This problem involves setting up a system of linear equations based on the given age relationships and their sum. We will assign a variable to Rosy's age, express the other two ages in terms of Rosy's age, and then solve the resulting equation.
Correct Option: B) 16 years
The diameter of a wheel is 63 cm. What is the distance covered by the wheel by making 100 revolutions?
[Use π = \( \frac{22}{7} \)]
To find the total distance covered by the wheel, we first need to calculate the distance covered in one revolution. This is equal to the circumference of the wheel. Once we have the distance for one revolution, we multiply it by the total number of revolutions to get the total distance. Finally, we convert the units to meters as required by the options.
The radius \(r\) is half of the diameter.
\[ r = \frac{D}{2} = \frac{63 \text{ cm}}{2} \]The circumference \(C\) of a circle is given by the formula \(C = \pi D\) or \(C = 2\pi r\). We'll use \(C = \pi D\).
\[ C = \pi D = \frac{22}{7} \times 63 \text{ cm} \]\[ C = 22 \times 9 \text{ cm} \]\[ C = 198 \text{ cm} \]The total distance covered is the circumference multiplied by the number of revolutions.
\[ \text{Total Distance} = C \times N \]\[ \text{Total Distance} = 198 \text{ cm} \times 100 \]\[ \text{Total Distance} = 19800 \text{ cm} \]Since \(1 \text{ meter} = 100 \text{ centimeters}\), we divide the distance in centimeters by 100 to get the distance in meters.
\[ \text{Total Distance (in meters)} = \frac{19800 \text{ cm}}{100 \text{ cm/m}} \]\[ \text{Total Distance (in meters)} = 198 \text{ m} \]B) 198 m is the correct distance covered by the wheel.
If the median and the mode of a set of data are 12 and 15, respectively, then find the value of thrice the mean of the data set.
\( \frac{63}{2} \)
\( \frac{33}{2} \)
\( \frac{35}{2} \)
\( \frac{23}{2} \)
This problem requires the application of the empirical relationship between mean, median, and mode for a moderately skewed distribution. The formula states that Mode \(= 3 \times\) Median \(- 2 \times\) Mean. We are given the median and the mode, and we need to find thrice the mean.
Correct Option: A) \( \frac{63}{2} \)
The calculation shows that thrice the mean is \( \frac{63}{2} \), which matches option A.
The question asks to identify the institution where Dr. Chetan Singh Solanki, the designer of the 'Energy Swaraj Yatra', is a professor. This requires knowledge of prominent personalities and their affiliations, especially in the context of significant national initiatives like the 'Energy Swaraj Yatra'.
C) IIT Bombay — Dr. Chetan Singh Solanki, often referred to as the 'Solar Man of India', is a professor in the Department of Energy Science and Engineering at IIT Bombay. He designed and developed the 'Energy Swaraj Yatra' to promote solar energy adoption and combat climate change.
In this question, the statement is followed by four conclusions. Find out which conclusion is true based on the given statement.
Statement:
K ≥ U = N > Q < R = T ≤ P
This question involves inequalities, a common topic in logical reasoning. We need to analyze the given statement and determine which of the conclusions logically follows from it. We will break down the compound inequality into simpler relationships and then check each option.
C) \(K > Q\)
A) \(T < R\)
B) \(K = N\)
D) \(Q > U\)
How many 7s are there in the following series, each of which is immediately preceded by 5 and immediately followed by 1?
2 7 3 5 7 1 5 7 3 5 7 1 9 7 3 5 7 1 7 3 6 5 7 1 8 1 4 7 3 5
The problem asks us to identify the number of times the digit '7' appears in a given series, such that each '7' is immediately preceded by '5' and immediately followed by '1'. This means we are looking for the sequence "571" within the given series of numbers.
B) Four. There are four instances of the sequence "571" in the given series, meaning there are four 7s that are immediately preceded by 5 and immediately followed by 1.
The question asks to identify which statement is NOT an objective of the "Beti Bachao Beti Padhao" (BBBP) programme. To answer this, we need to recall the core objectives of the BBBP scheme launched by the Government of India.
Correct Option: C) Ensuring safety of women during childbirth through institutional delivery (B.O.T.) is NOT an objective of the “Beti Bachao Beti Padhao” programme. This objective falls under maternal health initiatives rather than the specific mandate of BBBP.
The question asks about the primary tissues responsible for human body movement. Movement is a complex process that requires both the generation of force and the coordination of that force. We need to identify the tissues that fulfill these roles.
C) Combination of nervous and muscular tissues — Muscular tissues are responsible for contracting and generating the physical force needed for movement. Nervous tissues transmit electrical signals (nerve impulses) from the brain and spinal cord to the muscles, instructing them to contract or relax, thereby coordinating and controlling all voluntary and involuntary movements. This combination is essential for any form of body movement.
The question asks to identify the Islamic finance term that refers to the obligation of donating a certain proportion of wealth annually for charitable causes. We need to examine each option and determine which one matches this description.
Correct Option: C) Zakat — Zakat is an obligatory annual payment made to the poor and needy by Muslims who meet the necessary criteria of wealth. It is a fundamental principle of Islamic finance and a pillar of Islam, specifically designed for wealth redistribution and charitable causes.
If ‘+’ means ‘÷’, ‘−’ means ‘×’, ‘×’ means ‘+’, and ‘÷’ means ‘−’, what will come in place of the question mark (?) in the following equation?
45 + 9 − 4 × 15 ÷ 2 =?
This problem involves decoding mathematical operations based on a given set of rules and then evaluating the expression using the BODMAS/PEMDAS rule. First, substitute the given symbols with their new meanings. Then, perform the operations in the correct order: Division, Multiplication, Addition, and Subtraction.
Understand the given symbol changes:
Rewrite the given equation with the new symbols:
The original equation is: \(45 + 9 - 4 \times 15 \div 2 = ?\)
Applying the symbol changes:
Evaluate the expression using the BODMAS/PEMDAS rule:
The order of operations is Division, Multiplication, Addition, and Subtraction.
Step 1: Division
\[ 45 \div 9 = 5 \]The expression becomes:
\[ 5 \times 4 + 15 - 2 \]Step 2: Multiplication
\[ 5 \times 4 = 20 \]The expression becomes:
\[ 20 + 15 - 2 \]Step 3: Addition
\[ 20 + 15 = 35 \]The expression becomes:
\[ 35 - 2 \]Step 4: Subtraction
\[ 35 - 2 = 33 \]Final Result:
The value of the expression is \(33\).
D) 33 is the correct answer. After substituting the symbols and applying the BODMAS rule, the expression evaluates to 33.