Based on the given statement, four conclusions are drawn. Find out which conclusion is true based on the statement.
Statement:
P = L ≥ K > J < F < N
The problem requires us to analyze a given inequality statement and determine which of the four conclusions logically follows from it. We need to break down the compound inequality into simpler relationships and then check each option against these established relationships.
B) P > J
If a coil of a conductor with 500 Ω resistance is subjected to a time-varying magnetic field such that the EMF induced is 5 V, then the induced current in the coil is:
This problem involves applying Ohm's Law to calculate the induced current in a coil when the induced electromotive force (EMF) and the resistance are given. Ohm's Law states that the current flowing through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them.
Ohm's Law is given by the formula:
\[ V = I \times R \]To find the induced current, we can rearrange Ohm's Law as:
\[ I = \frac{V}{R} \]Substitute \(V = 5 \, \text{V}\) and \(R = 500 \, \Omega\) into the equation:
\[ I = \frac{5 \, \text{V}}{500 \, \Omega} \]Thus, the induced current in the coil is \(0.01 \, \text{A}\).
Correct Option: B) 0.01 A
The question asks to identify the collaborating organization with Atal Innovation Mission (AIM) and NITI Aayog for launching the Community Innovators Fellowship (CIF) on the International Day of Women and Girls in Science. This requires knowledge of recent initiatives and partnerships by NITI Aayog and AIM.
D) United Nations Development Programme (UNDP) — The Community Innovators Fellowship (CIF) was indeed launched by Atal Innovation Mission (AIM) and NITI Aayog in collaboration with the United Nations Development Programme (UNDP) India. This initiative aims to provide a platform for aspiring community innovators to design and implement solutions for sustainable development.
The sum of roots of the equation 5x² − 11x + 6 = 0 is:
\( \frac{6}{5} \)
\( \frac{11}{5} \)
-\( \frac{11}{5} \)
-\( \frac{6}{5} \)
To find the sum of the roots of a quadratic equation, we can use Vieta's formulas. For a standard quadratic equation of the form \(ax^2 + bx + c = 0\), the sum of the roots is given by the formula \( -b/a \).
Correct Option: B) \( \frac{11}{5} \)
The question asks to identify the highest executive of the country in India. This requires understanding the constitutional roles and powers of various officeholders in the Indian political system.
Correct Option: D) The President is the highest executive of the country in India, as per the Constitution. All executive actions of the Government of India are formally taken in their name, making them the constitutional head of the executive.
To find the value of 'x' in the given chemical reaction, we need to balance the equation. Chemical equations must obey the law of conservation of mass, meaning the number of atoms of each element must be the same on both the reactant and product sides of the equation.
C) 3 — The value of 'x' is 3, which balances the number of hydrogen atoms on both sides of the equation, thus satisfying the law of conservation of mass.
The question asks to identify the specific Act against which Mahatma Gandhi initiated a nationwide Satyagraha in 1919. This requires knowledge of key events in India's freedom struggle and the timeline of various British legislations.
Correct Option: B) The Rowlatt Act, passed in March 1919, authorized the British government to imprison any person suspected of terrorism without trial for up to two years. It was enacted based on the recommendations of the Rowlatt Committee, chaired by Sir Sidney Rowlatt. Mahatma Gandhi called for a nationwide Satyagraha against this draconian Act, leading to widespread protests and eventually the Jallianwala Bagh massacre.
To find the cost of fencing, we first need to determine the perimeter of the rectangular land. We are given the area and the length of one side. From these, we can calculate the other side's length, then the perimeter, and finally the total cost.
The area of a rectangle is given by the formula:
\[ \text{Area} = \text{Length} \times \text{Width} \]Given:
Let the width be \(W\).
\[ 100 \text{ m}^2 = 20 \text{ m} \times W \]\[ W = \frac{100 \text{ m}^2}{20 \text{ m}} \]\[ W = 5 \text{ m} \]The perimeter of a rectangle is given by the formula:
\[ \text{Perimeter} = 2 \times (\text{Length} + \text{Width}) \]Using the calculated width and given length:
\[ \text{Perimeter} = 2 \times (20 \text{ m} + 5 \text{ m}) \]\[ \text{Perimeter} = 2 \times (25 \text{ m}) \]\[ \text{Perimeter} = 50 \text{ m} \]The cost of fencing is Rs 30 per meter. The total length to be fenced is the perimeter.
\[ \text{Total Cost} = \text{Perimeter} \times \text{Rate per meter} \]\[ \text{Total Cost} = 50 \text{ m} \times \text{Rs } 30/\text{m} \]\[ \text{Total Cost} = \text{Rs } 1500 \]D) Rs 1,500 is the correct cost of fencing the rectangular land.
Which new mission has been announced in the Union Budget of India, 2021, for exceptional opportunities in mapping, exploring and utilising the oceanic resources?
Samudra Setu Mission
Deep Ocean Mission
Maritime Exercise Mission
Blue economic Mission
The question asks about a new mission announced in the Union Budget of India, 2021, focused on oceanic resources. This requires knowledge of key government initiatives and budget announcements from that period.
Correct Option: B) Deep Ocean Mission
The Union Budget 2021-22, presented by Finance Minister Nirmala Sitharaman, announced the launch of the Deep Ocean Mission. This mission is designed to explore the deep ocean for living and non-living resources, develop deep-sea technology for sustainable utilization of ocean resources, and promote ocean science and technology. It aims to support India's 'Blue Economy' initiatives.
A batsman scored the following runs in the last 5 innings. Find his score in the 4th innings if the average score is 43.
| 1st | 2nd | 3rd | 4th | 5th |
| 92 | 53 | 35 | x | 27 |
The problem provides the scores of a batsman in 5 innings, with one score unknown, and the average score across these 5 innings. We need to find the unknown score. The concept of average (arithmetic mean) will be used, which is defined as the sum of all values divided by the number of values.
The average is calculated as:
\[ \text{Average} = \frac{\text{Sum of all scores}}{\text{Number of innings}} \]We have the average and the individual scores (including the unknown \(x\)).
\[ 43 = \frac{92 + 53 + 35 + x + 27}{5} \]Add the known scores:
\[ 92 + 53 + 35 + 27 = 207 \]Multiply both sides by 5:
\[ 43 \times 5 = 207 + x \]\[ 215 = 207 + x \]Subtract 207 from both sides:
\[ x = 215 - 207 \]\[ x = 8 \]D) 8 — The calculated value for \(x\) (the score in the 4th innings) is 8, which matches option D.