The problem asks us to identify a set of numbers that follows the same relationship as the given sets. We need to find a mathematical operation or pattern that connects the two numbers in each of the example sets \((10, 144)\) and \((17, 361)\).
We need to find a relationship between 10 and 144. Let's consider common mathematical operations.
Let's test the hypothesis from step 1 with the second set.
This confirms the pattern: the second number in the set is the square of (the first number plus 2).
The general rule is: If the set is \((x, y)\), then \(y = (x+2)^2\).
D) \((21, 529)\)
This matches the given set \((21, 529)\).
The question asks to identify the true statements regarding respiration in terrestrial animals, specifically focusing on gas exchange by diffusion. We need to evaluate each statement based on biological principles of respiration.
A) a, b and c — Statements a, b, and c are all true descriptions of respiration and gas exchange in terrestrial animals.
The question asks about the target age group for the Kanya Shiksha Pravesh Utsav campaign. This requires knowledge of specific government initiatives related to girls' education.
Correct Option: B) 11 to 14 years
The Kanya Shiksha Pravesh Utsav campaign specifically targets adolescent girls aged 11 to 14 years who are out of school. The aim is to ensure their re-entry and continued education, thereby promoting gender equality in education.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. We need to find the conclusion(s) that logically follow from the statements.
Statement 1: All pens are sketch-pens.
This means the set of 'pens' is entirely contained within the set of 'sketch-pens'.
Diagrammatically: A smaller circle (Pens) inside a larger circle (Sketch-pens).
Statement 2: Some sketch-pens are markers.
This means there is an overlap between the set of 'sketch-pens' and the set of 'markers'.
Diagrammatically: The 'Markers' circle partially overlaps with the 'Sketch-pens' circle. This overlap can be such that it includes 'pens' or not, or partially includes 'pens'.
Statement 3: No marker is a drawing.
This means the set of 'markers' and the set of 'drawings' are completely separate; there is no overlap between them.
Diagrammatically: The 'Markers' circle and the 'Drawings' circle are disjoint.
Evaluate Conclusion I: Some drawings are markers.
From Statement 3, "No marker is a drawing," which directly implies that "No drawing is a marker." Therefore, "Some drawings are markers" is false.
Evaluate Conclusion II: No pen is a drawing.
We know that 'Pens' are inside 'Sketch-pens'. Some 'Sketch-pens' are 'Markers'. 'Markers' and 'Drawings' are separate. However, the relationship between 'Pens' and 'Drawings' is not directly established. It is possible that 'Pens' are not 'Drawings', but it's also possible that some 'Pens' (which are also 'Sketch-pens' but not 'Markers') could be 'Drawings' if the 'Drawings' circle overlaps with the 'Sketch-pens' circle in the area that does not include 'Markers'. Since we cannot definitively say "No pen is a drawing" in all possible Venn diagram configurations, this conclusion does not logically follow.
For example, a scenario where some pens are drawings: Imagine the 'Drawings' circle overlapping with the 'Pens' circle (which is inside 'Sketch-pens'), but not overlapping with the 'Markers' circle. This is consistent with all statements.
Evaluate Conclusion III: Some sketch-pens are pens.
From Statement 1, "All pens are sketch-pens." If all pens are sketch-pens, it logically follows that there must be at least some sketch-pens that are pens (specifically, all the pens are sketch-pens). This is a direct implication.
Correct Option: D) Only conclusion III follows
Conclusion III is a direct and undeniable consequence of Statement 1. If all members of set A are members of set B, then it must be true that some members of set B are members of set A.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then check which conclusions logically follow from these diagrams.
\[ \text{TVs} \subset \text{Radios} \]
\[ \text{Mobiles} \subset \text{Pen Drives} \]
A) Only conclusion I follows. As explained above, conclusion I logically follows from the statements, while conclusion II does not necessarily follow.
The question asks to identify a suitable mirror for focusing sunlight to a point. This requires understanding the properties of different types of mirrors, specifically how they reflect parallel rays of light.
Correct Option: B) A concave mirror
Which of the following fundamental duties is added by the 86th Amendment of the Constitution in 2002?
To cherish and follow the noble ideals which inspired our national struggle for freedom
To safeguard public property and to abjure violence
Who is a parent or guardian, to provide opportunities for education to his child, or as the case may be, ward between the age of six and fourteen years
To defend the country and render national service when called upon to do so
The question asks to identify the fundamental duty added by the 86th Constitutional Amendment Act of 2002. This requires knowledge of the fundamental duties and the specific amendments that introduced or modified them.
Correct Option: C) Who is a parent or guardian, to provide opportunities for education to his child, or as the case may be, ward between the age of six and fourteen years.
This duty was added as Article 51A(k) by the 86th Constitutional Amendment Act of 2002. It mandates that parents or guardians provide educational opportunities to their children/wards between the ages of six and fourteen years. This aligns with the amendment's focus on elementary education.
This problem involves ratios. We are given the ratio of aluminium to nickel in an alloy and the quantity of aluminium. We need to find the corresponding quantity of nickel to maintain the given ratio.
Identify the given ratio of aluminium to nickel:
\[ \text{Aluminium} : \text{Nickel} = 3 : 4 \] This means that for every 3 parts of aluminium, there are 4 parts of nickel.
Identify the given quantity of aluminium:
\[ \text{Quantity of Aluminium} = 36 \text{ kg} \]
Set up a proportion to find the quantity of nickel. Let the quantity of nickel be \(x\) kg.
\[ \frac{\text{Aluminium}}{\text{Nickel}} = \frac{3}{4} \] Substitute the known value for aluminium:
\[ \frac{36}{x} = \frac{3}{4} \]
Solve the proportion for \(x\). Cross-multiply the terms:
\[ 3 \times x = 36 \times 4 \]
\[ 3x = 144 \]
Divide both sides by 3 to find \(x\):
\[ x = \frac{144}{3} \]
\[ x = 48 \]
Therefore, the quantity of nickel required is 48 kg.
Correct Option: C) 48
Farah got married 8 years ago. Today her age is \( \frac{9}{7} \) times her age at the time of her marriage. At present her daughter’s age is \( \frac{1}{6} \) of her age. Her daughter’s age 3 years ago was:
This problem involves setting up equations based on the given age relationships and then solving for the unknown ages. We will first find Farah's current age, then her daughter's current age, and finally the daughter's age 3 years ago.
Define variables:
Formulate equations based on the given information:
Solve for Farah's current age (\(F_C\)):
Substitute Equation 1 into Equation 2:
\[ F_0 + 8 = \frac{9}{7} F_0 \]Multiply by 7 to eliminate the fraction:
\[ 7(F_0 + 8) = 9 F_0 \] \[ 7 F_0 + 56 = 9 F_0 \] \[ 56 = 9 F_0 - 7 F_0 \] \[ 56 = 2 F_0 \] \[ F_0 = \frac{56}{2} \] \[ F_0 = 28 \text{ years} \]Now, find Farah's current age using Equation 1:
\[ F_C = F_0 + 8 \] \[ F_C = 28 + 8 \] \[ F_C = 36 \text{ years} \]Solve for her daughter's current age (\(D_C\)):
Using Equation 3:
\[ D_C = \frac{1}{6} F_C \] \[ D_C = \frac{1}{6} \times 36 \] \[ D_C = 6 \text{ years} \]Calculate her daughter's age 3 years ago:
Daughter's age 3 years ago \( = D_C - 3 \)
\[ = 6 - 3 \] \[ = 3 \text{ years} \]D) 3 years. This is the calculated age of Farah's daughter 3 years ago.
The question asks about the primary system affected by AIDS. AIDS (Acquired Immunodeficiency Syndrome) is caused by the Human Immunodeficiency Virus (HIV). Understanding the mechanism of HIV infection and its progression is key to identifying the most affected system.
Therefore, the immune system is the primary and most directly affected system by AIDS.
Correct Option: A) Immune system