The first exercise in the topic of **Linear Equations in One Variable** usually involves solving equations of the form:

\[ ax + b = c \]

where \( a, b, \) and \( c \) are constants, and \( x \) is the variable to be solved.

Here’s a breakdown of how to solve such equations:

### General Steps:

1. **Simplify both sides** (if needed): Remove any parentheses and combine like terms on each side.

2. **Isolate the variable (x)**: Use addition, subtraction, multiplication, or division to move terms to the appropriate side.

3. **Solve for \( x \)**: Simplify the equation to find the value of \( x \).

4. **Verify your solution**: Substitute \( x \) back into the original equation to ensure it satisfies the equation.

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### Examples:

1. Solve:

\[ 2x + 5 = 15 \]

**Solution**:

- Subtract 5 from both sides:

\[ 2x = 10 \]

- Divide by 2:

\[ x = 5 \]

2. Solve:

\[ 3x - 7 = 2 \]

**Solution**:

- Add 7 to both sides:

\[ 3x = 9 \]

- Divide by 3:

\[ x = 3 \]

Correct Answer: Average product

Solution : The correct answer is Average product.

It denotes the average amount of production generated by each additional unit of a variable input, such as labour or capital, while other inputs remain constant. For instance, if a business generates 100 units of output from ten units of variable input, the variable input's average product is ten units per unit of input. This indicates that each variable input unit yields an average of ten units of output.

Correct Answer: negative return

Solution : The correct answer is the negative return.

Negative returns are the third step of the law of changing proportions. This is the point at which adding more variable inputs to the fixed inputs causes the overall product to start declining. The reason for this is the ineffective use of the variable inputs. There are several reasons why there could be negative returns. The different inputs could start to compete with one another for resources, for starters. For instance, workers on a production line may begin to obstruct one another if there are too many of them.

Correct Answer: Uniform velocity, variable acceleration

Solution : The correct option is Uniform velocity, variable acceleration.

A body moving on a circular route is an example of uniform velocity and variable acceleration. The body's speed remains constant (uniform velocity) in a uniform circular motion, but its direction changes continually as it goes around the circle. This shift in direction causes a centripetal acceleration towards the circle's centre. As a result, while the speed stays constant, the body feels varying acceleration, illustrating uniform velocity and varied acceleration.

Correct Answer: Variable cost reserve ratios

Solution : The correct option is Variable cost reserve ratios.

The objective of the variable reserve ratio (Cash Reserve Ratio), which is a quantitative technique, is to manage just the volume of credit, not the volume and purpose of the credit for which the bank makes loans. For these goals, both the qualitative approach and the selective control method are utilised. It has several drawbacks.

Correct Answer: continue to operate as long as it covers even the variable costs

Solution : The correct answer is to continue to operate as long as it covers even the variable costs.

A firm should keep operating, even if it's losing money, as long as it covers the costs that change with production (like materials or labour). This is because there are fixed costs (like rent and salaries) that the firm can't avoid. If it shuts down, it still has to pay these fixed costs but won't make any money. So, it's better to keep going, even if it means a short-term loss.

Cognition is a general term covering all the various modes of knowing-perceiving, intelligence, learning, remembering, etc.

Cognitive processes include those processes which help us to have the knowledge and understanding of self and the environment.

Psychologists have developed different tests to assess these cognitive processes.

1.ATTENTION

It Can be evaluated by performing various experiments. Fluctuations in attention can be studied using the double perspective figure, Masson disk, etc.

Distraction – using a distraction device such as a gramophone and adding leaves, an experiment can be conducted to see the effect of distraction.

Allocation - can be tested using the "Attention Allocation Board".

Span can be tested using a tool called a "Tachistoscope" and various cards with meaningful words and nonsense syllables.

2. Perception:

It can be tested to demonstrate how the illusion occurs, using instruments called the "Muller-Lyer illusion plate", the horizontal-vertical illusion plate, and the Phi-phenomenon apparatus can be used to study the illusion of motion.

3. Learning:

There are various theories to explain learning styles. These regimes can be studied experimentally.

Learning by trial and error - using a tool called a "Mirror Tracing Board" with a star pattern on a metal plate.

Learning insight - using a board called "Miles step maze" with random and systematic paths. It can also be used to study the effect of punishment on learning.

Repetition and recall experiments to learn their meaning can be done using two lists of words.

Transfer of Learning: Two-way transfer of learning can be studied using a “Mirror Tracing Board”.

4. Memory:

Experiments can be conducted to study memory and forgetting through retroactive and proactive inhibition, Effect of meaning on memory, Recall and Recognition experiments. Proactive and retroactive inhibition can be demonstrated by performing experiments as follows:

5. Proactive inhibition:

Experimental group:

Learn Task 'A', Learn Task 'B' (Retention Interval) Measure recall of Task 'B'.

Control group:

Rest—– Task 'B' Learned (Retention Interval) Recall Task B.

In this case, the distracting activity of the learning task "A" comes before the learning of the memorized items of the task "B". If there is proactive interference, the experimental group will recall the “B” task more poorly than the control group.

6. Retroactive inhibition:

Experimental group:

Learn Task 'A' Learn Task 'B' (Retention Interval) Measure recall of Task 'A'.

Control group:

Learn Task 'A', Rest (Retention Interval) Measure recall of Task 'A'. The difference between the two groups is in the learning of the "B" task.

This occurs after learning task "A" and if retroactive inhibition occurs, the experimental group will perform less well in recalling the items of task "A" than the control group (Note: This experiment can be performed using two lists of words prepared just for this purpose).

7. Thinking:

How thinking works in concept formation can be assessed using the "Kasanin and Haufmann Test of Concept Formation". Reasoning can be tested using the "Yerkes Multiple Choice Apparatus".

8. Intelligence:

There are various tests that are specially prepared for literate, illiterate, children, adults, for individuals, groups, etc., e.g., Alexander's Intelligence Performance Test Battery, Bhati's Intelligence Performance Test Battery, Raven's Progressive Matrices, Wechsler's Adult and Children's Intelligence Tests, Otis test, Stanford-Binet scales, etc.

9. Eligibility:

There are experiments called Mechanical-aptitude, Art aptitude, Differential aptitude tests, Manual, Finger and tweezer dexterity tests etc.

I hope this answer solves your query.

THANK YOU!!!!

Hello Aspirant.

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The answer of your question is that the local variables are not initiated by default Values. This statement means that the local variables can be assigned and declared a value before the variables are used for the first time Or the compiler can show an error.

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illustrate the relation between marginal cost, average total cost, average variable cost, and fixed cost cures, give a total cost function TC (Q) = 50Q2 + 10Q +75. Where Q represents the quantity of out put produced. find the expression of variable cost, fixed cost, AVC,AFC and ATC