Locate √5, √10 and √17 on the number line.
Let us represent √5 on the number line: 5 can be written as the sum of the square of two... View Article
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Represent the following numbers on the number line: 7, 7.2, −3/2 , −12/5
To represent 7, 7.2, −3/2 , −12/5
Insert a rational number and an irrational number between the following: (i) 2 and 3 (ii) 0 and 0.1 (iii) 1/3 and 1/2 (iv) – 2/5 and 1/2 (v) 0.15 and 0.16 (vi) √2 and √3 (vii) 2.357 and 3.121 (viii) .0001 and .001 (ix) 3.623623 and 0.484848 (x) 6.375289 and 6.375738.
Solution (i) 2 and 3 Rational number between 2 and 3 = 2.7 Irrational number between 2 and 3 = 2.312312312….. (ii)... View Article
Find three rational numbers between (i) -1 and -2 (ii) 0.1 and 0.11 (iii) 5/7 and 6/7 (iv) 1/4 and 1/5
Solution (i) –1 and –2 Three rational numbers between –1 and –2 are –1.1, –1.2 and –1.3. (ii) 0.1 and... View Article
Find which of the variables x, y, z and u represent rational numbers and which irrational numbers: (i) x2 = 5 (ii) y2 = 9 (iii) z2 = .04 (iv) u2 = 17/4
Solution Let us solve the given equations (i) x2 = 5 On simplifying, we obtain ⇒ x = ± √5 Therefore, x is... View Article
Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer by an example.
Solution The answer is No. If we consider x as rational number and y as irrational number Then the product of xy... View Article
Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.
Solution We know that the sum of rational and irrational number is mainly an irrational number. If we consider x as... View Article
The value of 1.999… in the form p/q, where p and q are integers and q ≠ 0 , is (A) 19/10 (B) 1999/1000 (C) 2 (D) 1/9
The correct answer is (C) 2 Solution Let us simplify the given choices (A) 19/10 = 1.9 (B) 1999/1000= 1.999... View Article
A rational number between √2 and √3 is (A) (√2 + √3)/2 (B) (√2. √3)/2 (C) 1.5 (D) 1.8
The correct answer is (C) 1.5 Solution We know that √2 =1.4142135…. √3 =1.732050807…. Let us see all the given... View Article
The decimal expansion of the number √2 is (A) a finite decimal (B) 1.41421 (C) non-terminating recurring (D) non-terminating non-recurring
The correct answer is (D) non-terminating non-recurring Solution The value of √2 is 1.414 √2 is an irrational number. ∴... View Article
Between two rational numbers (A) there is no rational number (B) there is exactly one rational number (C) there are infinitely many rational numbers (D) there are only rational numbers and no irrational numbers
The correct answer is (C) there are infinitely many rational numbers Solution A rational number is a type of real number,... View Article
Every rational number is (A) a natural number (B) an integer (C) a real number (D) a whole number
The correct answer is (C) a real number Solution A rational number is a type of real number, which is in the... View Article
Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is (i) 6 (ii) 12 (iii) 7
Solution Number of total outcomes = 36 (i) When product of the numbers on the top of the dice =... View Article
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is (i) 7? (ii) a prime number? (iii) 1?
Solution Two dice are thrown at the same time. So, total number of possible outcomes = 36 (i) Sum of... View Article
Two dice are thrown at the same time. Find the probability of getting ASame number on both dice. Different numbers on both dice.
Solution Two dice are thrown at the same time. So, total number of possible outcomes = 36 (i) Same number... View Article
The weight of coffee in 70 packets are shown in the following table : Weight (in g) Number of packets 200-201: 12 201-202 :26 202-203: 20 203-204 :9 204-205: 2 205-206 :1 Determine the modal weight.
Solution According to the given details we get to know that The highest frequency is 26, which lies in the interval... View Article
The monthly income of 100 families are given as below : Income (in Rs) Number of families 0-5000: 8 5000-10000: 26 10000-15000: 41 15000-20000 :16 20000-25000 :3 25000-30000: 3 30000-35000 :2 35000-40000 :1 Calculate the modal income.
Solution According to the given details we get to know that The highest frequency = 41, 41 lies in the interval... View Article
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows: Speed (km/h) 85-100, 100-115, 115-130 ,130-145 Number of players 11, 9 ,8 .5 Calculate the median bowling speed.
Solution Let us construct the cumulative frequency table at first Speed ( in km/h) Number of players Cumulative frequency 85 –... View Article
Weekly income of 600 families is tabulated below : Weekly income Number of families (in Rs) 0-1000 :250 1000-2000 :190 2000-3000 :100 3000-4000 :40 4000-5000 :15 5000-6000: 5 Total 600 Compute the median income.
Solution Weekly Income Number of families (fi) Cumulative frequency (cf) 0-1000 250 250 1000-2000 190 250 + 190 = 400... View Article
Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class: Marks Below 20, Below 40, Below 60, Below 80, Below 100: Number of students: 17 ,22 ,29, 37, 50 respectively Form the frequency distribution table for the data.
Solution Solution: The frequency distribution table for given data is tabulated below: Marks Number of students 0 – 20 12... View Article
