Ch – 1 Real Numbers Most important questions

CSCE TUTORIAL

Class – X                                                                                                                                                                                  Maths

Real Numbers

Worksheet – 1

 

  1. Express 98 as a product of its primes.
  2. Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.
  3. If the HCF of 408 and 1032 is expressible in the form 1032 × 2 + 408 × p, then find the value of p.
  4. HCF and LCM of two numbers is 9 and 459 respectively. If one of the numbers is 27, find the other number.
  5. Find HCF and LCM of 13 and 17 by prime factorisation method.
  6. Find LCM of numbers whose prime factorisation are expressible as 3 × 52and 32 × 72.
  7. Find the LCM of 96 and 360 by using fundamental theorem of arithmetic.
  8. Find the HCF (865, 255) using Euclid’s division lemma.
  9. Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.
  10. Three bells toll at intervals of 9, 12, 15 minutes respectively. If they start tolling together, after what time will they next toll together?
  11. Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times.
  12. The length, breadth, and height of a room are 8 m 50 cm, 6 m 25 cm and 4 m 75 cm respectively. Find the length of the longest rod that can measure the dimensions of the room exactly.
  13. Three alarm clocks ring at intervals of 4, 12 and 20 minutes respectively. If they start ringing together, after how much time will they next ring together?
  14. In a school, there are two Sections A and B of class X. There are 48 students in Section A and 60 students in Section B. Determine the least number of books required for the library of the school so that the books can be distributed equally among all students of each Section.
  15. There are 104 students in class X and 96 students in class IX in a school. In a house examination, the students are to be evenly seated in parallel rows such that no two adjacent rows are of the same class.
         (a) Find the maximum number of parallel rows of each class for the seating arrangement.
         (b) Also, find the number of students of class IX and also of class X in a row.
         (c) What is the objective of the school administration behind such an arrangement?
  1. Dudhnath has two vessels containing 720 ml and 405 ml of milk respectively. Milk from these containers is poured into glasses of equal capacity to their brim. Find the minimum number of glasses that can be filled.
  2. Amita, Sneha, and Raghav start preparing cards for all persons of an old age home. In order to complete one card, they take 10, 16 and 20 minutes respectively. If all of them started together, after what time will they start preparing a new card together?
  3. If two positive integers x and y are expressible in terms of primes as x = p2q3and y = p3q, what can you say about their LCM and HCF. Is LCM a multiple of HCF? Explain.
  4. Find the largest number, which divides 615 and 963, leaving the remainder 6 in each case.
  5. If the HCF of 408 and 1032 is expressible in the form 1032m – 408 x 5, find m.

Maths

Practice Worksheets

(These worksheets are prepared expertly with the Most Important questions to practice for 2023-24 exams)

  1. Chapter – 1 Real Numbers 

  2. Chapter 2 – Polynomials

  3. Chapter 3 – Linear Equations in Two Variables

  4. Chapter 4 – Quadratic Equations

  5. Chapter 5 – Arithmetic Progressions

  6. Chapter 6 – Triangles

  7. Chapter 7 – Coordinate Geometry

  8. Chapter 8 – Introduction to Trigonometry

  9. Chapter 9 – Some Applications of Trigonometry

  10. Chapter 10 – Circles

  11. Chapter 11 – Areas Related to Circles

  12. Chapter 12 – Surface Areas and Volume

  13. Chapter 13 – Statistics

  14. Chapter 14 – Probability