This question is based on the principle of electromagnetic induction, specifically Faraday's Law of Electromagnetic Induction. According to this law, a potential difference (or electromotive force, EMF) is induced in a closed conducting coil whenever there is a change in the magnetic flux linked with the coil. Magnetic flux is the product of the magnetic field strength and the area perpendicular to the field lines. A change in magnetic flux can be achieved by changing the magnetic field strength, the area of the coil, or the relative orientation between the coil and the magnetic field, or by changing the relative motion between the magnet and the coil.
A) either the bar magnet is moved towards the closed coil or the closed coil is moved towards the bar magnet
This statement correctly identifies the condition for inducing a potential difference. In both scenarios, there is relative motion between the magnet and the coil, leading to a change in the magnetic flux linked with the coil. This change in magnetic flux induces an EMF (potential difference) as per Faraday's Law of Electromagnetic Induction.
The problem requires us to find which pair of mathematical signs, when interchanged in the given equation, makes the equation true. We will test each option by interchanging the specified signs and then evaluating the expression using the order of operations (BODMAS/PEMDAS).
The given equation is: \(25 \div 5 - 2 \times 30 + 3 = 10\)
Let's evaluate the original expression first to see if it's already correct:
\(25 \div 5 - 2 \times 30 + 3\)
\(= 5 - 60 + 3\)
\(= -55 + 3\)
\(= -52\)
Since \(-52 \neq 10\), the original equation is incorrect.
Now, let's test each option:
Option A: Interchanging \(\div\) and \(+\)
The equation becomes: \(25 + 5 - 2 \times 30 \div 3 = 10\)
Evaluate the left side:
\(25 + 5 - 2 \times 30 \div 3\)
\(= 25 + 5 - 2 \times 10\)
\(= 25 + 5 - 20\)
\(= 30 - 20\)
\(= 10\)
Since \(10 = 10\), this option makes the equation correct.
A) Interchanging \(\div\) and \(+\) makes the equation \(25 + 5 - 2 \times 30 \div 3 = 10\), which simplifies to \(10 = 10\). Thus, this is the correct pair of signs to be interchanged.
B) Interchanging \(\times\) and \(+\)
The equation becomes: \(25 \div 5 - 2 + 30 \times 3 = 10\)
Evaluate the left side:
\(25 \div 5 - 2 + 30 \times 3\)
\(= 5 - 2 + 90\)
\(= 3 + 90\)
\(= 93\)
Since \(93 \neq 10\), this option is incorrect.
C) Interchanging \(\times\) and \(-\)
The equation becomes: \(25 \div 5 \times 2 - 30 + 3 = 10\)
Evaluate the left side:
\(25 \div 5 \times 2 - 30 + 3\)
\(= 5 \times 2 - 30 + 3\)
\(= 10 - 30 + 3\)
\(= -20 + 3\)
\(= -17\)
Since \(-17 \neq 10\), this option is incorrect.
D) Interchanging \(\div\) and \(-\)
The equation becomes: \(25 - 5 \div 2 \times 30 + 3 = 10\)
Evaluate the left side:
\(25 - 5 \div 2 \times 30 + 3\)
\(= 25 - 2.5 \times 30 + 3\)
\(= 25 - 75 + 3\)
\(= -50 + 3\)
\(= -47\)
Since \(-47 \neq 10\), this option is incorrect.
The question asks to identify the type of reaction that occurs when natural gas burns. This involves understanding the definitions of different types of chemical reactions, particularly those related to energy changes (exothermic and endothermic) and structural changes (substitution and decomposition).
Correct Option: B) an exothermic reaction — Burning of natural gas is a combustion reaction that releases a large amount of heat and light energy into the surroundings. Reactions that release energy are called exothermic reactions.
This problem can be solved using the concept of work rate. We will calculate the filling rate of the pipe and the combined filling rate (pipe minus leakage). From these, we can determine the emptying rate of the leakage alone and then the time it takes for the leakage to empty the full tank.
The pipe fills the tank in 15 hours. So, in one hour, the pipe fills \(\frac{1}{15}\) of the tank.
\[ \text{Pipe's filling rate} = \frac{1}{15} \text{ tank/hour} \]Due to leakage, the tank is filled in 20 hours. So, in one hour, the net filling (pipe - leakage) is \(\frac{1}{20}\) of the tank.
\[ \text{Net filling rate} = \frac{1}{20} \text{ tank/hour} \]Let the emptying rate of the leakage be \(L\) (tank/hour). The net filling rate is the pipe's filling rate minus the leakage rate.
\[ \text{Pipe's filling rate} - \text{Leakage rate} = \text{Net filling rate} \] \[ \frac{1}{15} - L = \frac{1}{20} \]Now, solve for \(L\):
\[ L = \frac{1}{15} - \frac{1}{20} \]Find a common denominator, which is 60:
\[ L = \frac{4}{60} - \frac{3}{60} \] \[ L = \frac{1}{60} \text{ tank/hour} \]This means the leakage empties \(\frac{1}{60}\) of the tank in one hour.
If the leakage empties \(\frac{1}{60}\) of the tank in one hour, it will take 60 hours to empty the entire tank.
\[ \text{Time} = \frac{1}{\text{Leakage rate}} = \frac{1}{\frac{1}{60}} = 60 \text{ hours} \]Correct Option: D) 60 hours
The question asks about the chemical reaction that forms bleaching powder. We need to identify the reactant that combines with dry slaked lime to produce bleaching powder.
Correct Option: B) chlorine
This is a logical reasoning problem involving arrangement on different floors. We need to deduce the exact floor on which each person lives based on the given clues and then answer the question about the number of people living above P.
Floor 6:
Floor 5:
Floor 4:
Floor 3: G
Floor 2:
Floor 1:
Floor 6:
Floor 5: M
Floor 4:
Floor 3: G
Floor 2:
Floor 1:
Floor 6:
Floor 5:
Floor 4:
Floor 3: G
Floor 2:
Floor 1: M
Floor 6:
Floor 5: M
Floor 4:
Floor 3: G
Floor 2: K
Floor 1:
Floor 6: K
Floor 5:
Floor 4:
Floor 3: G
Floor 2:
Floor 1: M
Floor 6: K
Floor 5: S
Floor 4: P
Floor 3: G
Floor 2:
Floor 1: M
Floor 6: K
Floor 5: S
Floor 4: P
Floor 3: G
Floor 2: V
Floor 1: M
Correct Option: A) Two
The problem presents a number series, and we need to find the next number in the sequence. We will analyze the pattern of operations (addition, subtraction, multiplication, division, or a combination) between consecutive numbers to determine the rule governing the series.
Let's list the operations:
The pattern of operations is alternating multiplication and addition. The numbers involved in these operations are consecutive integers: 1, 2, 3, 4.
Following the established pattern, the next operation should be multiplication by 5.
So, the next number will be \(28 \times 5\).
\[ 28 \times 5 = 140 \]Thus, the number that replaces the question mark is 140.
A) 140 is the correct answer, derived by following the alternating multiplication and addition pattern with consecutive integers.
The problem states that when birthday caps are packed in groups of 8 or 10, one cap is always left out. This means that the total number of caps, when divided by 8 or 10, leaves a remainder of 1. We need to find a number within the range of 250 to 300 that satisfies this condition.
Understand the remainder condition: The problem states that when caps are packed in groups of 8 or 10, one cap is always left out. This implies that if the total number of caps is \(N\), then \(N \equiv 1 \pmod{8}\) and \(N \equiv 1 \pmod{10}\).
Find the Least Common Multiple (LCM): If \(N-1\) is perfectly divisible by both 8 and 10, then \(N-1\) must be a multiple of the LCM of 8 and 10.
LCM \((8, 10) = 2^3 \times 5 = 8 \times 5 = 40\).
Formulate the general expression for N: Since \(N-1\) is a multiple of 40, we can write \(N-1 = 40k\) for some integer \(k\). Therefore, \(N = 40k + 1\).
Apply the given range: We are given that the number of caps is more than 250 but less than 300. So, \(250 < N < 300\).
Substitute and solve for k: Substitute the expression for \(N\) into the inequality:
\[ 250 < 40k + 1 < 300 \]Subtract 1 from all parts of the inequality:
\[ 250 - 1 < 40k < 300 - 1 \] \[ 249 < 40k < 299 \]Divide by 40:
\[ \frac{249}{40} < k < \frac{299}{40} \] \[ 6.225 < k < 7.475 \]Since \(k\) must be an integer, the only possible value for \(k\) is 7.
Calculate N: Substitute \(k=7\) back into the equation \(N = 40k + 1\):
\[ N = 40(7) + 1 \] \[ N = 280 + 1 \] \[ N = 281 \]This number (281) is between 250 and 300.
Correct Option: C) 281
To solve this problem, we need to track Manjul's movements in a coordinate system or by visualizing the directions. We will break down each step of his walk, noting the direction and distance, and then calculate his final position relative to his starting point (house).
Manjul's final position is \((0, -10)\) relative to his house at \((0,0)\). This means he is 10 m in the south direction from his house.
Correct Option: D) 10 m, south
The question asks for the location where Rameshbabu Praggnanandhaa defeated Magnus Carlsen in the FTX Crypto Cup in August 2022. This is a factual recall question related to current affairs in sports.
Correct Option: A) The FTX Crypto Cup, where Rameshbabu Praggnanandhaa defeated Magnus Carlsen in August 2022, was held in Miami, USA. This was a significant achievement for the young Indian chess master.