The question asks to identify the place where Shah Mal led the revolt during the 1857 uprising. This requires knowledge of key leaders and their associated regions during the Indian Rebellion of 1857.
Correct Option: C) Baraut. Shah Mal was a prominent rebel leader from the Baraut pargana in the Baghpat district (Uttar Pradesh) who led the local revolt during the 1857 uprising. He mobilized the villagers and challenged British rule in his area.
Solve the following.
\(\left(\frac{1}{5}x-\frac{1}{6}y\right)\)(5x + 6y) = ?
x² + \( \frac{11xy}{30} \) - y²
x + \( \frac{11xy}{30} \) - y²
\( x^{2} + \) \( \frac{11xy}{30} \) - y
\( y^{2} \)
To solve this problem, we need to multiply the two binomials using the distributive property, often referred to as the FOIL method (First, Outer, Inner, Last) for binomials, or simply by multiplying each term of the first expression by each term of the second expression.
A) \(x^2 + \frac{11xy}{30} - y^2\) is the result obtained after performing the multiplication and combining like terms.
This question tests knowledge of organic chemistry nomenclature, specifically the suffixes used for different functional groups according to IUPAC (International Union of Pure and Applied Chemistry) naming conventions.
A) Aldehydes
Aldehydes are organic compounds containing a formyl group \((-\text{CHO})\). According to IUPAC nomenclature, the suffix 'al' is used to denote the presence of an aldehyde functional group. For example, \(\text{CH}_3\text{CHO}\) is ethanal, and \(\text{HCHO}\) is methanal.
The problem states that three numbers are in a given ratio and their Highest Common Factor (HCF) is known. We need to find the actual numbers. The key concept here is that if numbers are in a certain ratio, they can be expressed as multiples of their HCF.
Let the three numbers be \(N_1\), \(N_2\), and \(N_3\).
The given ratio of the numbers is \(1 : 2 : 3\). This means we can represent the numbers as \(1x\), \(2x\), and \(3x\) for some common factor \(x\).
The HCF (Highest Common Factor) of these numbers is given as 12.
By definition, the HCF of a set of numbers is the largest positive integer that divides each of the numbers without leaving a remainder. If the numbers are \(x\), \(2x\), and \(3x\), their HCF is \(x\).
Therefore, we can equate the common factor \(x\) with the given HCF:
\[ x = 12 \]Now, substitute the value of \(x\) back into the expressions for the three numbers:
The three numbers are 12, 24, and 36.
Correct Option: A) 12, 24, 36
This is an analogy question. We need to identify the relationship between the first pair of words and then apply the same relationship to the third word to find the fourth word.
Correct Option: B) Prison
The relationship is that of a person and their primary place of residence or confinement. A King resides in a Palace, and a Convict is confined in a Prison.
The problem states that a carton containing a dozen mirrors is dropped. A "dozen" means 12 items. When the carton is dropped, some mirrors will break, and some will remain unbroken. The total number of mirrors (broken + unbroken) must always be 12. We need to find which of the given ratios of broken mirrors to unbroken mirrors is possible. This means the sum of the ratio parts must be a factor of the total number of mirrors (12).
Understand the total number of mirrors: A dozen mirrors means there are 12 mirrors in total.
Define variables: Let \(B\) be the number of broken mirrors and \(U\) be the number of unbroken mirrors. The total number of mirrors is \(B + U = 12\).
Analyze the given ratios: For each option, we are given a ratio of broken mirrors to unbroken mirrors, say \(B:U = x:y\). This implies that \(B = kx\) and \(U = ky\) for some common multiplier \(k\). Therefore, the total number of mirrors is \(B + U = kx + ky = k(x+y)\).
Apply the condition: Since \(B+U=12\), we must have \(k(x+y) = 12\). This means that \((x+y)\) must be a factor of 12. We will check each option based on this condition.
Option A) 3 : 7
Here, \(x=3\) and \(y=7\). The sum of the ratio parts is \(x+y = 3+7 = 10\). Since 10 is not a factor of 12, this ratio is not possible.
Option B) 3 : 2
Here, \(x=3\) and \(y=2\). The sum of the ratio parts is \(x+y = 3+2 = 5\). Since 5 is not a factor of 12, this ratio is not possible.
Option C) 4 : 7
Here, \(x=4\) and \(y=7\). The sum of the ratio parts is \(x+y = 4+7 = 11\). Since 11 is not a factor of 12, this ratio is not possible.
Option D) 5 : 1
Here, \(x=5\) and \(y=1\). The sum of the ratio parts is \(x+y = 5+1 = 6\). Since 6 is a factor of 12 (specifically, \(12 \div 6 = 2\)), this ratio is possible. If \(k=2\), then the number of broken mirrors would be \(B = 5 \times 2 = 10\) and the number of unbroken mirrors would be \(U = 1 \times 2 = 2\). The total is \(10+2=12\), which is consistent with the problem statement.
Correct Option: D) 5 : 1
The sum of the ratio parts \(5+1=6\), which is a factor of 12. This means it is possible to have 10 broken mirrors and 2 unbroken mirrors, totaling 12 mirrors.
The question asks for the original name of the Indira Gandhi Canal Command Area. This requires knowledge of the historical naming conventions and development phases of major irrigation projects in India, specifically the Indira Gandhi Canal.
B) Rajasthan Canal — The Indira Gandhi Canal was originally known as the Rajasthan Canal. It was renamed in 1984.
The question asks to identify the Indian Air Force Wing Commander who was captured and subsequently released by Pakistani forces in 2019. This is a factual recall question related to a significant geopolitical event involving India and Pakistan.
The pilot in question was Wing Commander Abhinandan Varthaman, who was flying a MiG-21 Bison aircraft when it was shot down over Pakistan-occupied Kashmir on February 27, 2019. He was captured by Pakistani forces and released on March 1, 2019, at the Attari-Wagah border.
Correct Option: D) Abhinandan Varthaman is the correct name of the Indian Air Force Wing Commander who was captured and later released by Pakistani forces in 2019. He became a national hero for his bravery and composure during captivity.
Who founded the famous Vikramashila University in the 9th century?
The question asks about the founder of Vikramashila University. This requires knowledge of ancient Indian history, specifically the Pala dynasty and its contributions to education.
Correct Option: A) Dharmapala
Dharmapala (c. 781 to 821 CE) was the second ruler of the Pala Empire of Bengal and Bihar. He was a great patron of Buddhism and founded the famous Vikramashila Mahavihara (University) in Bhagalpur, Bihar. He also revived the Nalanda University.
A shopkeeper cheats to the extent of 10% while buying as well as while selling. While he was eventually caught and punished, at what percent was he gaining till then?