to your website through organic search engine results.
The question asks to identify a type of malware that loads onto a computer without the user's knowledge and runs against their wishes. We need to evaluate each option based on the characteristics described.
Correct Option: A) A virus is a type of malware that attaches itself to legitimate programs and spreads, often loading and running on a computer without the user's explicit knowledge or consent, and performing malicious actions against their wishes.
To find the number of tiles needed, we first need to ensure all measurements are in the same units. Then, we calculate the area of the kitchen floor and the area of one tile. Finally, we divide the total floor area by the area of a single tile.
The kitchen length is 2.4 m and width is 1.6 m. Since 1 m = 100 cm:
\[ \text{Kitchen Length} = 2.4 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 240 \text{ cm} \] \[ \text{Kitchen Width} = 1.6 \text{ m} \times 100 \frac{\text{cm}}{\text{m}} = 160 \text{ cm} \]The area of a rectangle is given by Length \(\times\) Width.
\[ \text{Area of Kitchen} = \text{Length} \times \text{Width} = 240 \text{ cm} \times 160 \text{ cm} = 38400 \text{ cm}^2 \]Each tile is square with a side of 10 cm.
\[ \text{Area of one tile} = \text{Side} \times \text{Side} = 10 \text{ cm} \times 10 \text{ cm} = 100 \text{ cm}^2 \]Divide the total area of the kitchen floor by the area of one tile.
\[ \text{Number of tiles} = \frac{\text{Area of Kitchen}}{\text{Area of one tile}} = \frac{38400 \text{ cm}^2}{100 \text{ cm}^2} = 384 \]Correct Option: C) 384
The question asks to identify the strait that separates Tamil Nadu (India) and Mannar (Sri Lanka). This requires knowledge of the geographical features connecting and separating India and Sri Lanka.
Correct Option: D) Palk strait. The Palk Strait is a strait between the Tamil Nadu state of India and the Mannar district of the Northern Province of the island nation of Sri Lanka. It connects the Bay of Bengal in the northeast with the Palk Bay and then the Gulf of Mannar in the southwest.
The question asks to identify the year of the budget known as the "Black Budget" in India. This requires knowledge of significant historical budgets and their common appellations.
Correct Option: A) 1973-74 — The Union Budget presented by then Finance Minister Yashwantrao Chavan on February 28, 1973, is famously known as the "Black Budget." This budget was presented during a period of severe economic crisis, including the aftermath of the 1971 Indo-Pak war, drought, and the oil shock. It recorded a massive budget deficit of Rs 550 crore and introduced several harsh measures and new taxes to address the financial crunch.
The question asks to identify the dam on the Congo River that has a very high electric power generation capacity. This requires knowledge of major hydroelectric projects, particularly in Africa.
B) Inga — The Inga Dams are a series of hydroelectric dams on the Congo River in the Democratic Republic of Congo. The full potential of the Grand Inga project, if all phases are completed, is estimated to be around 40,000 MW (or 40 GW), making it the largest proposed hydroelectric power station in the world. Currently, Inga I and Inga II are operational, with Inga III and Grand Inga in various stages of planning or development.