To determine if a number is divisible by 4, we only need to check the divisibility of the number formed by its last two digits by 4. If the number formed by the last two digits is divisible by 4, then the entire number is divisible by 4.
Let's apply this rule to each option:
B) 8978624 is divisible by 4 because its last two digits, 24, form a number that is divisible by 4 (\(24 \div 4 = 6\)).
The question asks for the term that defines the work done by a motor per unit time. This is a fundamental definition in physics related to the rate at which work is performed or energy is transferred.
A) Power is defined as the rate at which work is done or energy is transferred. Mathematically, it is expressed as:
\[ P = \frac{W}{t} \]where \(P\) is power, \(W\) is work done, and \(t\) is time. Therefore, the work done by the motor per unit time is power.
where \(a\) is acceleration, \(\Delta v\) is the change in velocity, and \(\Delta t\) is the change in time. This is unrelated to work done per unit time.
where \(p\) is momentum, \(m\) is mass, and \(v\) is velocity. This concept is also unrelated to the rate of work done.
The problem asks us to identify symbols that are immediately preceded by a number and immediately followed by a number in the given series. We need to scan the series from left to right and apply this condition to each symbol.
A) Four. There are four symbols (@, ^, &, Ω) that are immediately preceded by a number and immediately followed by a number.
This problem involves analyzing statements and conclusions based on the principles of syllogism, often visualized using Venn diagrams. We need to determine which conclusions logically follow from the given statements, assuming the statements are true.
This means there is an overlap between the set of giraffes and the set of rhinos. We can represent this with two intersecting circles, one for "Giraffes" and one for "Rhinos".
This means the entire set of "Rhinos" is contained within the set of "Tigers". In a Venn diagram, the circle representing "Rhinos" would be completely inside the circle representing "Tigers".
Imagine three circles: Giraffes (G), Rhinos (R), and Tigers (T).
When R is entirely inside T, and G overlaps with R, it implies that G must also overlap with T. The portion of G that is R is also T.
Since some giraffes are rhinos (Statement 1), and all rhinos are tigers (Statement 2), it logically follows that those giraffes that are rhinos must also be tigers. Therefore, there is an overlap between giraffes and tigers. This conclusion is true.
Statement 2 says "All rhinos are tigers," which means the set of rhinos is a subset of tigers. However, it does not imply that all tigers are rhinos. There could be tigers that are not rhinos. For example, if there are 10 rhinos and 20 tigers, and all 10 rhinos are tigers, there are still 10 tigers that are not rhinos. Therefore, this conclusion does not logically follow.
C) Only conclusion (I) follows
This problem involves substituting given symbol transformations into a mathematical expression and then evaluating it using the order of operations (BODMAS/PEMDAS).
+ means -- means ×× means ÷÷ means +BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. We perform operations in this order from left to right.
A) 129 is the correct result after applying the symbol changes and following the order of operations.
To find the area of the rectangle, we first need to determine its length and breadth. We are given the ratio of the sides and the perimeter. We can use these to set up equations and solve for the actual dimensions.
Represent the sides: Let the ratio of the sides (length and breadth) be \(l:b = 8:10\). We can represent the length as \(l = 8x\) and the breadth as \(b = 10x\) for some common multiplier \(x\).
Use the perimeter formula: The perimeter of a rectangle is given by the formula \(P = 2(l+b)\). We are given that the perimeter is 90 cm.
\[ 90 = 2(8x + 10x) \]Solve for \(x\): \[ 90 = 2(18x) \] \[ 90 = 36x \] \[ x = \frac{90}{36} \] To simplify the fraction, divide both numerator and denominator by their greatest common divisor, which is 18: \[ x = \frac{90 \div 18}{36 \div 18} = \frac{5}{2} = 2.5 \]
Calculate the actual dimensions: Now substitute the value of \(x\) back into the expressions for length and breadth: Length \(l = 8x = 8 \times 2.5 = 20 \text{ cm}\) Breadth \(b = 10x = 10 \times 2.5 = 25 \text{ cm}\)
Calculate the area: The area of a rectangle is given by the formula \(A = l \times b\). \[ A = 20 \text{ cm} \times 25 \text{ cm} = 500 \text{ cm}^2 \]
Correct Option: D) 500 cm²
The question asks for the product formed when chlorine gas reacts with dry slaked lime. This is a common chemical reaction used in industrial processes, particularly for the production of a substance with bleaching properties.
Correct Option: D) Bleaching powder
The question states that a sum of money doubles itself in 12 years at a certain rate of compound interest, compounded annually. We need to determine how many years it will take for the same sum to become eight times its original value. We can solve this using the relationship between doubling periods and compound growth.
Identify the given information:
Understand the doubling period:
Since the principal doubles every 12 years at the same compound interest rate, its value becomes:
Here, \(P\) represents the original principal.
Express eight times the principal as a power of 2:
\[ 8=2^3 \]This means that the principal must double three times to become eight times its original value.
Calculate the total time required:
Each doubling takes 12 years.
\[ \text{Total time}=3\times12 \] \[ =36\text{ years} \]Therefore, the sum becomes eight times its original value in 36 years.
Correct Option: A) 36 — Since the principal doubles every 12 years, it becomes four times its original value in 24 years and eight times its original value in 36 years. As \(8=2^3\), three doubling periods are required. Therefore, the total time is \(3\times12=36\) years. Hence, Option A is the correct answer.
B) 12: This is incorrect because the principal only doubles in 12 years, becoming twice its original value rather than eight times.
C) 48: This is incorrect because 48 years represents four doubling periods. The principal would become \(2^4=16\) times its original value, not eight times.
D) 24: This is incorrect because 24 years represents two doubling periods. The principal would become \(2^2=4\) times its original value, not eight times.
The question asks to identify which of the given options is NOT an example of a homogeneous mixture. To answer this, we need to understand the definition of a homogeneous mixture and differentiate it from a heterogeneous mixture.
D) Oil in water — When oil is mixed with water, they form separate layers or droplets because they are immiscible. This lack of uniform distribution makes it a heterogeneous mixture, not a homogeneous one.