To find the ratio of two quantities, we express them as a fraction and then simplify the fraction to its lowest terms. It is important that both quantities are in the same units before forming the ratio.
Identify the two quantities given:
Since both quantities are already in the same unit (minutes), we can directly form the ratio.
Write the ratio as a fraction:
\[ \text{Ratio} = \frac{30 \text{ min}}{40 \text{ min}} \]Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor. In this case, both 30 and 40 are divisible by 10.
\[ \text{Ratio} = \frac{30 \div 10}{40 \div 10} = \frac{3}{4} \]Express the simplified fraction as a ratio using a colon:
\[ \text{Ratio} = 3 : 4 \]Correct Option: A) 3 : 4 is the correct ratio obtained by simplifying the given quantities.
Which of the option figures bears the closest resemblance to the question figure?
Question Figure:
Option Figures:
To solve this problem, we need to determine which option figure most closely resembles the question figure. This involves analyzing the shapes, orientations, and positions of elements within the figures.
Correct Option: D) The arrangement and orientation of elements in this option match the question figure.
When considering the given arguments, which of the following is the correct conclusion?
During examination time, many students spend more time watching television. Hence, it is recommended that schools should be closed during examination days.
Arguments:
I. Yes, because students will then concentrate more on their exams.
II. No, because students will misuse the time at home in different ways.
Only II follows
Only I follows
Both I and II follow
Neither I nor II follows
The problem presents a statement and two arguments related to it. We need to evaluate each argument independently to determine if it logically follows from the given statement or provides a valid counter-point.
Correct Option: C) Both I and II follow
The weight of an object is the force exerted on it due to gravity. It is calculated by multiplying the object's mass by the acceleration due to gravity.
Weight (\(W\)) is given by the formula:
\[ W = m \times g \]The unit of weight is Newtons (N), which is equivalent to kg·m/s\(-^2\).
D) 196 N is the correct answer. The weight of the object is 196 Newtons.
Which of the following channels won the award for the ‘Best News Channel – Hindi’ at the 17th Indian Television Academy Awards?
The question asks to identify the news channel that received the 'Best News Channel – Hindi' award at the 17th Indian Television Academy Awards. This is a factual recall question related to awards and honors in the media industry.
At the 17th Indian Television Academy Awards, held in 2017, the award for 'Best News Channel – Hindi' was conferred upon Aaj Tak.
D) Aaj Tak — Aaj Tak won the award for 'Best News Channel – Hindi' at the 17th Indian Television Academy Awards.
To determine the face value of 'x' in the number x4584, given that the number is divisible by 11, we will use the divisibility rule for 11. This rule states that a number is divisible by 11 if the alternating sum of its digits is a multiple of 11 (including 0).
For the number x4584:
Sum of odd place digits \( = 4 + 5 + x = 9 + x \)
Sum of even place digits \( = 8 + 4 = 12 \)
According to the rule, the difference between these sums must be 0 or a multiple of 11.
\[ (9 + x) - 12 = 0 \text{ or a multiple of } 11 \]\[ x - 3 = 0 \text{ or a multiple of } 11 \]Since 'x' is a single digit (0-9) representing a face value, the only possible value for \(x - 3\) to be 0 or a multiple of 11 is 0.
\[ x - 3 = 0 \]\[ x = 3 \]If \(x = 3\), the number is 34584. Let's check the divisibility by 11:
Sum of odd place digits \( = 4 + 5 + 3 = 12 \)
Sum of even place digits \( = 8 + 4 = 12 \)
Difference \( = 12 - 12 = 0 \)
Since the difference is 0, the number 34584 is divisible by 11.
C) 3 — As calculated, the face value of x must be 3 for the number to be divisible by 11.
Which of the options bears the closest resemblance to the following figure?
To solve this question, we need to carefully examine the given figure and compare it with each of the options provided. The task is to identify which option most closely resembles the given figure.
After comparing all options, Option B is found to be the closest match to the given figure.
Correct Option: B) Option B matches the given figure in terms of arrow direction and line orientation.
A line segment of length 2.05 m was measured as 2 m by mistake. Find the error percent.
\( \frac{100}{51} \)%
4.1 %
42 %
\( \frac{100}{41} \)%
To find the error percent, we first need to calculate the absolute error, which is the difference between the actual value and the measured value. Then, we divide this absolute error by the actual value and multiply by 100 to express it as a percentage.
Absolute Error \( = | \text{Actual Value} - \text{Measured Value} | \)
\[ \text{Absolute Error} = |2.05 \, \text{m} - 2 \, \text{m}| = 0.05 \, \text{m} \]The formula for error percent is:
\[ \text{Error Percent} = \left( \frac{\text{Absolute Error}}{\text{Actual Value}} \right) \times 100\% \]Substitute the values:
\[ \text{Error Percent} = \left( \frac{0.05}{2.05} \right) \times 100\% \]To simplify the fraction, multiply the numerator and denominator by 100 to remove decimals:
\[ \text{Error Percent} = \left( \frac{0.05 \times 100}{2.05 \times 100} \right) \times 100\% \] \[ \text{Error Percent} = \left( \frac{5}{205} \right) \times 100\% \]Divide both the numerator and the denominator by 5:
\[ \text{Error Percent} = \left( \frac{5 \div 5}{205 \div 5} \right) \times 100\% \] \[ \text{Error Percent} = \left( \frac{1}{41} \right) \times 100\% \] \[ \text{Error Percent} = \frac{100}{41}\% \]The question asks about the Sports Minister of India as of 2018. This requires knowledge of the Union Cabinet appointments during that specific period. We need to identify the individual who held the portfolio of Minister of State (Independent Charge) for Youth Affairs and Sports in 2018.
Correct Option: A) Rajyavardhan Singh Rathore was the Minister of State (Independent Charge) for Youth Affairs and Sports from September 2017 to May 2019. Thus, he held this portfolio in 2018.
The problem asks us to find the code for the word LIGHT based on a given coding pattern for the word EARN. We need to identify the rule used to convert letters into numbers and then apply that rule to the target word.
The word EARN is coded as 4073.
Let's see how these positions relate to the code 4073.
Observe the pattern for each letter:
It appears the rule is: (Alphabetical position of the letter - 1), and if the result is a two-digit number, only the unit digit is taken.
Let's verify this rule:
The rule is consistent.
The code for LIGHT is 18679.
Correct Option: C) 18679