To find the gain percentage, we first need to calculate the actual gain (profit) by subtracting the cost price from the selling price. Then, we divide this gain by the cost price and multiply by 100 to express it as a percentage.
Correct Option: C) 22.7%
Shimla Agreement 1972 between India & Pakistan was signed in
Barne's Court
Ellerslie Building
Viceregal Lodge
Gorton Castle
The question asks for the specific location in Shimla where the Shimla Agreement of 1972 between India and Pakistan was signed. This requires knowledge of the historical details surrounding the agreement.
Correct Option: A) Barne's Court was indeed the venue where the Shimla Agreement was signed on July 2, 1972. It was then the Himachal Pradesh Raj Bhavan.
The problem asks us to expand the expression \( (\sin \theta + \cos \theta )^{2} \). This can be solved by using the algebraic identity \( (a+b)^2 = a^2 + b^2 + 2ab \) and the fundamental trigonometric identity \( \sin^2 \theta + \cos^2 \theta = 1 \).
Identify the algebraic form: The given expression is \( (\sin \theta + \cos \theta )^{2} \). This is in the form \( (a+b)^2 \), where \( a = \sin \theta \) and \( b = \cos \theta \).
Apply the algebraic identity: The algebraic identity is \( (a+b)^2 = a^2 + b^2 + 2ab \). Substituting \( a = \sin \theta \) and \( b = \cos \theta \) into the identity, we get:
\[ (\sin \theta + \cos \theta )^{2} = (\sin \theta)^2 + (\cos \theta)^2 + 2(\sin \theta)(\cos \theta) \]Simplify the terms: This simplifies to:
\[ \sin^2 \theta + \cos^2 \theta + 2\sin \theta \cos \theta \]Apply the fundamental trigonometric identity: We know that \( \sin^2 \theta + \cos^2 \theta = 1 \). Substitute this into the expression:
\[ 1 + 2\sin \theta \cos \theta \]Rearrange the terms (optional, for matching options): The expression can also be written as \( 1 + 2\cos \theta \sin \theta \).
C) 1 + 2cosθsinθ — This matches our derived expression \( 1 + 2\sin \theta \cos \theta \).
The question asks for the instrument used to regulate temperature to a specific degree. We need to identify which of the given options performs this function.
Correct Option: A) Thermostat is an instrument used to regulate temperature to a particular degree. It automatically controls a heating or cooling device to maintain a set temperature.
The question asks about the fundamental quantities used to define pressure. We need to recall the definition and formula for pressure to identify the correct components.
Correct Option: C) Pressure is fundamentally defined as Force per unit Area. Therefore, it is measured in terms of Force and Area.
To find how many times the number 3 occurs in the unit's place for numbers ranging from 1 to 100, we need to list all numbers in this range that have 3 in their unit's place and then count them.
The numbers are: 3, 13, 23, 33, 43, 53, 63, 73, 83, 93.
There are 10 such numbers.
C) 10. The number 3 appears exactly 10 times in the unit's place for numbers from 1 to 100.
The question asks to compare the lengths of the small and large intestines in humans. This is a factual question related to human anatomy. To answer correctly, one needs to recall the typical lengths of these organs.
Correct Option: A) Small intestine is longer than the large intestine. The small intestine measures approximately 6-7 meters, while the large intestine is about 1.5 meters long.
The question asks for the location of the Biosafety Laboratory in India established for detailed study of disease-causing organisms in livestock. This is a factual question requiring knowledge of specific research facilities in India.
Correct Option: B) The National Institute of Veterinary Epidemiology and Disease Informatics (NIVEDI), located in Bengaluru, is a premier institution under the Indian Council of Agricultural Research (ICAR) that focuses on research in animal disease epidemiology, surveillance, and diagnostics. It houses advanced biosafety facilities for the detailed study of disease-causing organisms in livestock.
This problem involves comparing the heights of different objects. We can solve it by establishing a series of inequalities based on the given statements and then identifying the object with the smallest height.
The complete order from tallest to shortest is not fully determined for all objects, but we can clearly see that the Tree is the shortest among all mentioned entities.
Correct Option: C) Tree
Find the missing (?) in the series
NA, PC, RE, TG, ?, XK, ZM
The problem presents a series of two-letter codes. We need to identify the pattern in both the first and second letters of each code to find the missing term.
The first letters in the series are N, P, R, T, ?, X, Z.
Thus, the first letter of the missing term is V.
The second letters in the series are A, C, E, G, ?, K, M.
Thus, the second letter of the missing term is I.
The missing term is formed by combining the first letter V and the second letter I, which gives VI.
B) VI — Based on the analysis of both the first and second letters, the pattern consistently involves skipping one letter in the alphabet. For the first letters (N, P, R, T, ?, X, Z), the missing letter is V. For the second letters (A, C, E, G, ?, K, M), the missing letter is I. Combining these gives VI.