Brief Summary
This video features a math practice set geared towards the upcoming NTPC exams. The instructor, Shivam Pandit, works through 20 questions, providing explanations and shortcuts. Key takeaways include the importance of practicing easy questions thoroughly, understanding concepts like similarity of triangles and properties of zero, and avoiding careless mistakes. The video also touches on test-taking strategies and motivational pep talk.
- Focus on practicing easy questions thoroughly.
- Understand key mathematical concepts.
- Avoid careless mistakes.
Introduction
Shivam Pandit welcomes viewers to the session, wishing good luck to those taking the NTPC exam. He humorously mentions the lack of AC due to a missing remote. He confirms that the audio and video are clear and expresses concern about the studio's heat affecting his health.
Question 1: Percentage Difference in Salaries
The problem involves finding the percentage difference between the lowest and highest paid CEOs from a given diagram. The highest salary is 75 and the lowest is 50. The difference is 25, and the percentage difference is calculated as 25/50, which equals 50%. Many viewers initially answered incorrectly, highlighting the importance of understanding what the question is asking.
Question 2: Identifying a Right Angle Triangle
The task is to identify a right-angled triangle from a set of options. This requires knowledge of Pythagorean triplets. The correct answer is 7, 24, 25, as it forms a valid triplet.
Question 3: Rationalization
The problem involves simplifying an expression by rationalizing the denominator. Shivam explains that when the difference between the squares of the terms in the denominator is one, rationalization simply involves changing the sign. He also reviews the basic process of rationalization for those unfamiliar with the shortcut.
Question 4: Cost of Books and Square Trick
The question involves finding the cost of 56 books given the cost of 10 books. Shivam uses this as an opportunity to teach a trick for squaring numbers close to 50. He explains that for numbers near 50, you adjust 25 based on how much more or less the number is than 50, and then add the square of that difference. He applies this to find 56 squared, which is needed to solve the problem.
Question 5: Similarity of Triangles
This question tests the understanding of similar triangles. Shivam explains that the ratio of perimeters of similar triangles is equal to the ratio of their corresponding sides. Using this property, the length of a side is calculated.
Question 6: HCF and LCM
The problem involves finding the second number when the HCF, LCM, and one number are given. Shivam uses the formula: LCM * HCF = First Number * Second Number to solve the problem. He emphasizes that the questions are not difficult if one avoids making mistakes.
Question 7: Trigonometry
The question involves finding the value of 'a' that satisfies a trigonometric equation. Shivam explains that the equation sin 2a = 2 sin a is only true when a is zero.
Question 8: Similarity of Triangles (Angles and Sides)
The question asks under which condition triangle ABC is similar to triangle PQR. Shivam explains that for triangles to be similar, either their corresponding angles must be equal, or the ratios of their corresponding sides must be the same.
Question 9: Time and Work
This problem involves calculating how many additional workers are needed to complete a task within a specified timeframe. Shivam uses the MDH (Men, Days, Hours) concept to determine the number of additional workers required. He also recommends a video on his channel that explains the MDH concept in detail.
Question 10: Time and Work (Punctures)
The question is a time and work problem disguised as a puncture problem. Shivam explains that the first puncture takes 9 minutes to flatten a tire, and the second takes 6 minutes. He calculates the combined time it would take for both punctures to flatten the tire.
Question 11: Fractions and Composite Numbers
The problem asks what fraction of numbers from 2 to 12 are composite numbers. Shivam lists the numbers from 2 to 12 and identifies the composite numbers. He then calculates the fraction of composite numbers out of the total numbers.
Question 12: Additive Property of Zero
This question tests the knowledge of basic mathematical properties. Shivam explains that adding zero to any number does not change the number, which is known as the additive property of zero.
Question 13: Algebra - Factoring
The problem involves factoring an algebraic expression. Shivam uses the identity a³ - b³ = (a - b)(a² + ab + b²) to simplify the expression and find the correct answer.
Question 14: Percentage Calculation
The question involves finding the value of x when 35% of x is given. Shivam solves the problem mentally, emphasizing that no pen should be used for such simple calculations.
Question 15: Volume of a Sphere
The problem involves finding the ratio of the new volume to the original volume of a sphere when the radius is doubled. Shivam explains that since volume is related to the cube of the radius, the volume increases by a factor of 8.
Question 16: Population Growth
The question involves calculating the population of a city after two years, given an annual growth rate. Shivam uses a shortcut to calculate the effective growth rate over two years and then applies it to the initial population.
Question 17: Time and Work (Combined Effort)
This problem involves calculating the time it takes for a person's son to complete a task independently, given the time it takes for the person and son to complete the task together. Shivam uses the concept of efficiency to solve the problem.
Question 18: LCM and Bells Tolling
The problem involves finding how many times bells toll together in a given time interval. Shivam calculates the LCM of the time intervals at which the bells toll and then determines how many times they toll together in the given time. He also points out the common mistake of forgetting to add one for the initial toll.
Question 19: Volume of Cylinder and Cone
The question involves finding the ratio of the volume of a cylinder to that of a cone with the same base and height. Shivam explains that the volume of a cone is one-third of the volume of a cylinder, so the ratio is 3:1.
Question 20: Decimal Comparison
The problem involves comparing decimal numbers. Shivam compares the given decimal numbers and identifies the largest one.
Conclusion
Shivam reviews the answers and discusses the importance of aiming for a perfect score in practice sets. He encourages viewers to continue practicing and learning mathematics. He ends the session with motivational words and appreciation for his viewers.
