CBSE Board Students Helpline

Chapter 1. Real Numbers 1. Express 140 as a product of its prime factors. (1-mark) 2. Find the LCM and HCF of 12, 15 and 21 by the prime factorization method. (1-mark) 3. Find the LCM and HCF of 6 and 20 by the prime factorization method. (1-mark) 4. State whether will have a terminating decimal expansion or a non-terminating repeating decimal. (1-mark) 5. State whether will have a terminating decimal expansion or a non-terminating repeating decimal. (1-mark) 6. Find the LCM and HCF of 26 and 91 and verify that LCM x HCF = product of the two numbers. (3-marks) 7. Use Euclid’s division algorithm to find the HCF of 135 and 225 (3-marks) 8. Use Euclid’s division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m. (3-marks) 9. Prove that is irrational. (3-marks) 10. Show that is irrational. (3-marks) 11. Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer. (3-marks) 1

1. (1) A dice is thrown once. Find the probability of getting (a) A number greater than 3 (b) A number less than 5 A. ½,2/3, 4/3, 2/3 B. 2/3, 4/3, 2/3 C. 4/3, 4/3, 2/3 D. 4/3, 2/3,13/8 2. A bag contain 5 black, 7 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is (a) Red (b) Black or white (c) Not black A. 7/15 B. 8/15 C. 2/3 D. 4/3 3. A bag contains 4 red 5 black and 6 white balls. A ball is drawn from the bag a random. Find the probability that the ball drawn is (a) White (b) Red (c) Not black (d) Red or white A. 2/5, 4/15, 2/3, 2/3 B. 4/3, 4/15, 1/3, 2/3 C. 4/15, 2/3, 2/3 1/3 D. 4/15, 2/3, 4/3 2/3 4. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack. A. 11/13 B. 12/13 C. 11/14 D. 11/12