Brief Summary
This video focuses on number system questions relevant to Railway Recruitment Board (RRB) Group D exams. It emphasizes the importance of understanding basic concepts and applying them to solve problems quickly. The session includes discussions on number properties, simplification techniques, and strategies for cracking exam questions efficiently. The video also provides information about available online and offline coaching batches for RRB exam preparation.
- Importance of number system in Railway and SSC exams.
- Discussion of various types of number system questions.
- Strategies for quick problem-solving.
- Information on available coaching batches.
Introduction
The session starts with a welcome message and an introduction to the topic of discussion: important questions from the number system relevant to the RRB Group D exam. The speaker highlights the significance of the number system as a fundamental topic for various Railway and SSC exams, emphasizing that a strong understanding of basic concepts is essential for success.
Importance of Number System
The number system is a crucial topic for Railway and SSC exams because it forms the basis for many mathematical concepts. Learning numbers, their properties, and the operations between them is essential. The number system is the first chapter to study when starting math for exams, and it underlies simplification, decimals, fractions, percentages, and ratios.
RRB Group D Exam Details
The Railway Group D exam notification is upcoming, and it is expected to have the most vacancies. Educational qualifications typically require a 10th-grade pass, possibly with an ITI certificate. The speaker encourages candidates with ITI qualifications not to underestimate the value of their certificates and hopes the notification will give equal importance to both 10th-grade and ITI qualifications.
Coaching Batch Information
Information about the already-ready Group D batch is shared, highlighting that over 300 classes have started. The batch includes live classes, syllabus completion, previous year questions, and mock tests. The complete package is available for ₹299, covering the entire syllabus, test series, previous year question discussions, and doubt clearance sections.
Question 1: Sum and Difference of Two Numbers
The first question involves finding the greatest number when the sum of two numbers is 32 and one exceeds the other by 18. The problem is solved by setting up two equations: x + y = 32 and x - y = 18. By adding the equations, 2x = 50, so x = 25. The greatest number is 25. A shortcut is also provided: add the sum and difference (32 + 18 = 50) and divide by 2 to find the larger number (25).
Question 2: Product of Consecutive Natural Numbers
The next question asks for the greater of two consecutive positive natural numbers whose product is 72. The solution involves recognizing that 72 is the product of 8 and 9, which are consecutive natural numbers. Therefore, the greater number is 9.
Question 3: Identifying Irrational Numbers
The task is to identify which of the given numbers is irrational. An irrational number cannot be expressed in the form of P/Q. The options are evaluated: the tenth root of 1024 is 2, the fifth root of 1024 is rational, and the square root of 1024 is 32. Option A, the square root of the fourth root of 1024, simplifies to the fourth root of 32, which is irrational.
Question 4: Square Root of Irrational Numbers
The question asks which number has an irrational square root. The options are evaluated, and it's determined that 4465 does not have a perfect square root, making its square root irrational. The speaker explains a trick to quickly identify perfect squares ending in 5.
Question 5: Rationalizing the Denominator
The problem involves expressing 1 / (2 + √3) as a rational number. The solution involves rationalizing the denominator by multiplying both the numerator and denominator by the conjugate of the denominator, which is (2 - √3). This simplifies to 2 - √3. A shortcut is provided: if the difference of the squares of the terms in the denominator is 1, the answer is simply the conjugate of the denominator.
Question 6: Perfect Square Factors
The question asks how many factors of 729 are perfect squares. First, 729 is expressed as 3^6. A perfect square has an even power. The factors of 729 that are perfect squares are 3^0, 3^2, 3^4, and 3^6, which are 1, 9, 81, and 729, respectively. Thus, there are four perfect square factors.
Question 7: Finding the Last Digit
The problem is to find the last digit of 213^6. The last digit of powers of 3 repeats in a cycle of 4: 3, 9, 7, 1. Since 6 divided by 4 leaves a remainder of 2, the last digit of 213^6 is the same as the last digit of 3^2, which is 9.
Question 8: Face Value and Place Value
The question requires calculating the sum of the face value and place value of 7 in the number 3728456. The face value of 7 is 7, and the place value is 700,000. The sum is 700,007.
Question 9: Sum of Squares of Numbers
The task is to find the sum of the squares of numbers from 3 to 18. This is done by finding the sum of the squares from 1 to 18 and subtracting the sum of the squares from 1 to 2. The formula for the sum of the first n squares is n(n+1)(2n+1)/6. After calculating and subtracting, the unit digit is found to be 4.
Question 10: Ratio and Proportion
Prayaga invited males and females to her birthday party in the ratio 7:6. If there were 56 males, the total number of guests is to be determined. Since 7 units correspond to 56 males, 1 unit is 8. Therefore, the total number of guests (13 units) is 13 * 8 = 104.
Question 11: Sum of Cubes of Natural Numbers
The problem involves finding the sum of the cubes of natural numbers from 5 to 14. This is solved by finding the sum of the cubes from 1 to 14 and subtracting the sum of the cubes from 1 to 4. The formula for the sum of the first n cubes is [n(n+1)/2]^2. After calculating and subtracting, the answer is found to be 10925.
Question 12: One-Third of a Number
The question states that one-third of a number is six more than the number itself. The task is to find the number. By testing the options, it is found that one-third of -9 is -3, and -3 is six more than -9.
Question 13: Ratio of Two Parts
A number is split into two parts such that one part is 14 more than the other, and the ratio of the two parts is 7:5. The number is to be found. The difference between the two parts is 2 units, which equals 14. Therefore, 1 unit is 7. The total number is 12 units, which is 12 * 7 = 84.
NTPC Offline Batch Information
Information about the NTPC offline batch is shared, noting that a second batch is starting due to popular demand. The batch offers similar features to the already running offline batch, including experienced faculty, library facilities, doubt clearance, and study materials.
Question 14: Sum of Squares of Consecutive Natural Numbers
The problem is to find the smaller of two consecutive natural numbers such that the sum of their squares is 313. By testing the options, it is found that 12^2 + 13^2 = 144 + 169 = 313. Therefore, the smaller number is 12.
Question 15: Mango Tree Plantation
A man plants 2125 mango trees in his garden such that the number of rows equals the number of trees in each row. The number of rows is to be found. This means finding x such that x^2 = 2025. The square root of 2025 is 45.
Question 16: Three-Digit Number Puzzle
A three-digit number has digits in the ratio 1:2:3. Reversing the digits and adding the reversed number to the original number results in 1332. The sum of the digits of the original number is to be found. By testing the options, it is found that 369 + 963 = 1332. Therefore, the original number is 369, and the sum of its digits is 3 + 6 + 9 = 18.
Question 17: Pencil Packets
If 12 packets contain 96 pencils, and one needs 304 pencils, the number of packets to purchase is to be determined. Each packet contains 96/12 = 8 pencils. To get 304 pencils, one needs 304/8 = 38 packets.
Question 18: Digit Manipulation
If each even digit is divided by two and two is added to each odd digit in the number 4723361, the sum of the largest and smallest digits in the resulting number is to be found. After the transformation, the number becomes 2915533. The largest digit is 9, and the smallest digit is 1. Their sum is 10.
Question 19: Divisibility by Nine
If the 15-digit number 4A5124356789734 is divisible by nine, the value of A is to be found. For a number to be divisible by nine, the sum of its digits must be a multiple of nine. The sum of the known digits is 64. Therefore, A must be 4 to make the total sum 68, which is not divisible by 9. The correct sum of the known digits is 74. Therefore, A must be 2 to make the total sum 72, which is divisible by 9.
Study Tips and Closing Remarks
The speaker advises viewers to revise the topics discussed in class for ten to fifteen minutes immediately after the session to reinforce learning. The session concludes with encouragement to join the RRB Group D batch and a reminder about the importance of studying effectively.
