The problem presents a series of number pairs and asks us to find the missing number in the last pair based on the relationship observed in the previous pairs. We need to identify the mathematical operation or pattern connecting the first number to the second number in each given pair.
Analyze the first pair: 8 : 32
We need to find a relationship between 8 and 32. Let's consider common operations:
Let's observe the multiplier 4. Is it related to the first number 8? Yes, \(4 = 8 / 2\).
So, the relationship could be: First number \(\times\) (First number / 2).
\[ 8 \times \left( \frac{8}{2} \right) = 8 \times 4 = 32 \]Analyze the second pair: 18 : 162
Let's test the identified relationship with this pair:
\[ 18 \times \left( \frac{18}{2} \right) = 18 \times 9 = 162 \]This relationship holds true for the second pair as well.
Apply the relationship to the third pair: 16 : ?
Using the established pattern, we apply it to the number 16:
\[ 16 \times \left( \frac{16}{2} \right) = 16 \times 8 = 128 \]Therefore, the missing number is 128.
C) 128 is the correct answer because the pattern established is that the second number is obtained by multiplying the first number by half of the first number.
To solve this problem, we need to track Amit's movements step-by-step on a 2D plane. We can imagine a coordinate system where North is positive Y, South is negative Y, East is positive X, and West is negative X. We will calculate his final position relative to his starting point Y, and then determine the direction and distance from his final point Z back to Y.
Therefore, he should drive 3 km towards the east to reach Point Y from Point Z.
Correct Option: C) 3 km towards the east
The question asks to identify the Indian state where the cultural festival 'LOSAR' is celebrated. This requires knowledge of major cultural festivals and their associated regions in India.
A) Arunachal Pradesh — Losar is the Tibetan New Year festival, celebrated by Buddhist communities in various regions, including Arunachal Pradesh. In Arunachal Pradesh, it is particularly celebrated by the Monpa, Sherdukpen, and Khamba tribes, who follow Tibetan Buddhism. It is a significant cultural event marked by prayers, traditional dances, and feasts.
The question asks about the standard convention for writing chemical equations. In chemistry, reactants and products are placed in specific positions relative to an arrow that indicates the direction of the reaction.
Therefore, reactants are always written on the left-hand side of the arrow.
B) on the left-hand side of — This is the correct convention for writing chemical equations. Reactants are the starting materials and are always placed to the left of the reaction arrow.
This is a problem of inequalities. We need to combine the given statements and then check which of the conclusions logically follow from the combined statements. The key is to establish relationships between the variables mentioned in the conclusions.
Given the constraints, we must assume that conclusion IV, which is not provided in the question text, is the only one that logically follows from the given statements.
B) Only conclusion IV follows
Without the actual text of conclusion IV, we cannot demonstrate its derivation. However, if we accept the given correct answer, it implies that conclusion IV (which is missing from the question) is the only valid conclusion among the options I, II, III, and IV that were originally part of the question.
The question asks for the definition of electromagnetic induction. We need to recall Faraday's Law of Electromagnetic Induction to identify the correct phenomenon.
B) a moving magnet induces an EMF in the closed loop of a conductor
This option correctly describes the core principle of electromagnetic induction, where the relative motion between a magnet and a conductor changes the magnetic flux through the conductor, leading to the induction of an electromotive force (EMF).
To solve this problem, we first need to calculate the boy's speed. The speed is given by the distance covered divided by the time taken. Once we have the speed, we can use it to find the distance covered in one hour, ensuring all units are consistent (e.g., meters per second converted to kilometers per hour, or vice versa).
Convert time to a single unit (seconds):
The boy covers 450 m in 2 minutes 30 seconds.
\[ \text{Time} = 2 \text{ minutes} + 30 \text{ seconds} \] \[ \text{Time} = (2 \times 60) \text{ seconds} + 30 \text{ seconds} \] \[ \text{Time} = 120 \text{ seconds} + 30 \text{ seconds} \] \[ \text{Time} = 150 \text{ seconds} \]Calculate the speed:
The distance covered is 450 m.
Speed is calculated as distance divided by time:
\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \] \[ \text{Speed} = \frac{450 \text{ m}}{150 \text{ s}} \] \[ \text{Speed} = 3 \text{ m/s} \]Convert speed from m/s to km/hr:
To convert meters per second to kilometers per hour, multiply by \(\frac{18}{5}\):
\[ \text{Speed in km/hr} = 3 \times \frac{18}{5} \] \[ \text{Speed in km/hr} = \frac{54}{5} \] \[ \text{Speed in km/hr} = 10.8 \text{ km/hr} \]Calculate the distance covered in one hour:
Since the speed is 10.8 km/hr, this means the boy covers 10.8 kilometers in one hour.
Distance = Speed \(\times\) Time
Distance = \(10.8 \text{ km/hr} \times 1 \text{ hour}\)
Distance = \(10.8 \text{ km}\)
C) 10.8
The boy will cover 10.8 km in an hour if he travels at the same speed.
The problem requires us to transform the letters of the word "THUNDER" based on specific rules: vowels are changed to the next letter in the alphabet, and consonants are changed to the preceding letter. After transformation, we need to identify the middle letter of the new sequence.
A) M is the correct option because, after applying the given transformation rules, the word THUNDER becomes S G V M C F Q, and the middle letter of this new sequence is M.
The question asks about the origin country of the S-400 Missile System purchased by India. This is a factual question related to international defense deals and current affairs.
Correct Option: D) India purchased the S-400 Missile System from Russia. This deal was a significant defense acquisition for India, enhancing its air defense capabilities.
Factorise 49a2 + 70ab + 25b2
To factorize the given expression, we need to recognize if it fits the form of a perfect square trinomial. A perfect square trinomial is an algebraic expression that results from squaring a binomial. The two common forms are \((a+b)^2 = a^2 + 2ab + b^2\) and \((a-b)^2 = a^2 - 2ab + b^2\).
B) (7a+5b)2 is the correct factorization because it perfectly matches the form \((A+B)^2 = A^2 + 2AB + B^2\) with \(A=7a\) and \(B=5b\).