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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, which is in the... 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 form of p/q where q is... 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 = 6. The possible outcomes = (1, 6), (2,3), (3,... 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 the numbers appearing on the dice is 7.... 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 on both dice. Possible outcomes =... 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 201 – 202 Here,... 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 10000 – 15000. Now... 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

Find the unknown entries a, b, c, d, e, f in the following distribution of heights of students in a class: Height Frequency Cumulative frequency (in cm) 150-155 :12 -a 155-160: b- 25 160-165 :10 -c 165-170: d -43 170-175: e- 48 175-180: 2 f Total 50

Solution Height (in cm) Frequency Cumulative frequency given Cumulative frequency 150 – 155 12 a 12 155 – 160... View Article

Form the frequency distribution table from the following data : Marks (out of 90) Number of candidates More than or equal to 80- 4 More than or equal to 70- 6 More than or equal to 60- 11 More than or equal to 50 -17 More than or equal to 40 -23 More than or equal to 30 -27 More than or equal to 20- 30 More than or equal to 10- 32 More than or equal to 0 -34

Solution The frequency distribution table for the given data is tabulated below: Class Interval Number of students 0-10 34 –... View Article

The following table shows the cumulative frequency distribution of marks of 800 students in an examination: Marks Number of students Below 10 -10 Below 20- 50 Below 30- 130 Below 40- 270 Below 50 -440 Below 60 -570 Below 70 -670 Below 80 -740 Below 90 -780 Below 100- 800 Construct a frequency distribution table for the data above.

Solution The frequency distribution table for the given data is tabulated below: Class Interval Number of students 0-10 10... View Article

The following is the distribution of weights (in kg) of 40 persons : Weight (in kg) 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 Number of persons 4 4 13 5 6 5 2 1 Construct a cumulative frequency distribution (of the less than type) table for the data above.

Weight (in kg) Cumulative frequency Less than 45 4 Less than 50 4 + 4 = 8 Less than 55 8 + 13 = 21 Less than 60 21... View Article

The mileage (km per litre) of 50 cars of the same model was tested by a manufacturer and details are tabulated as given below : Mileage (km/l) 10-12 12-14 14-16 16-18 Number of cars 7 12 18 13 Find the mean mileage. The manufacturer claimed that the mileage of the model was 16 km/litre. Do you agree with this claim?

Mileage (km L-1) Class –Marks (xi) Number of cars (fi) fixi 10 – 12 11 7 77 12 – 14 13 12 156 14... View Article

The weights (in kg) of 50 wrestlers are recorded in the following table : Find the mean weight of the wrestlers.

Weight (in kg) 100-110 110-120 120-130 130-140 140-150 Number of wrestlers 4 14 21 8 3 Solution: Weight (in... View Article

An aircraft has 120 passenger seats. The number of seats occupied during 100 flights is given in the following table : Number of seats 100-104 104-108 108-112 112-116 116-120 Frequency 15 20 32 18 15 Determine the mean number of seats occupied over the flights.

Solution Class Interval Class Marks (xi) Frequency (fi) Deviation (di = xi – a) fidi 100 – 104 102 15 – 8... View Article

The daily income of a sample of 50 employees are tabulated as follows : Income (in Rs) 1-200 201-400 401-600 601-800 Number of employees 14 15 14 7 Find the mean daily income of employees.

Solution C.I xi di = (xi – a) Fi fidi 1 – 200 100.5 – 200 14 – 2800 201 – 400... View Article