The table given below shows the record of the number of students who got selected in the entrance exam of M.Phil. in a particular central university from five different states of India over the years. Study the table and answer the question.
| Years | Kashmir | Bihar | MP | Punjab | Delhi |
| 2017 | 300 | 440 | 250 | 350 | 280 |
| 2018 | 400 | 400 | 280 | 400 | 320 |
| 2019 | 450 | 350 | 240 | 260 | 260 |
| 2020 | 500 | 380 | 400 | 320 | 400 |
| 2021 | 430 | 420 | 540 | 280 | 350 |
Number of students who got selected in 2020 from Bihar was approximately what percentage of the total number of students who got selected from Delhi for all the years together?
To solve this problem, we need to first identify the number of students selected from Bihar in 2020 from the given table. Then, we need to calculate the total number of students selected from Delhi over all the years. Finally, we will express the number of students from Bihar in 2020 as a percentage of the total students from Delhi.
Correct Option: C) 23.6 %
We are looking for the greatest number that divides 72 and 119, leaving specific remainders. This means that if we subtract the remainders from the original numbers, the resulting numbers must be perfectly divisible by the required greatest number. Therefore, the problem reduces to finding the HCF (Highest Common Factor) of these new numbers.
Correct Option: A) 23 is the greatest number that divides 72 and 119, leaving remainders 3 and 4 respectively.
The problem provides a statement of inequalities and equalities between several variables. We need to analyze this statement to determine which of the given conclusions logically follows from it. We will break down the main statement and then evaluate each option against it.
From the combined statement \(R > N > E > G\), it is clear that \(R\) is greater than \(G\). This means \(G < R\). This conclusion is true.
The statement is \(N > E > G < W\). While we know \(N > G\), the relationship between \(G\) and \(W\) is \(G < W\). This means \(W\) is greater than \(G\). However, there is no direct or indirect relationship established between \(W\) and \(N\). \(W\) could be greater than, less than, or equal to \(N\). Therefore, this conclusion cannot be definitively true.
From the statement, we have \(K = R\) and \(R > N\). If \(K = R\) and \(R > N\), then it must be that \(K > N\). Therefore, \(K = N\) is false.
As explained for Option C, we have \(K = R\) and \(R > N\). This implies \(K > N\). Therefore, \(K < N\) is false.
A) G < R — From the given statement \(K = U = R > N > E > G < W\), we can deduce the chain \(R > N > E > G\). This directly implies that \(R\) is greater than \(G\), or \(G < R\). Thus, this conclusion is true.
The question asks for the Controller General of Accounts (CGA) as of a specific date, June 15, 2022. This requires knowledge of current affairs and appointments in key government positions around that time.
Correct Option: B) Sonali Singh was holding the additional charge of Controller General of Accounts (CGA) as on June 15, 2022. She was appointed to this role on February 1, 2022, and served until October 2022.
The question asks for the year in which The Indian Official Language Act was passed. This is a direct factual question related to Indian polity and history. Recalling the key legislative milestones regarding official languages in India is essential.
D) 1963 — The Indian Official Language Act was passed in 1963. This Act provided for the continued use of English, in addition to Hindi, for official purposes of the Union and for transaction of business in Parliament even after January 26, 1965.
To find the angle traced by the hour hand in 18 minutes, we need to determine the speed of the hour hand in degrees per minute. We know that the hour hand completes a full circle (360°) in 12 hours. We will convert 12 hours into minutes and then calculate the angle traced per minute. Finally, we will multiply this rate by 18 minutes.
There are 60 minutes in 1 hour.
\[ \text{Total minutes} = 12 \text{ hours} \times 60 \text{ minutes/hour} = 720 \text{ minutes} \]The hour hand covers 360° in 720 minutes.
\[ \text{Speed of hour hand} = \frac{360^\circ}{720 \text{ minutes}} = 0.5^\circ/\text{minute} \]Multiply the speed of the hour hand by 18 minutes.
\[ \text{Angle traced} = 0.5^\circ/\text{minute} \times 18 \text{ minutes} = 9^\circ \]The angle traced by the hour hand in 18 minutes is 9°.
D) 9° is the correct answer, as calculated above.
To find the number of sides of a regular polygon given its interior angle, we can use the formula for the interior angle of a regular polygon, or first find the exterior angle and then use the relationship between the exterior angle and the number of sides.
Method 1: Using the interior angle formula
The formula for each interior angle of a regular polygon with \(n\) sides is given by:
\[ \text{Interior Angle} = \frac{(n-2) \times 180^{\circ}}{n} \]We are given that the interior angle is \(135^{\circ}\). So, we can set up the equation:
\[ 135^{\circ} = \frac{(n-2) \times 180^{\circ}}{n} \]Multiply both sides by \(n\):
\[ 135n = (n-2) \times 180 \] \[ 135n = 180n - 360 \]Subtract \(180n\) from both sides:
\[ 135n - 180n = -360 \] \[ -45n = -360 \]Divide by \(-45\):
\[ n = \frac{-360}{-45} \] \[ n = 8 \]Method 2: Using the exterior angle
The sum of an interior angle and its corresponding exterior angle of any polygon is \(180^{\circ}\). Given the interior angle is \(135^{\circ}\), the exterior angle is:
\[ \text{Exterior Angle} = 180^{\circ} - \text{Interior Angle} \] \[ \text{Exterior Angle} = 180^{\circ} - 135^{\circ} \] \[ \text{Exterior Angle} = 45^{\circ} \]For a regular polygon, the sum of all exterior angles is always \(360^{\circ}\). If there are \(n\) sides, and thus \(n\) equal exterior angles, then each exterior angle is:
\[ \text{Exterior Angle} = \frac{360^{\circ}}{n} \]We found the exterior angle to be \(45^{\circ}\), so:
\[ 45^{\circ} = \frac{360^{\circ}}{n} \]Rearrange to solve for \(n\):
\[ n = \frac{360^{\circ}}{45^{\circ}} \] \[ n = 8 \]Both methods yield the same result.
A metallic wire having resistivity ρ is cut into four equal parts. The resistivity of each part is:
The question asks about the resistivity of parts of a metallic wire after it is cut. Resistivity is an intrinsic property of a material, meaning it depends only on the nature of the material and its temperature, not on its dimensions (length or cross-sectional area).
Correct Option: A) \( \rho \)
The resistivity of each part remains \( \rho \) because resistivity is an intrinsic property of the material and does not depend on the dimensions of the wire.
The question asks to identify the first city planned by the Mughal Empire. This requires knowledge of Mughal history, specifically the reign of Emperor Akbar and his architectural endeavors.
D) Fatehpur Sikri — Emperor Akbar commissioned the construction of Fatehpur Sikri in 1569, intending it to be a new capital city. It was a meticulously planned city, featuring grand palaces, mosques, and public buildings, making it the first truly planned city by the Mughal Empire.
The question asks to identify the Chief Election Commissioner of India as of March 2022. This requires knowledge of current affairs and appointments in constitutional bodies.
Correct Option: B) Sushil Chandra was the Chief Election Commissioner of India from April 13, 2021, to May 14, 2022. Thus, as of March 2022, he held this position.