The question involves dividing Rs 720 among five people, A, B, C, D, and E, such that the amounts received by them form an arithmetic progression (AP) in ascending order. We are also given that E receives Rs 40 more than A. To determine the amount received by B, we can represent the five amounts using the first term and common difference of an AP, form equations using the given conditions, and solve them.
Identify the given information:
Represent the five amounts in arithmetic progression:
Let the first amount received by A be \(a\) and the common difference be \(d\).
Since the amounts form an arithmetic progression, they can be represented as:
Apply the condition that E receives Rs 40 more than A:
According to the question:
\[ E-A=40 \]Substituting the expressions:
\[ (a+4d)-a=40 \] \[ 4d=40 \]Dividing both sides by 4:
\[ d=\frac{40}{4} \] \[ d=10 \]Therefore, the common difference between consecutive amounts is Rs 10.
Apply the condition that the total amount is Rs 720:
The sum of the five amounts is:
\[ a+(a+d)+(a+2d)+(a+3d)+(a+4d)=720 \]Combining like terms:
\[ 5a+10d=720 \]Substitute the common difference:
Since \(d=10\):
\[ 5a+10(10)=720 \] \[ 5a+100=720 \]Subtract 100 from both sides:
\[ 5a=620 \]Dividing both sides by 5:
\[ a=\frac{620}{5} \] \[ a=124 \]Therefore, A receives Rs 124.
Calculate the amount received by B:
Since B receives the second amount in the arithmetic progression:
\[ B=a+d \]Substituting the values:
\[ B=124+10 \] \[ B=134 \]Therefore, B receives Rs 134.
Correct Option: A) 134 — The five amounts form an arithmetic progression with a common difference of Rs 10. Using the total amount of Rs 720, the first amount is Rs 124. Therefore, B receives \(124+10=134\) rupees. Hence, Option A is the correct answer.
B) 154: This is incorrect because Rs 154 is the amount received by D, the fourth person in the arithmetic progression. The amounts are Rs 124, Rs 134, Rs 144, Rs 154, and Rs 164. Therefore, Rs 154 is not the amount received by B.
C) 144: This is incorrect because Rs 144 is the amount received by C, the third person in the arithmetic progression. B receives the second amount, which is Rs 134.
D) 124: This is incorrect because Rs 124 is the amount received by A, the first person in the arithmetic progression. Since the common difference is Rs 10, B receives Rs 10 more than A, which is Rs 134.
The question asks to identify the actor who played the role of Allauddin Khilji in the movie 'Padmavat'. This requires knowledge of popular Indian cinema and the cast of specific films.
Correct Option: B) Ranveer Singh portrayed the character of Allauddin Khilji in the movie 'Padmavat'. His performance was highly praised.
The question asks for the total number of medals won by India at the US Open Karate Championship in April 2017. This is a factual recall question related to sports achievements.
B) 16
India won a total of 16 medals (5 gold, 3 silver, and 8 bronze) at the US Open Karate Championship held in Las Vegas in April 2017.
The question asks to identify the mission founded by Dayanand Saraswati. This requires knowledge of prominent social and religious reform movements and their founders in 19th-century India.
Correct Option: C) Arya Samaj was founded by Dayanand Saraswati in 1875. Its motto was "Back to the Vedas" and it aimed to reform Hinduism by rejecting idol worship, caste discrimination, and other practices that were not based on Vedic principles.
The mass of the Earth is:
This question asks for the approximate mass of the Earth. This is a fundamental constant in astronomy and physics that is often memorized for competitive exams. The mass of the Earth is a very large number, typically expressed in scientific notation.
Correct Option: D) The mass of the Earth is approximately \(6 \times 10^{24} \text{ kg}\). This is a standard value used in scientific calculations and general knowledge related to planetary science.
The problem presents a series consisting of a number and a letter. We need to identify the pattern for both the numerical sequence and the alphabetical sequence separately to find the next term.
The numbers are 5, 7, 11, 17.
The differences are 2, 4, 6. This is an arithmetic progression with a common difference of 2. The next difference should be \(6 + 2 = 8\).
So, the next number in the series will be \(17 + 8 = 25\).
The letters are I, J, L, O. Let's find their positions in the English alphabet (A=1, B=2, ..., Z=26).
Now let's find the difference in their positions:
The differences are 1, 2, 3. This is an arithmetic progression with a common difference of 1. The next difference should be \(3 + 1 = 4\).
So, the next letter will be 4 positions after O. O is the 15th letter, so \(15 + 4 = 19\). The 19th letter in the alphabet is S.
The next number is 25 and the next letter is S. Therefore, the next term in the series is 25S.
Correct Option: A) 25S
This question asks us to identify the implicit assumptions based on a given statement. We need to analyze each assumption to see if it must be true for the statement to make sense.
A) Only I is implicit. As established, student 1's request for notes implies that student 2 has notes. The reason for studying is not specifically limited to verifying understanding.
When two trains cross each other while moving in opposite directions, the total distance covered is the sum of their lengths. The relative speed is the sum of their individual speeds. We can calculate the combined speed in meters per second (m/s) and then convert it to kilometers per hour (km/h).
Correct Option: D) 120 km
In the modern periodic table, which group elements have a complete outer shell?
The question asks to identify the group in the modern periodic table whose elements have a complete outer electron shell. This refers to elements that are chemically stable and generally unreactive. We need to recall the electron configurations of elements in different groups, particularly focusing on their valence electrons.
B) 18 th — Elements in Group 18, the noble gases, have a complete outer electron shell (2 electrons for Helium, and 8 electrons for all other noble gases), which makes them chemically stable and unreactive.
The problem presents a series of terms, each consisting of a letter, a number, and another letter. To find the next term, we need to identify the pattern for each component (first letter, number, second letter) separately.
Based on the analysis, the next term in the series will be H19S.
Correct Option: B) H19S