A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is

  1. a square number
  2. a multiple of 7

This is a question of CBSE Sample Paper - Class 10 - 2017/18.

You can download the question paper here  https://www.teachoo.com/cbse/sample-papers/

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Question 11 - CBSE Class 10 Sample Paper for 2018 Boards - Part 2
Question 11 - CBSE Class 10 Sample Paper for 2018 Boards - Part 3 Question 11 - CBSE Class 10 Sample Paper for 2018 Boards - Part 4

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Transcript

Question 11 A box contains cards numbered 11 to 123. A card is drawn at random from the box. Find the probability that the number on the drawn card is a square number a multiple of 7 Numbers on card = 11, 12, 13, 14, 15, ……… 123 Theory Numbers between 1 & 3 (including 1 and 3) = 1, 2, 3 ∴ Total Numbers = 3 Writing in formula ∴ Total Numbers = 3 – 1 + 1 = 3 Numbers between 5 & 10 (including 5 and 10) = 5, 6, 7, 8, 9, 10 ∴ Total Numbers = 6 Writing in formula ∴ Total Numbers = 10 – 5 + 1 = 6 Total cards = 123 – 11 + 1 = 113 (i) Number is a square number Square numbers = 12, 22, 32, 42, 52, 62, 72, 82, 92, 102, 112, 122,…. Square numbers = 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, … Square numbers between 11 & 123 = 16, 25, 36, 49, 64, 81, 100, 121 Number of possible numbers = 8 Theory Square numbers are square of some number. Eg: 12 = 1, 22 = 4, 32 = 9, 42 = 16 ∴ 1, 4, 9, 16 are square numbers Probability = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠) Probability = 𝟖/𝟏𝟏𝟑 (ii) Number is a multiple of 7 Multiple of 7 are those numbers which come in table of 7 Theory 7 × 1 = 7 7 × 2 = 14 7 × 3 = 21 7 × 4 = 28 7 × 5 = 35 7 × 6 = 42 7 × 7 = 49 7 × 8 = 56 7 × 9 = 63 7 × 10 = 70 7 × 11 = 77 7 × 12 = 84 7 × 13 = 91 7 × 14 = 98 7 × 15 = 105 7 × 16 = 112 7 × 17 = 119 7 × 17 = 126

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.