The twinkling of stars is a common atmospheric phenomenon. We need to identify the specific optical phenomenon responsible for this effect.
Correct Option: D) Refraction of light by the atmosphere. The twinkling of stars is primarily caused by the atmospheric refraction of starlight. The constantly changing refractive index of the Earth's atmosphere bends the light rays from the star by varying amounts, leading to fluctuations in the apparent position and brightness of the star, which we perceive as twinkling.
The question asks to identify the instrument used for determining the density of milk. This requires knowledge of common scientific instruments and their specific applications.
B) Lactometer is specifically designed to measure the density or specific gravity of milk. It is a specialized hydrometer calibrated for milk, indicating its purity or the extent of adulteration with water.
The problem involves percentages and algebraic manipulation. We are given a relationship between \(x\) and \(y\), and we need to express a certain percentage of 25 in terms of \(x\). The strategy is to first convert the percentage relationship into an algebraic equation, then substitute to find the required expression.
Correct Option: B) 50% of x
To solve this problem, we need to calculate two separate values: "0.6 of 35" and "half of 75". Then, we will add these two results together to find the final answer.
Calculate 0.6 of 35:
"Of" in mathematics usually means multiplication. So, we need to multiply 0.6 by 35.
\[ 0.6 \times 35 \]To make the multiplication easier, we can write 0.6 as \(\frac{6}{10}\) or \(\frac{3}{5}\).
\[ \frac{3}{5} \times 35 \]Now, perform the multiplication:
\[ 3 \times \frac{35}{5} = 3 \times 7 = 21 \]So, 0.6 of 35 is 21.
Calculate half of 75:
"Half of" means dividing by 2.
\[ \frac{75}{2} \]Performing the division:
\[ 75 \div 2 = 37.5 \]So, half of 75 is 37.5.
Add the two results:
Now, add the value from step 1 and the value from step 2.
\[ 21 + 37.5 \] \[ 21 + 37.5 = 58.5 \]Therefore, 0.6 of 35 + half of 75 is 58.5.
Correct Option: A) 58.5
The question asks to identify the instrument used to measure the distance traveled in an automobile. We need to evaluate each option based on its function.
B) Odometer — An odometer is an instrument used for measuring the distance traveled by a vehicle, such as a car or bicycle. It is typically found on the dashboard of an automobile.
To determine which quantities share the same SI unit, we need to recall the definitions and standard SI units for each term mentioned in the options: velocity, displacement, speed, and distance.
B) Speed and Velocity — Both speed and velocity are measures of rate of motion. Speed is the scalar magnitude of the rate of change of distance, while velocity is the vector magnitude of the rate of change of displacement. Despite one being scalar and the other vector, their SI units are identical: meters per second (\(\text{m/s}\)).
This problem involves substituting given mathematical operators with new ones and then evaluating the expression using the BODMAS/PEMDAS rule (Brackets, Orders/Exponents, Division, Multiplication, Addition, Subtraction).
+ means ×- means ÷× means -÷ means +The original expression is \(18 + 32 - 4 \times 8 \div 3\).
Applying the substitutions:
\[ 18 \times 32 \div 4 - 8 + 3 \]First, perform Division and Multiplication from left to right.
Division: \(32 \div 4 = 8\)
The expression becomes:
\[ 18 \times 8 - 8 + 3 \]Multiplication: \(18 \times 8 = 144\)
The expression becomes:
\[ 144 - 8 + 3 \]Next, perform Addition and Subtraction from left to right.
Subtraction: \(144 - 8 = 136\)
The expression becomes:
\[ 136 + 3 \]Addition: \(136 + 3 = 139\)
C) 139 is the correct value of the expression after applying the given operator changes and following the order of operations.
The question asks about the percentage reduction in interest rates on small savings schemes by the central government. This is a factual question related to recent economic policy decisions.
Correct Option: A) 1.10% — This option accurately reflects the approximate percentage by which the central government reduced interest rates on several small savings schemes in April 2020.
The question asks to identify the type of fruit Alphonso is. This is a general knowledge question related to common fruit varieties.
Correct Option: B) Alphonso is a renowned variety of Mango. It is often referred to as the "King of Mangoes" due to its superior taste and texture. It is primarily grown in the Konkan region of Maharashtra, India.
To find the final balance in Ravi's account, we need to perform a series of additions and subtractions. First, calculate the total amount after the deposit. Then, calculate the total cost of the five shirts. Finally, subtract the total cost of the shirts from the updated account balance.
The balance in Ravi's account is Rs. 545.19.
D) 545.19 is the correct balance after all transactions.