Directions for the following 3 (three) items:
Read the following two passage and answer the items that follow. Your answers to these items should be based on the passage only.
Passage-1
The main threat to maintaining progress in human development comes from the increasingly evident unsustainability of production and consumption patterns. Current production models rely heavily on fossil fuels. We now know that this is unsustainable because the resources are finite. The close link between economic growth and greenhouse gas emissions needs to be severed for human development to become truly sustainable. Some developed countries have begun to alleviate the worst effects by expanding recycling and investing in public transport and infra structure. But most developing countries are hampered by the high costs and low availability of clean energy sources. Developed countries need to support developing countries' transition to sustainable human development.
Unsustainability in production pattern is due to which of the following?
1. Heavy dependence on fossil fuels
2. Limited availability of resources
3. Expansion of recycling
Select the correct answer using the code given below.
The question asks to identify the reasons for unsustainability in production patterns based on the provided passage. We need to carefully read the passage and extract the points directly mentioned as causes of unsustainability in production.
A) 1 and 2 only. This option correctly identifies heavy dependence on fossil fuels and limited availability of resources as the reasons for unsustainability in production patterns, as stated in the passage.
Consider the following statements: Developed countries can support developing countries' transition to sustainable human development by
1. making clean energy sources available at low cost.
2. Provide loans for improving their public transport at nominal interest rates
3. Encouraging them to change their production and consumption patterns
Which of the statements given above is/are correct?
The question asks to identify which statements correctly describe how developed countries can support developing countries' transition to sustainable human development. We need to evaluate each statement based on its relevance and practicality in fostering sustainable development.
A) 1 only — Statement 1 is the most direct, impactful, and universally accepted method by which developed countries can genuinely support sustainable human development in developing nations by addressing a core need (clean energy) in an affordable manner, without necessarily creating debt burdens or simply 'encouraging' without tangible support.
Passage-2
Unless the forces and tendencies which are responsible for destroying the country's environment are checked in the near future and afforestation of denuded areas is taken up on a massive scale, the harshness of the climatic conditions and soil erosion by wind and water will increase to such an extent that agriculture, which is the mainstay of our people, will gradually become impossible. The desert countries of the world and our own desert areas in Rajasthan are a grim reminder of the consequences of large-scale deforestation, Pockets of desert-like landscape. are now appearing in other parts of the country including the Sutlej-Ganga Plains and the Deccan Plateau. Where only a few decades back there used to be lush green forests with perennial streams and springs, there is only brown earth, bare of vegetation, without any water in the streams and springs except in the rainy season.
According to the passage given above, deforestation and denudation will ultimately lead to which of the following?
1. Depletion of soil resource
2. Shortage of land for the common man
3. Lack of water for cultivation
Select the correct answer using the code given below,
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
The question asks us to identify the ultimate consequences of deforestation and denudation based on the provided passage. We need to carefully read the passage and extract the direct and indirect effects mentioned.
Therefore, statements 1 and 3 are the direct consequences mentioned or strongly implied by the passage.
Correct Option: C) 1 and 3 only
The problem presents a numerical sequence, and we need to find the next term, X. We will analyze the relationship between consecutive terms to identify the pattern and then apply it to find the missing value.
The sequence follows the pattern where each term is obtained by multiplying the previous term by an increasing factor that starts from 0.5 and increases by 0.5 each time.
D) 225 is the correct answer because it follows the identified pattern of multiplying by factors increasing by 0.5.
This problem involves tracking the movements of two individuals, X and Y, in a 2D plane. We need to determine the final distance between them. We can solve this by breaking down each person's movement into segments and then calculating their final positions relative to their starting point or to each other.
X is at C (60, 100) and Y is at E (-40, 100).
Since their Y-coordinates are the same, the distance between them is the absolute difference of their X-coordinates.
\[ \text{Distance} = |X_{\text{C}} - X_{\text{E}}| \]\[ \text{Distance} = |60 - (-40)| \]\[ \text{Distance} = |60 + 40| \]\[ \text{Distance} = |100| \]\[ \text{Distance} = 100 \text{ m} \]A) The final positions are (60, 100) for X and (-40, 100) for Y. The distance between them is the difference in their x-coordinates, which is \(60 - (-40) = 100\) m.
To determine the day of the week for a specific date, we use the concept of odd days. We will calculate the total number of odd days from a reference date (e.g., January 1, 1 AD) to the given date (June 1, 2099) and then adjust for the remaining days in June.
Reference Point: We know that January 1, 1 AD was a Monday. We can assign 0 to Sunday, 1 to Monday, 2 to Tuesday, and so on.
Calculate Odd Days for Years: We need to find the number of odd days from 1 AD to 2098 AD. The formula for odd days in a century is: 100 years = 5 odd days, 200 years = 3 odd days, 300 years = 1 odd day, 400 years = 0 odd days.
Years up to 2098 can be split as:
Number of leap years in 98 years:
\[ \text{Leap years} = \left\lfloor \frac{98}{4} \right\rfloor = 24 \] (Note: 2100 is not a leap year as it's a century year not divisible by 400).Number of ordinary years in 98 years:
\[ \text{Ordinary years} = 98 - 24 = 74 \]Odd days in 98 years:
\[ (24 \times 2) + (74 \times 1) = 48 + 74 = 122 \text{ odd days} \]Convert to odd days by dividing by 7:
\[ 122 \div 7 = 17 \text{ weeks and } 3 \text{ odd days} \]So, total odd days from 1 AD to 2098 AD = \(0 + 3 = 3\) odd days.
Calculate Odd Days for Months in 2099: We need to find the odd days from January 1, 2099 to June 1, 2099.
2099 is an ordinary year (not divisible by 4).
Total odd days for months in 2099 = \(3 + 0 + 3 + 2 + 3 + 1 = 12\) odd days.
Convert to odd days by dividing by 7:
\[ 12 \div 7 = 1 \text{ week and } 5 \text{ odd days} \]Total Odd Days: Add the odd days from years and months:
\[ \text{Total odd days} = 3 \text{ (from years)} + 5 \text{ (from months)} = 8 \text{ odd days} \]Convert to final odd days:
\[ 8 \div 7 = 1 \text{ week and } 1 \text{ odd day} \]So, June 1, 2099 has 1 odd day.
Determine the Day of the Week for June 1, 2099:
Since January 1, 1 AD was a Monday (1st day), and we have 1 odd day, June 1, 2099 will be the day corresponding to 1. This means June 1, 2099 is a Monday.
Find the Sunday in June 2099:
If June 1, 2099 is a Monday, then:
Therefore, the 7th of June 2099 is a Sunday.
D) 7 — As calculated, if June 1, 2099 is a Monday, then June 7, 2099 will be a Sunday.
A bill for ₹1,840 is paid in the denominations of ₹ 50, ₹20 and ₹10 notes. 50 notes in all are used.
Consider the following statements:
1. 25 notes of ₹50 are used and the remaining are in the denominations of ₹ 20 and ₹10.
2. 35 notes of ₹20 are used and the remaining are in the denominations of ₹50 and ₹10.
3. 20 notes of ₹10 are used and the remaining are in the denominations of ₹50 and ₹20.
Which of the above statements are not correct?
1 and 2 only
2 and 3 only
1 and 3 only
1, 2 and 3
We are given a total bill amount and the total number of notes used, with three denominations: ₹50, ₹20, and ₹10. We need to check each statement by assuming the given number of notes for one denomination and then forming a system of two linear equations with two variables for the remaining two denominations. We will then solve these equations to see if we get a valid (non-negative integer) number of notes.
Let \(x\) be the number of ₹50 notes, \(y\) be the number of ₹20 notes, and \(z\) be the number of ₹10 notes.
We are given two conditions:
Let's check each statement:
If \(x = 25\), the equations become:
And for the number of notes:
Now, we solve Equation A and Equation B. Multiply Equation B by 10:
Subtract Equation C from Equation A:
Substitute \(y = 34\) into Equation B:
Since the number of notes cannot be negative, statement 1 is incorrect.
If \(y = 35\), the equations become:
And for the number of notes:
Now, we solve Equation D and Equation E. Multiply Equation E by 10:
Subtract Equation F from Equation D:
Since the number of notes must be an integer, statement 2 is incorrect.
If \(z = 20\), the equations become:
And for the number of notes:
Now, we solve Equation G and Equation H. Multiply Equation H by 20:
Subtract Equation I from Equation G:
Since the number of notes must be an integer, statement 3 is incorrect.
All three statements are incorrect.
D) 1, 2 and 3
Which number amongst 240 , 321 418 and 812 is the smallest?
To find the smallest number among the given options, we need to compare them. A common strategy for comparing numbers with different bases and exponents is to express them with a common exponent or a common base. In this case, finding a common exponent will be easier. We will find the Highest Common Factor (HCF) of the exponents and rewrite each number.
The exponents are 40, 21, 18, and 12. Let's find their HCF.
The only common factor among 40, 21, 18, and 12 is 1. This means we cannot simplify them to a common exponent other than 1, which doesn't help in comparison directly. However, we can try to find a common factor for some of them or express them in a way that allows comparison.
Let's re-examine the exponents and try to express them with a common power if possible, or simplify the bases.
The exponents are 40, 21, 18, 12. The HCF of these numbers is 1. This approach of finding a common exponent for all might not be the most straightforward here.
Let's try to simplify the bases where possible:
Now the numbers are \(2^{40}\), \(3^{21}\), \(2^{36}\), \(2^{36}\).
We can immediately see that \(2^{36}\) is smaller than \(2^{40}\). So, \(4^{18}\) and \(8^{12}\) are equal and smaller than \(2^{40}\).
Now we need to compare \(3^{21}\) with \(2^{36}\).
Let's try to find a common exponent for 21 and 36. The HCF of 21 and 36 is 3.
Now we compare \(3^7\) and \(2^{12}\).
Since \(2187 < 4096\), it means \(3^7 < 2^{12}\).
Therefore, \((3^7)^3 < (2^{12})^3\), which implies \(3^{21} < 2^{36}\).
So, \(3^{21}\) is the smallest among all the numbers.
B) \(3^{21}\)
The problem asks us to find the number of possible combinations of three-digit numbers that can be formed in three rows using digits 1 to 9 without repetition. The conditions are that the second row number is twice the first row number, and the third row number is thrice the first row number. Additionally, the first row can only use three out of the four given digits (2, 3, 7, 9).
Let the number formed in the first row be \(N\). Then the number in the second row is \(2N\), and the number in the third row is \(3N\).
The total number of digits used will be 9 (3 for \(N\), 3 for \(2N\), and 3 for \(3N\)). All these 9 digits must be distinct and chosen from 1 to 9.
The first row number \(N\) must be a three-digit number. Since \(3N\) must also be a three-digit number, \(N\) cannot be too large. The maximum value for a three-digit number is 999. So, \(3N \le 999 \implies N \le 333\).
The first digit of \(N\) cannot be 0. Also, the first digit of \(2N\) and \(3N\) cannot be 0. Since we are using digits 1 to 9, this condition is naturally satisfied for the first digits of \(2N\) and \(3N\) if \(N\) is a three-digit number.
The problem states that only three of the four digits (2, 3, 7, 9) are allowed to be used in the first row. This means the digits of \(N\) must be chosen from a subset of these four digits. Let the digits of \(N\) be \(d_1 d_2 d_3\).
We need to test combinations of three digits from {2, 3, 7, 9} to form \(N\). The possible sets of three digits are:
For each set, we need to form a three-digit number \(N\) such that \(2N\) and \(3N\) also consist of three digits, and all 9 digits (\(N\), \(2N\), \(3N\)) are distinct and from 1 to 9.
Case 1: Digits of \(N\) are from {2, 3, 7}
If \(N\) is formed using 2, 3, 7, then \(N\) must be less than or equal to 333. The possible numbers are 237, 273, 327, 372. Let's check them:
Case 2: Digits of \(N\) are from {2, 3, 9}
Possible numbers for \(N\) (less than or equal to 333): 239, 293, 329.
Case 3: Digits of \(N\) are from {2, 7, 9}
Possible numbers for \(N\) (less than or equal to 333): 279, 297.
Case 4: Digits of \(N\) are from {3, 7, 9}
Possible numbers for \(N\) (less than or equal to 333): 327 (not possible as 2 is not in the set), 379 (not possible as 7 and 9 are too large for the first digit to keep \(N \le 333\)). The only possible number starting with 3 using these digits would be 379, but \(379 \times 3 = 1137\), which is a four-digit number. No numbers formed from {3, 7, 9} are \(\le 333\).
From the analysis, we found two valid combinations:
Therefore, there are 2 such combinations possible.
C) 2