To find the odd one out, we need to identify a common characteristic shared by three of the given options and then find the option that does not share that characteristic. In this case, we will consider the ability of the birds to fly.
Correct Option: A) Ostrich
Simplify \(\sqrt{(1-\sin^2\theta)\div(1-\cos^2\theta)}\)
To simplify the given trigonometric expression, we will use the fundamental trigonometric identity \(\sin^2\theta + \cos^2\theta = 1\). This identity allows us to express \((1 - \sin^2\theta)\) in terms of \(\cos^2\theta\) and \((1 - \cos^2\theta)\) in terms of \(\sin^2\theta\). After substitution, we can simplify the fraction under the square root and then take the square root.
The primary identity is \(\sin^2\theta + \cos^2\theta = 1\).
From \(\sin^2\theta + \cos^2\theta = 1\), we can derive:
The given expression is \(\sqrt{(1-\sin^2\theta)\div(1-\cos^2\theta)}\).
Substitute the rewritten terms:
\[ \sqrt{\frac{\cos^2\theta}{\sin^2\theta}} \]We know that \(\frac{\cos\theta}{\sin\theta} = \cot\theta\).
Therefore, \[\frac{\cos^2\theta}{\sin^2\theta} = \left(\frac{\cos\theta}{\sin\theta}\right)^2 = \cot^2\theta\].
The expression becomes:
\[ \sqrt{\cot^2\theta} \]The square root of \(\cot^2\theta\) is \(\cot\theta\).
\[ \sqrt{\cot^2\theta} = |\cot\theta| \] (Assuming \(\theta\) is in a quadrant where \(\cot\theta\) is positive, or considering the principal value, we take \(\cot\theta\)).A) cot \(\theta\) is the simplified form of the given expression.
The problem asks us to identify the odd one out from a given series of numbers: 28, 44, 68, 80, 92. We need to find a common pattern or property among most of the numbers and identify the one that does not fit this pattern.
Correct Option: C) 80 is the odd one out because when divided by 4, it results in 20, which is a composite number. The other numbers (28, 44, 68, 92) when divided by 4 result in 7, 11, 17, and 23 respectively, all of which are prime numbers.
This question tests knowledge of metric prefixes and their corresponding multipliers. Specifically, it asks for the conversion of a decalitre to litres. Understanding the meaning of the prefix "deca-" is key to solving this problem.
B) 10 litre — As established, the prefix "deca-" signifies a multiplication by 10. Thus, one decalitre is equal to 10 litres.
The question asks to identify the river historically known as the 'Sorrow of Bengal'. This is a factual question related to Indian geography and history, specifically concerning the impact of rivers on regional life.
D) Damodar — The Damodar River was historically known as the 'Sorrow of Bengal' due to its devastating floods that frequently ravaged the plains of West Bengal. These floods caused widespread destruction, loss of life, and agricultural ruin, earning the river this somber title. The construction of the Damodar Valley Corporation (DVC) was a major effort to tame this river and mitigate its destructive power.
This is an analogy-based question. We need to identify the relationship between the first pair of words (TEACHER: BOOKS) and then find a word that shares the same relationship with the second word (DOCTOR).
C) Stethoscope. A stethoscope is an essential instrument used by doctors for diagnosis, just as books are essential resources for teachers.
The question asks to identify the country represented by the letter 'B' in the acronym BRICS. This requires knowledge of what BRICS stands for.
C) Brazil is the correct answer because 'B' in the BRICS acronym stands for Brazil.
The question asks to identify the profession of Mrinalini Sarabhai, a prominent personality who passed away in 2016. This requires general knowledge about famous Indian personalities, particularly in the fields of arts and sciences.
C) Classical Dancer — Mrinalini Sarabhai was a celebrated Indian classical dancer, choreographer, and instructor, known for her contributions to Bharatanatyam and Kathakali.
To find the tallest person, we need to establish the height order of all individuals mentioned. We can do this by converting the given statements into inequalities or by creating a relative height sequence.
Statement 1: "Mohan is taller than Rohan but shorter than Farhan."
This can be written as: Rohan < Mohan < Farhan.
Statement 2: "Kannan is shorter than Mohan but taller than Rohan."
This can be written as: Rohan < Kannan < Mohan.
Statement 3: "Shankar is taller than Rohan and Farhan."
This implies: Rohan < Shankar and Farhan < Shankar.
Combine the information:
Final order of height (from shortest to tallest):
Rohan < Kannan < Mohan < Farhan < Shankar
From this final order, it is clear that Shankar is the tallest.
Correct Option: C) Shankar
Based on the combined statements, Shankar is taller than Farhan, and Farhan is taller than Mohan, who is taller than Kannan and Rohan. Therefore, Shankar is the tallest among all.
This is a logical reasoning question that requires careful understanding of the phrasing "last but one contestant." We need to determine your position relative to the end of the race after overtaking this specific contestant.
B) Second from last. If you overtake the contestant who is second from last, you take their position, making you second from last. The person you overtook is now third from last, and the very last person remains last.