The question asks about the specific project that led India to boycott the first Belt and Road Forum in 2017. This requires knowledge of India's stance on China's Belt and Road Initiative (BRI) and the particular project that raised sovereignty concerns.
Correct Option: D) China-Pakistan Economic Corridor. India boycotted the first Belt and Road Forum in 2017 primarily because the China-Pakistan Economic Corridor (CPEC), a flagship project of the BRI, passes through Gilgit-Baltistan in Pakistan-occupied Kashmir (PoK). India considers PoK its integral territory and views CPEC as a violation of its sovereignty.
To solve this problem, we need to represent two consecutive positive odd integers algebraically. Then, we will set up an equation based on the given condition that the difference between their squares is 56. Finally, we will solve the equation to find the integers.
Represent the integers: Let the first positive odd integer be \(x\). Since the integers are consecutive positive odd integers, the next consecutive odd integer will be \(x+2\).
Formulate the equation: The problem states that the difference between the squares of these two integers is 56. Since \(x+2\) is greater than \(x\), its square will be larger. So, the equation is:
\[ (x+2)^2 - x^2 = 56 \]Solve the equation: Expand the equation using the identity \((a+b)^2 = a^2 + 2ab + b^2\):
\[ (x^2 + 4x + 4) - x^2 = 56 \]Simplify the equation: Cancel out \(x^2\):
\[ 4x + 4 = 56 \]Isolate \(x\): Subtract 4 from both sides:
\[ 4x = 56 - 4 \] \[ 4x = 52 \]Find the value of \(x\): Divide by 4:
\[ x = \frac{52}{4} \] \[ x = 13 \]Determine the two integers: The first integer is \(x = 13\). The second integer is \(x+2 = 13+2 = 15\). So, the two consecutive odd integers are 13 and 15.
Verify the answer: Check if the difference of their squares is 56:
\[ 15^2 - 13^2 = 225 - 169 = 56 \]The condition is satisfied.
A) 13, 15 — As calculated, the two consecutive positive odd integers are 13 and 15, and the difference of their squares is \(15^2 - 13^2 = 225 - 169 = 56\).
The following table shows the number of days taken by five boys individually to complete a piece of work. If Saurabh and Kirpal work together, find the number of days taken by them to complete the work.
| Boy | Amit | Saurabh | Kirpal | Rishabh | Prithvi |
| No. of days | 25 | 30 | 20 | 35 | 40 |
To find the number of days taken by two individuals working together, we first determine their individual work rates (the fraction of work they complete in one day). Then, we add their individual work rates to find their combined work rate. Finally, the reciprocal of the combined work rate gives the total number of days they take to complete the work together.
From the table, Saurabh takes 30 days to complete the work.
Kirpal takes 20 days to complete the work.
Saurabh's one day's work \( = \frac{1}{30} \) of the total work.
Kirpal's one day's work \( = \frac{1}{20} \) of the total work.
When Saurabh and Kirpal work together, their combined one day's work is the sum of their individual work rates:
\[ \text{Combined work rate} = \frac{1}{30} + \frac{1}{20} \]The least common multiple (LCM) of 30 and 20 is 60.
\[ \text{Combined work rate} = \frac{2}{60} + \frac{3}{60} = \frac{2+3}{60} = \frac{5}{60} \]If they complete \(\frac{1}{12}\) of the work in one day, then they will complete the entire work in the reciprocal of this fraction.
\[ \text{Days taken together} = \frac{1}{\text{Combined work rate}} = \frac{1}{\frac{1}{12}} = 12 \text{ days} \]Correct Option: A) 12 days
The electronic configuration of an element describes the arrangement of electrons in its atomic shells. The numbers in the configuration (e.g., 2, 8, 7) represent the number of electrons in successive electron shells (K, L, M, etc.). The sum of these numbers gives the total number of electrons in a neutral atom, which is equal to its atomic number.
Understand Electronic Configuration: The given electronic configuration is 2, 8, 7. This means:
Calculate Total Electrons: To find the total number of electrons, sum the electrons in all shells:
\[ \text{Total electrons} = 2 + 8 + 7 = 17 \]
Determine Atomic Number: For a neutral atom, the number of electrons is equal to the number of protons, which is the atomic number.
\[ \text{Atomic Number} = \text{Total electrons} = 17 \]
Identify the Element: Refer to the periodic table to find the element with atomic number 17. The element with atomic number 17 is Chlorine (Cl).
Correct Option: C) Chlorine
The question asks to identify which of the given options is NOT an initiative by the Government of India to attract Foreign Direct Investments (FDI). We need to evaluate each option to determine if it directly relates to promoting or facilitating FDI.
Correct Option: D) The Government of India announced 'Entrepreneurship Curriculum' to be taken up by the states.
This initiative primarily aims to promote domestic entrepreneurship and skill development among the youth, rather than directly attracting Foreign Direct Investments (FDI) from abroad. While a strong entrepreneurial ecosystem can indirectly make a country more attractive for investment, the curriculum itself is not a direct policy tool for FDI attraction.
The question asks to identify the country that ranked first in the Human Development Index (HDI) for the year 2020. This requires knowledge of the HDI report for that specific year.
B) Norway was indeed ranked first in the Human Development Index for 2020, continuing its trend of high rankings in human development.
The question asks to identify the protocol that facilitates remote login on a computer. We need to evaluate each option based on its primary function in network communication.
Correct Option: B) Telnet is a network protocol used to provide a command-line interface for communication with a remote server or device. It allows users to log in to a remote computer and execute commands as if they were physically present at the machine, thus facilitating remote login.
This question requires evaluating logical conclusions based on given statements. We will use Venn diagrams or syllogistic reasoning to determine if the third statement in each set (A, B, C) logically follows from the first two.
Based on the analysis, sets A and B have logical conclusions, while set C does not.
C) A and B only
When is World Book and Copyright Day celebrated?
The question asks for the date on which World Book and Copyright Day is celebrated. This is a factual question about an internationally recognized day. Recalling the correct date for this specific event is key.
Correct Option: B) 23 rd April is the correct date for World Book and Copyright Day. This date was chosen because it marks the death of several prominent authors, including William Shakespeare, Miguel de Cervantes, and Inca Garcilaso de la Vega.
When is National Panchayati Raj Day observed in India?
The question asks for the date on which National Panchayati Raj Day is observed in India. This is a factual question related to important days and dates in Indian governance and history.
Correct Option: B) 24 th April is the correct answer because the 73rd Constitutional Amendment Act, which gave constitutional status to Panchayati Raj institutions, came into effect on this date in 1993. This day is celebrated to acknowledge the decentralization of power and the importance of local self-governance.