The question asks to identify the strait that connects the Atlantic Ocean with the Pacific Ocean. This requires knowledge of major straits and their geographical locations and the bodies of water they connect.
Correct Option: A) The Strait of Magellan — This strait is a navigable sea route immediately south of mainland South America and north of Tierra del Fuego. It connects the Atlantic Ocean to the Pacific Ocean, allowing ships to pass between the two without navigating the treacherous Drake Passage.
The question asks to identify the largest coffee-producing country globally. This requires knowledge of current global agricultural statistics, specifically related to coffee production.
Brazil has historically been and continues to be the largest producer of coffee in the world, accounting for a significant portion of global coffee supply. Its favorable climate, vast land area, and established agricultural practices contribute to its high output.
B) Brazil is the largest producer of coffee in the world. It has held this position for many years, producing both Arabica and Robusta varieties.
The question asks to identify which of the given countries is NOT a member of the BRICS group. To answer this, one needs to know the current member countries of BRICS.
If A + B = 90° and sin A = \( \frac{3}{5} \), then the value of tan B is:
\( \frac{5}{4} \)
\( \frac{3}{5} \)
\( \frac{5}{3} \)
\( \frac{4}{3} \)
The problem provides a relationship between two angles, A and B, and the sine of angle A. We need to find the value of the tangent of angle B. We will use trigonometric identities and the given information to solve this.
We are given that \(A + B = 90^\circ\). From this, we can express B in terms of A:
\[ B = 90^\circ - A \]We need to find \(\tan B\). Substitute the expression for B from step 1:
\[ \tan B = \tan (90^\circ - A) \]Using the trigonometric identity \(\tan (90^\circ - \theta) = \cot \theta\), we get:
\[ \tan B = \cot A \]We know that \(\cot A = \frac{1}{\tan A}\). So, we need to find \(\tan A\).
We are given \(\sin A = \frac{3}{5}\). We can use the Pythagorean identity \(\sin^2 A + \cos^2 A = 1\) to find \(\cos A\):
\[ \left(\frac{3}{5}\right)^2 + \cos^2 A = 1 \]\[ \frac{9}{25} + \cos^2 A = 1 \]\[ \cos^2 A = 1 - \frac{9}{25} \]\[ \cos^2 A = \frac{25 - 9}{25} \]\[ \cos^2 A = \frac{16}{25} \]\[ \cos A = \sqrt{\frac{16}{25}} \]\[ \cos A = \frac{4}{5} \quad (\text{Assuming A is an acute angle, which is typical in such problems}) \]Now, we can find \(\tan A\):
\[ \tan A = \frac{\sin A}{\cos A} \]\[ \tan A = \frac{3/5}{4/5} \]\[ \tan A = \frac{3}{4} \]Finally, substitute the value of \(\tan A\) into the expression for \(\tan B\):
\[ \tan B = \cot A = \frac{1}{\tan A} = \frac{1}{3/4} \]\[ \tan B = \frac{4}{3} \]D) \( \frac{4}{3} \) is the correct value for \(\tan B\).
The problem is a coding-decoding question. We need to identify the pattern or mapping between the letters of the given word "STORMY" and its coded form "ABFIDG". Once the pattern is identified, we apply the same pattern to decode the word "LOTUS".
The word STORMY is coded as ABFIDG.
This is a direct letter-to-letter substitution. Each letter in STORMY corresponds to a specific letter in ABFIDG.
We need to find the code for LOTUS.
Since 'L' and 'U' are not present in the word STORMY, we need to look for a different pattern or assume that the code provided is a fixed substitution for these specific letters only, and any new letters will follow a similar, but perhaps unstated, pattern. However, in such coding-decoding questions, if a direct substitution is given for a set of letters, and the new word contains some of those letters, it's implied that the same substitution rule applies. For the letters not present, we must re-examine the problem or look for a more complex pattern.
Let's re-examine the provided solution and the options. The options suggest a direct substitution for all letters. This implies that the mapping is not just for the letters in "STORMY" but a general rule. Let's check the alphabetical positions.
There doesn't seem to be a simple arithmetic progression or shift. This indicates that it is a direct letter substitution code where each letter of the original word is assigned a unique code letter, and this mapping is consistent. The letters 'L' and 'U' must also have their corresponding codes. Let's look at the options.
If we consider the option D) CFBCA:
This option correctly uses the given codes for O, T, and S. It also provides codes for L and U. This is the most plausible approach for such problems when new letters appear in the target word.
The code for 'O' is 'F', for 'T' is 'B', and for 'S' is 'A'. These are consistent with the given example STORMY → ABFIDG. The codes for 'L' and 'U' are 'C'. This implies that 'L' and 'U' both map to 'C'. This is possible in a direct substitution code where multiple input letters can map to the same output letter, or it could be a typo in the question/options if it's meant to be a one-to-one mapping. However, given the options, this is the only one that maintains consistency for the common letters.
D) CFBCA
This option correctly uses the established codes for O, T, and S, and provides codes for L and U that fit the structure of the answer.
To find the volume of a cube, we first need to determine the length of its side. We are given the total surface area of the cube. We can use the formula for the total surface area of a cube to find the side length, and then use the side length to calculate the volume.
Recall the formula for the total surface area of a cube:
If \(a\) is the side length of a cube, its total surface area (TSA) is given by:
\[ \text{TSA} = 6a^2 \]Substitute the given total surface area into the formula:
We are given \(\text{TSA} = 1944 \text{ cm}^2\). So,
\[ 1944 = 6a^2 \]Solve for the side length \(a\):
Divide both sides by 6:
\[ a^2 = \frac{1944}{6} \]\[ a^2 = 324 \]Find the square root to get \(a\):
Take the square root of both sides:
\[ a = \sqrt{324} \]\[ a = 18 \text{ cm} \]Recall the formula for the volume of a cube:
The volume (V) of a cube with side length \(a\) is given by:
\[ V = a^3 \]Substitute the calculated side length into the volume formula:
Using \(a = 18 \text{ cm}\):
\[ V = (18)^3 \]\[ V = 18 \times 18 \times 18 \]\[ V = 324 \times 18 \]\[ V = 5832 \text{ cm}^3 \]C) 5832 cm³ is the correct volume of the cube.
The question asks to identify the author of the famous Bangla novel 'Pather Panchali'. This requires knowledge of prominent Bengali literature and their authors.
Correct Option: C) Bibhutibhushan Bandopadhyay
Bibhutibhushan Bandopadhyay (1894–1950) was a renowned Bengali writer. His most famous work is 'Pather Panchali' (Song of the Little Road), which was first published in 1929. This novel is a classic of Bengali literature and is known for its vivid portrayal of rural Bengal and the life of its protagonist, Apu.
The question asks for the botanical name of common wheat. Botanical names, also known as scientific names, are binomial names (genus and species) used to uniquely identify organisms. We need to identify the correct binomial name for common wheat from the given options.
Correct Option: C) Triticum Aestivum is the botanical name for common wheat, which is one of the most important cereal crops globally.
This problem involves calculating the correct average weight after a systematic error in measurement. We are given the initially calculated average weight and the error per item. We need to find the total sum of the incorrect weights, correct it by adding the error for each item, and then calculate the new, correct average.
\[ \text{Correct average weight} = \text{Incorrect average weight} + \text{Error per apple} \]\[ = 104 \text{ g} + 20 \text{ g} = 124 \text{ g} \]
D) 124 g is the correct average weight of an apple in that sample.
The question asks for the name of the first Indian satellite launched into orbit. This is a factual question related to India's space program history. We need to identify the correct satellite among the given options.
India's first satellite, Aryabhata, was launched on April 19, 1975. It was named after the ancient Indian astronomer Aryabhata. The satellite was built by the Indian Space Research Organisation (ISRO) and launched by the Soviet Union using a Kosmos-3M launch vehicle from Kapustin Yar.
Correct Option: C) Aryabhata was the first Indian satellite launched into orbit on April 19, 1975.