The problem involves calculating the average age. We will use the formula for average age, which is the sum of ages divided by the number of individuals. We will calculate the initial total age, then adjust it for the boy who left and the two new boys who joined, keeping the final average age constant to find the sum of ages of the newcomers.
Initial total age:
Given that the average age of 40 boys is 18 years.
\[ \text{Initial total age} = \text{Number of boys} \times \text{Average age} \\ \text{Initial total age} = 40 \times 18 = 720 \text{ years} \]Total age after one boy left:
One boy, aged 26 years, left the class.
Number of boys remaining = \(40 - 1 = 39\)
\[ \text{Total age after one boy left} = 720 - 26 = 694 \text{ years} \]Total age after two new boys joined:
Two new boys joined the class. Let their combined age be \(X\) years.
Number of boys now in the class = \(39 + 2 = 41\)
The problem states that the average age of all boys now in the class remains 18 years.
\[ \text{New total age} = \text{Total age after one boy left} + X \\ \text{New total age} = 694 + X \]Calculate the new total age using the new average:
The new average age is 18 years for 41 boys.
\[ \text{New total age} = \text{New number of boys} \times \text{New average age} \\ \text{New total age} = 41 \times 18 = 738 \text{ years} \]Find the combined age of the two newcomers:
Equating the two expressions for the new total age:
\[ 694 + X = 738 \\ X = 738 - 694 \\ X = 44 \text{ years} \]Calculate the average age of the two newcomers:
The combined age of the two newcomers is 44 years.
\[ \text{Average age of newcomers} = \frac{\text{Combined age of newcomers}}{\text{Number of newcomers}} \\ \text{Average age of newcomers} = \frac{44}{2} = 22 \text{ years} \]Correct Option: C) 22 years
The problem requires us to evaluate a given mathematical expression after interchanging certain arithmetic operators. We need to replace '+' with '−', '−' with '+', '×' with '÷', and '÷' with '×'. After performing these substitutions, we will evaluate the new expression following the order of operations (BODMAS/PEMDAS).
\[ 11 + 37 - 5 \times 40 \div 24 = ? \]
Substituting these into the original expression, we get:
\[ 11 - 37 + 5 \div 40 \times 24 = ? \]
First, perform division:
\[ 5 \div 40 = \frac{5}{40} = \frac{1}{8} \]
The expression becomes:
\[ 11 - 37 + \frac{1}{8} \times 24 \]
Next, perform multiplication:
\[ \frac{1}{8} \times 24 = \frac{24}{8} = 3 \]
The expression becomes:
\[ 11 - 37 + 3 \]
Finally, perform addition and subtraction from left to right:
\[ 11 - 37 = -26 \]
Then,
\[ -26 + 3 = -23 \]
So, the value of the expression is \(-23\).
Correct Option: D) \(-23\)
Two sets of numbers are given below. In each set of numbers, certain mathematical operation(s) on the first number result(s) in the second number. Similarly, certain mathematical operation(s) on the second number result(s) in the third number and so on. Which of the given options follows the same set of operations as in the given sets?
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
6-18-72-102; 8-20-80-110
The problem asks us to identify the mathematical operations that transform the numbers in the given sequences and then apply the same operations to the options to find the one that follows the same pattern. We need to find the rule for transforming the first number to the second, the second to the third, and the third to the fourth in the given sets.
Let's check the operations: \((+12), (\times 4), (+30)\).
Comparing the operations for both sets:
So, the pattern of operations is: Add 12, Multiply by 4, Add 30.
Correct Option: C) 7-19-76-106
All operations match the established pattern.
This question tests general knowledge regarding the publication year of a specific book. To answer this, one needs to be aware of the publication details of the mentioned work by Arunima Hoskote.
D) 2020 is the correct publication year for the specified book by Arunima Hoskote.
To evaluate the given expression, we must follow the order of operations, commonly known as BODMAS/PEMDAS. This acronym stands for Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
The value of the expression is \(0\).
A) 0 — The calculation following the BODMAS rule correctly leads to 0.
The question asks about the primary function of devices like Copper-T in family planning. Understanding the mechanism of action of Intrauterine Devices (IUDs) like Copper-T is key to answering this question.
Correct Option: A) To prevent fertilised eggs from implanting in the uterus
The question asks about the asexual mode of reproduction in yeast. We need to identify the specific method yeast uses from the given options.
A) Budding — Yeast reproduces predominantly through budding. A small bud develops on the parent yeast cell, grows, and then detaches to become a new individual.
The question asks to identify a famous temple complex in Tamil Nadu known for its Dravidian architecture and a 1,000-pillar hall. We need to evaluate each option based on these characteristics.
Correct Option: D) Meenakshi Temple
The Meenakshi Amman Temple in Madurai, Tamil Nadu, is celebrated for its exquisite Dravidian architecture, intricate carvings, and its iconic "Hall of Thousand Pillars" (Ayiram Kaal Mandapam), which contains 985 carved pillars.
Balancing a chemical equation is a fundamental concept in chemistry, ensuring that the Law of Conservation of Mass is upheld. This law states that matter cannot be created or destroyed in a chemical reaction. Therefore, the number of atoms of each element must be the same on both the reactant and product sides of the equation. The process begins by accurately representing the reactants and products.
D) Writing the skeleton equation is the first and most crucial step. Without the correct formulas for reactants and products, one cannot proceed to balance the equation.