The question asks to identify a medieval Indian book on mathematics from the given options. This requires knowledge of prominent historical Indian texts and their subject matter.
Correct Option: B) Leelavati is a well-known medieval Indian book on mathematics. It was written by Bhaskara II in the 12th century and is a comprehensive treatise on arithmetic, algebra, and geometry.
Answer the next 3 Questions.
Comprehension:
Read the following information and answer the following questions.
Bindu is standing exactly in the middle of a line of girls. Asha is 6th to the left of Bindu and Ritu is 16th to Bindu's right.
SubQuestion No: 1
What is Asha's position in the line?
The problem describes the relative positions of three girls in a line: Bindu, Asha, and Ritu. Bindu is in the exact middle. We are given Asha's position relative to Bindu and Ritu's position relative to Bindu. To find Asha's position in the line, we need to first determine Bindu's position, which is the middle position. Since Bindu is in the middle, the number of girls to her left must be equal to the number of girls to her right. We can use Ritu's position to find the number of girls to Bindu's right, and then use that information to find Bindu's position and subsequently Asha's position.
Thus, Asha is at the 11th position in the line.
D) 11 — As calculated, Asha's position is 11th in the line.
SubQuestion No: 2
What should be the minimum number of girls in the line?
This question is based on the given passage, which describes a line of girls with Bindu standing exactly in the middle, Asha 6th to the left of Bindu and Ritu 16th to the right of Bindu. This sub-question asks for the minimum number of girls in the line. We need to find the least number of girls that must stand on Bindu's right and then use the fact that Bindu is exactly in the middle.
Identify the given information:
Find the minimum number of girls on Bindu's right:
Ritu is 16th to the right of Bindu, so there must be at least 16 girls to the right of Bindu (Ritu being the last of them in the smallest case).
Use the middle position:
Since Bindu is exactly in the middle, the number of girls on her left equals the number on her right. So, there are at least 16 girls on her left as well. This also covers Asha, who is only 6th to the left.
Compute the total:
\[ \text{Minimum total} = 16 + 1 + 16 = 33 \]Correct Option: C) 33 — At least 16 girls stand on each side of Bindu, giving 16 + 1 + 16 = 33 girls. Hence, Option C is the correct answer.
A) 22: This is incorrect because with 22 girls there cannot be 16 girls to Bindu's right while she stands in the middle.
B) 28: This is incorrect because 28 is even, so no girl can stand exactly in the middle, and it is also fewer than 33.
D) 32: This is incorrect because 32 is even, so no girl can stand exactly in the middle; the minimum works out to 33.
SubQuestion No: 3
What is Bindu's position in the line?
This question is based on the given passage, which describes a line of girls with Bindu standing exactly in the middle, Asha 6th to the left of Bindu and Ritu 16th to the right of Bindu. This sub-question asks for Bindu's position in the line. We need to take the minimum possible line (as used throughout this set), count the girls on each side of Bindu and find her position from the left.
Identify the given information:
Find the minimum length of the line:
Ritu is 16th to the right of Bindu, so at least 16 girls stand to Bindu's right. Since Bindu is in the middle, at least 16 girls also stand to her left.
\[ \text{Total} = 16 + 1 + 16 = 33 \]Find Bindu's position:
With 16 girls to her left, Bindu is the 17th girl from the left (and also the 17th from the right).
\[ \text{Bindu's position} = 16 + 1 = 17 \]Check with Asha's position:
Asha is 6th to the left of Bindu, so Asha is at position 17 − 6 = 11, which matches the first sub-question of this set.
Correct Option: D) 17 — In the line of 33 girls, Bindu has 16 girls on each side, so she stands 17th. Hence, Option D is the correct answer.
A) 11: This is incorrect because 11 is Asha's position, not Bindu's.
B) 14: This is incorrect because the correct value works out to 17; this value cannot be obtained mathematically from the given data.
C) 16: This is incorrect because 16 is the number of girls on each side of Bindu, not her position.
The question asks to identify which of the given options is an animal reared for its fleece or fiber. This requires knowledge of common animals known for their textile-producing qualities.
Correct Option: A) Alpaca is an animal known for its fine, soft fleece, which is highly valued in the textile industry.
The question asks to fill in the blank in the trigonometric identity: \(\sin A = \text{_____} \times \cos A\). To solve this, we need to recall the fundamental trigonometric ratios and their relationships, specifically the definition of \(\tan A\).
B) tan A is the correct option because, by definition, \(\tan A = \frac{\sin A}{\cos A}\), which implies \(\sin A = \tan A \times \cos A\).
The question asks for the launch site of India's Mars Orbiter Mission, commonly known as Mangalyaan. This requires knowledge of India's primary space launch facilities.
Correct Option: B) Sriharikota
Mangalyaan, India's Mars Orbiter Mission, was successfully launched from the Satish Dhawan Space Centre (SDSC) in Sriharikota, Andhra Pradesh. This is ISRO's primary spaceport for launching satellites and rockets.
The question asks about the core technology used in a compact disc (CD). Understanding how CDs store and retrieve data is key to identifying the correct answer.
Therefore, laser technology is fundamental to the operation of a compact disc.
Correct Option: B) Laser is the technology used to read and write data on a compact disc. A laser beam precisely scans the disc surface to detect the microscopic pits and lands that represent digital information.
The question asks about the origin of paper invention. This is a historical fact that requires knowledge of world history, specifically the history of technology and innovation.
A) China: Paper was invented in China around 105 AD by Cai Lun, a court official during the Han Dynasty. This invention was a significant technological advancement that revolutionized writing and record-keeping.
The question asks to identify the revolutionary among the given options who committed suicide. This requires knowledge of the lives and deaths of prominent Indian revolutionaries.
Correct Option: D) Chandrashekhar Azad took his own life during a gun battle with the British police in Alfred Park, Allahabad, to avoid capture.