Mathematics Problem Solving Quiz
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Questions and Answers

If Ankita is 25 years old and Rahul's age is 25% greater than Ankita's, how much is Ankita's age less than Rahul's age in percent?

  • 40%
  • 35%
  • 20% (correct)
  • 10%

In an election, if a candidate received 25% of the total votes and lost by 270 votes, what percentage of the total votes did the winning candidate receive?

  • 70%
  • 75% (correct)
  • 60%
  • 50%

What is the total number of votes polled if a candidate received 25% and lost by 270 votes?

  • 540 votes (correct)
  • 450 votes
  • 600 votes
  • 480 votes

What is the result of the expression $4 + 10 - 3 \times 6 \div 3 + 4$?

<p>12 (C)</p> Signup and view all the answers

If 20% of students failed in both subjects and 50% passed in Science, what percent of students passed in at least one subject?

<p>80% (B)</p> Signup and view all the answers

What is the simplified form of the expression $9 - { 7 - 24 \div ( 8 + 6 \times 2 - 16 ) }$?

<p>11 (C)</p> Signup and view all the answers

How many students appeared in an exam if 270 students passed in both Science and Social?

<p>540 students (A)</p> Signup and view all the answers

Which is the correct evaluation of $(25)^3 - (30)^3 + (5)^3$?

<p>-1125 (A)</p> Signup and view all the answers

Evaluate $\frac{9}{42} \div \frac{108}{63} \times 328 - \frac{5}{7} + \frac{7}{5}$. What is the result?

<p>40 (D)</p> Signup and view all the answers

How would you calculate the net change if x is 20 and y is 25 using the formula x - y - xy/100?

<p>−10 (A)</p> Signup and view all the answers

If $x = \frac{\sqrt{126} \times \sqrt{63} \times \sqrt{45}}{\sqrt{147} \times \sqrt{243}}$, what is the value of $x$?

<p>\sqrt{10} (A)</p> Signup and view all the answers

What is the percentage decrease calculated if the net change resulted in −10?

<p>10% (D)</p> Signup and view all the answers

What net effect results from the equation x - y - xy/100 where x = 20 and y = 25?

<p>−10 (D)</p> Signup and view all the answers

What is the result of evaluating $\sqrt{2809.001} \div 7.98 \times (12.01)^2 + 46.002$?

<p>1000 (C)</p> Signup and view all the answers

Calculate $(35% \text{ of } 74000) \div ? = (123 % \text{ of } 13.02)^2 \times 2.01$. What is the missing value?

<p>50 (D)</p> Signup and view all the answers

The term percent means what?

<p>For every hundred (A)</p> Signup and view all the answers

What is the correct order of operations according to the BODMAS rule?

<p>Brackets, Order, Division, Addition (A)</p> Signup and view all the answers

Which operation comes first when simplifying an expression using BODMAS?

<p>Order (A)</p> Signup and view all the answers

The primary objective of simplification is to:

<p>Eliminate unnecessary parts and simplify processes (A)</p> Signup and view all the answers

In the context of simplification, what does the 'Order' refer to?

<p>Powers and Square Roots (C)</p> Signup and view all the answers

Which of the following correctly interprets the BODMAS acronym?

<p>Brackets, Order, Division, Multiplication, Addition, Subtraction (A)</p> Signup and view all the answers

Which of the following operations is performed last in BODMAS?

<p>Addition (B)</p> Signup and view all the answers

How does simplification affect the clarity of a mathematical expression?

<p>It enhances understanding by clarifying necessary processes. (B)</p> Signup and view all the answers

What is a common misconception about simplification in mathematics?

<p>Simplification always leads to a smaller number. (A)</p> Signup and view all the answers

What word does the code 'Si' represent in the given code language?

<p>Money (A)</p> Signup and view all the answers

If 'Money market easy' is written as 'Bi Si Ci', what is the code for the word 'Market'?

<p>Either Si or Ci (D)</p> Signup and view all the answers

How is the word 'CHILDREN' encoded if 'TEACHER' is represented as 'VGCEJGT'?

<p>EJKNFTGP (C)</p> Signup and view all the answers

What is the code for the word 'DANGER' if it is encoded as 'MACHINE' = 19-7-9-14-15-20-11?

<p>13-7-20-9-11-25 (D)</p> Signup and view all the answers

Using the given code language, which code represents 'coffee is hot'?

<p>753 (D)</p> Signup and view all the answers

If 'air' is known as 'green', 'green' as 'red', and so forth, what is the color of grass?

<p>Air (D)</p> Signup and view all the answers

If 'blue' means 'green', and the chain continues, what does 'human blood' refer to?

<p>White (D)</p> Signup and view all the answers

If 'PROMPT' is coded as 'QSPLOS', how is 'PLAYER' encoded?

<p>QMBZFS (B)</p> Signup and view all the answers

What mathematical concepts were discussed in Unit-5?

<p>Simplification and Coding &amp; Decoding (D)</p> Signup and view all the answers

Which of the following topics is NOT mentioned in the summary of Unit-5?

<p>Calculus (B)</p> Signup and view all the answers

What is the purpose of the suggested video links provided in Unit-5?

<p>To offer visual teaching alternatives (D)</p> Signup and view all the answers

Which reference website is provided for students in Unit-5?

<p><a href="http://www.GovernmentAdda.com">www.GovernmentAdda.com</a> (A)</p> Signup and view all the answers

Which of the following topics is specifically listed under the 'Suggested Links' section?

<p>Average (C)</p> Signup and view all the answers

What type of mathematical problems were emphasized in Unit-5?

<p>MCQs related to various topics (A)</p> Signup and view all the answers

What is likely a prerequisite topic for the concepts taught in Unit-5?

<p>Basic Arithmetic (B)</p> Signup and view all the answers

Which author is mentioned for book references in Unit-5?

<p>R.S. Agrawal (C)</p> Signup and view all the answers

What does the discriminant of a quadratic equation determine?

<p>The type of roots the equation has (A)</p> Signup and view all the answers

What is the value of the discriminant for the equation $x^2 + 4x - 5 = 0$?

<p>16 (A)</p> Signup and view all the answers

If the quadratic equation has two equal real roots, what is the condition for the discriminant?

<p>b² - 4ac = 0 (A)</p> Signup and view all the answers

Using the quadratic formula, what would be the roots of the equation $2x^2 + x - 528 = 0$?

<p>$16$ and $-33/2$ (B)</p> Signup and view all the answers

What is the critical value of the discriminant that indicates there are no real roots?

<p>Any negative number (D)</p> Signup and view all the answers

After losing 5 marbles each, if the product of the number of marbles that Rahul and Rohan have is 124, how many marbles did Rohan originally have if they had 45 marbles together?

<p>20 (C)</p> Signup and view all the answers

In the quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, which part represents the roots?

<p>Both A and B (C)</p> Signup and view all the answers

How do you classify a quadratic equation with roots $x = 3$ and $x = -3$?

<p>Two distinct real roots (C)</p> Signup and view all the answers

Flashcards

Percentage decrease

The decrease in the value of a quantity is expressed as a percentage of the original value.

Term

A term refers to a number or a variable that represents a part of a whole or a specific amount.

Net effect

The net effect is the overall change in a quantity after considering all the factors.

Total number of votes polled

The total number of votes cast in an election.

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Candidate

An individual competing in an election.

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Percentage of votes

The percentage of votes received by each candidate in an election.

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Examination

An examination or test used to assess knowledge or skills.

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Passing in an exam

A measure of academic performance on an examination, indicating a successful completion of the test.

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BODMAS Rule

An approach to solving mathematical expressions involving multiple operations, ensuring the correct order of operations is followed.

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Simplification

A process of reducing a complex expression to a simpler form, by eliminating unnecessary components and combining like terms, aiming to make it easier to understand and manipulate.

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Operations

Mathematical operations including addition, subtraction, multiplication, division, powers, square roots, and more.

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Order of Operations

The order of operations in which brackets should be evaluated, followed by orders, then division and multiplication, and finally addition and subtraction. Incorrect order may lead to incorrect results.

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Simplifying Mathematical Expressions

Simplifying a complex mathematical expression with the aim of making it easier to understand and manipulate by systematically removing unnecessary elements, combining similar parts, and rearranging them.

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Mathematical Expression

A mathematical expression that involves a combination of numbers, variables, and operations.

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Problem Decomposition

The ability to break down a complex problem into smaller, more manageable parts, simplifying the process.

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Goal of Simplification

The core goal of simplification is to express any given mathematical expression or a problem in its simplest form, making it easier to understand and solve.

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PEMDAS

The order of operations in mathematics: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

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Expression

A mathematical expression involving numbers, variables, and operations (addition, subtraction, multiplication, division, exponentiation, etc.).

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Simplifying a Fraction

A simplified fraction where the numerator and denominator have no common factors other than 1.

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Equation

A mathematical statement claiming the equality of two expressions.

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Percentage

A number expressed as a fraction of 100, often denoted with the symbol %.

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Solving an Equation

Solving an equation means finding the value of the unknown variable that makes the equation true.

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Square Root

The square root of a number is the value that, when multiplied by itself, equals the original number.

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Letter Shift Code

In this code, each letter is replaced by the next letter in the alphabet. For example, 'T' becomes 'U', and 'E' becomes 'F'.

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Letter-Number Code

The code is based on assigning numbers to letters. Each letter is assigned a unique number, creating a code mapping.

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Coded Language

A code is created where a word or phrase is represented by a set of numbers or symbols. This code has a specific mapping where certain numbers or symbols correspond to words in the code language.

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Unclear Code

This code requires analyzing the given words and their corresponding codes to decipher the rules. The code might use a pattern, like a shift, or even be entirely random.

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Reverse Letter Shift Code

The code is based on replacing each letter with the one that comes before it in the alphabet. For example, 'A' becomes 'Z', 'B' becomes 'A', and 'C' becomes 'B'.

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Letter-Value Code

The code is based on assigning each letter a numerical value, which is then converted to a corresponding code. The mapping between letters and numbers can vary.

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Coded Word Replacement

The code uses a set of rules or patterns to replace words or phrases with codes. The rules can vary based on the code system.

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Decoding a Sequence

This type of problem involves identifying the hidden meaning in a sequence of codes. You need to analyze the patterns and relationships between words, numbers, or symbols to decode the message.

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Quadratic Equation

A mathematical expression in the form ax² + bx + c = 0, where 'a', 'b', and 'c' are constants and 'x' is a variable. It's characterized by the highest power of the variable being 2.

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Roots of a Quadratic Equation

The solution(s) to a quadratic equation. They represent the x-values where the curve intersects the x-axis.

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Quadratic Formula

A formula used to find the roots of a quadratic equation. It involves the coefficients of the equation and the square root of a specific expression.

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Discriminant

The expression b² - 4ac within the quadratic formula. It helps determine the nature of the roots (real or imaginary, distinct or equal).

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Two Distinct Real Roots

The discriminant is greater than zero. This indicates two distinct real roots, meaning the graph intersects the x-axis at two different points.

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Two Equal Real Roots

The discriminant is equal to zero. This indicates two equal real roots, meaning the graph touches the x-axis at only one point (the vertex).

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No Real Roots

The discriminant is less than zero. This indicates no real roots, meaning the graph never intersects the x-axis. The roots are imaginary.

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Factoring Method

A method of solving quadratic equations by factoring the expression into two linear factors. The roots are then found by setting each factor to zero.

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Profit and Loss

The difference between the selling price of an item and its cost price. If the selling price is higher than the cost price, it's a profit. If the selling price is lower, it's a loss.

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Average

The average is the central value of a set of numbers. You calculate it by adding all the numbers together and dividing by the total count of numbers.

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Number and Series

A sequence of numbers that follow a specific pattern or rule. There can be arithmetic series (where the difference between terms is constant) or geometric series (where the ratio between terms is constant).

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Coding and Decoding

A method of encoding or decoding information using a specific set of rules or a key. It's used to secure communication or solve puzzles.

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Algebra

A branch of mathematics that deals with symbols and their relationships. It involves using variables to represent unknown quantities and solving for them.

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MCQs

A type of question that has multiple choices (a, b, c, d) and only one correct answer.

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Study Notes

Aptitude 1 Study Notes

  • Unit V: Elementary Mathematics (BBT0101) for B.Tech. 1st Semester
  • Topics Covered:
    • Simplification
    • Percentage
    • Profit, Loss & Discount
    • Average
    • Number & Series
    • Coding & Decoding
    • Algebra

Unit Objective (CO 5)

  • Course objective: Sensitize students with the skills to enhance employability and build stronger connections with their work environment.

Simplification (CO 5)

  • BODMAS Rule: Defines the correct order of operations (Brackets, Order, Division, Multiplication, Addition, Subtraction) for simplifying mathematical expressions.

Topic objective of Simplification (CO 5)

  • Eliminate unnecessary parts of a process.
  • Combine and rearrange parts of a process.
  • Simplify the necessary parts of the process.

Simplification (Contd.) (CO5)

  • Q.1: Solve: 4 + 10 - 3 × 6 ÷ 3 + 4 = 12
  • Q.2: Evaluate expressions with multiple operations, following BODMAS rule accurately. Examples: 9 - 7-24 ÷ (8 + 6 × 2 - 16), etc.

Multiple Choice Questions (CO5)

  • Ques. 1-5: Multiple-choice questions covering various simplification and percentage topics. Examples include evaluating expressions with percentages, fractions, or roots (e.g., 9/42 ÷ 108/63 × 328–5/7 + 7/5).

Ans. Of Multiple Choice Questions (CO5)

  • Answers: Solutions to the multiple-choice questions.

Quiz(CO5)

  • Questions: Problems related to evaluating expressions and simplifying mathematical expressions (ex: Evaluate (2³)³ + (-15)³ + (-8)³).
  • Simplification examples: Problems related to simplifying expressions with square roots, cube roots, etc.

Percentages (CO5)

  • Definition: A percentage represents a fraction with a denominator of 100.
  • Key Concept: X% of Y is (X/100) * Y

Application of percentage (CO5)

  • Type 1: Salary based Problems: Examples on how income and expenditure changes affect savings percentages.
  • Type 2: Population Related Problems: Examples on calculating population growth over time.
  • Type 3: Examination based problems: Examples on solving problems related to marks in exams.

Application of percentage (CO5) (Contd.)

  • Example Questions:
    • Finding percentage decrease in savings when income and expenditure increase.
    • Calculating percentage of Q's income less than P's income where P's income is 20% higher than Q's.
    • Calculating reduced price percentage of rice.

Application of percentage (CO5) (Contd.)

  • Examples Questions and solutions:
    • Detailed example problems and solutions are shown for understanding different types of percentage calculation.

Multiple Choice Questions (CO5)

  • Multiple-choice questions: Practice problems to check understanding.

Ans. Of Multiple Choice Questions (CO5)

  • Answers: Solutions to multiple choice questions.

Quiz(CO5)

  • Questions: Practice problems.

Exercise (CO5)

  • Questions: Various problems related to applications of percentages.

Basic Concept of Profit & Loss (CO5)

  • Profit: Selling Price - Cost Price
  • Loss: Cost Price - Selling Price
  • Profit %: [(Selling Price - Cost Price)/Cost Price] x 100
  • Loss %: [(Cost Price - Selling Price)/Cost Price] x 100

Profit & Loss (CO5) (Contd.)

  • Formulae: - Selling Price = Cost Price (1 ± x/100) - where +x = profit percentage - where -x = loss percentage

Topic objective of Profit & Loss (CO5)

  • Detail the preparation of profit and loss accounting.
  • Summarize the operating results of a business at the end of an accounting period.
  • Define profit and loss account as a nominal accounting entry.

Profit & Loss (CO5) (Contd.)

  • Example Questions and Solutions: Solve various problems related profit and loss calculations

Discount (CO5)

  • Marked Price (MP): The price marked on a product.
  • Discount: The reduction given on the marked price.
  • Selling Price (SP): The price at which an item is sold after the discount.
  • Discount Formula: SP = MP (1 - d/100), where d is the discount percentage.

Topic objective of Discount (CO5)

  • Detail the objective of offering discounts in business.
  • Summarize the methods for calculating single and successive discounts.

Discount (CO5) (Contd.)

  • Example Questions and Methods: Solve problems related to different scenarios of discount calculation.

Average (CO5)

  • Definition: Average = (Sum of Observations) / (Number of Observations)

Number & Series (CO5)

  • Tips for Number Series:
    • Observe familiar patterns (e.g., prime numbers, squares, cubes).
    • Examine differences between numbers to identify patterns (addition, subtraction, multiplication).
    • Identify complex patterns requiring a combination of operations or relationships between consecutive terms.

Number & Series (CO5) (Contd.)

  • Possible patterns in number series:
    • Addition or subtraction of a constant value.
    • Multiplication or division by a constant value.
    • Combination of operations (addition, subtraction, multiplication, and division).
    • Patterns are growing or decreasing.
    • Square and cube series.

Coding & Decoding (CO5)

  • Fundamentals: Methods for encoding and deciphering information.
  • Types: Letter, number, symbol coding; deciphering message word coding; substitution coding.
  • Example Problems: Various substitution-based encoding and decoding practices.

Additional Notes (General):

  • Each topic has examples and exercises to understand and apply concepts.
  • All terms are defined and examples are used to show application of the knowledge.

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Test your skills with this engaging mathematics quiz covering topics such as percentages, vote calculations, and expression simplifications. Tackle a variety of problems including age comparisons, election outcomes, and student performance metrics. Perfect for enhancing your analytical and problem-solving abilities!

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