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Put given value of x in the given equation. Solve each of the following equations using the formula :. Solve each of the following equations for x and give, in each case, your answer correct to one decimal place :. Solve each of the following equations for x and give, in each case, your answer correct to two decimal places :. Solve each of the following equations for x and give, in each case, your answer correct to 3 decimal places :.
Solve the equation. Write your answer correct to two decimal places. Solve the following equation and give your answer correct to 3 significant figures:.
Consider the given equation:. Solve for x using the quadratic formula. Write your answer correct to two significant figures. Solve each of the following equations, giving answer upto two decimal places. Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots. One root of the quadratic equation is. Also, find the other root of the equation. Given quadratic equation is �. One of the roots of i is , so it satisfies i.
So, the equation i becomes. Hence, the other root is. One root of the quadratic equation is -3, find its other root.
One of the roots of i is -3, so it satisfies i. Hence, the other root is 2a. If and ;find the values of x. Given i. So, the given quadratic equation becomes. Hence, the values of x are and. Find the solution of the equation ; if and. Given quadratic equation is �.. Also, given and. Hence, the solution of given quadratic equation are and. Given quadratic equation is. Since, m and n are roots of the equation, we have.
Hence ,. Solve, using formula :. Using quadratic formula,. Solve the quadratic equation. Find the value of m for which the equation has real and equal roots. The quadratic equation has real and equal roots if its discriminant is zero. Find the values of m for which equation has equal roots. Also, find the roots of the given equation. The quadratic equation has equal roots if its discriminant is zero. When , equation i becomes.
Find the value of k for which equation has real roots. The quadratic equation has real roots if its discriminant is greater than or equal to zero. Hence, the given quadratic equation has real roots for.
Find, using quadratic formula, the roots of the following quadratic equations, if they exist. Using quadratic formula, we have. Since D. But as x. Enter the OTP sent to your number Change. Resend OTP. Starting early can help you score better! Avail Offer. Chapter 5 - Quadratic Equations Exercise Ex. Question 1 v. Question 1 vi.
Use a suitable scale for your ogive. Use your ogive to estimate:. Through mark Using a graph paper, draw an ogive for the following distribution which shows a record of the width in kilograms of students.
Use your ogive to estimate the following:. Therefore, percentage of students weighing 55 kg or more. The distribution, given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution. Marks obtained. Marks obtained x. The mean of the following distribution is 52 and the frequency of class interval is 'f'.
Find f. The monthly income of a group of employees in a company is given below:. Monthly Income thousands. From the graph determine :.
Through mark , draw a parallel line to x-axis which meets the curve at A, From A draw a perpendicular to x-axis meeting it at B. A mathematics aptitude test of 50 students was recorded as follows:. Draw a histogram for the above data using a graph paper and locate the mode.
Marks obtained by students in an examination are given below:. Using the graph:. The marks obtained by 40 students in a short assessment is given below, where a and b are two missing data.
If mean of the distribution is 7. Find the mode and the median of the following frequency distribution. According to the table it can be observed that the value of x from the 13 th term to the 17 th term is Find the value of x and hence Ncert Solutions Of Class 10th Science Chapter 4 find the mean.
The number 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x. Use a graph paper for this question. The daily pocket expenses of students in a school are given below :. Pocket expenses in Rs. Draw a histogram representing the above distribution and estimate the mode from the graph. Histogram is as follows:. From E, draw a perpendicular to x-axis meeting at L. Value of L is the mode. The marks obtained by students in a mathematics test are given below :.
Use the ogive to estimate :. Number of students. The ogive is as follows:. The mean of following numbers is Find the value of 'x'. Hence, estimate the median. The marks of 10 students of a class in an examination arranged in ascending order is as follows:.
If the median marks is 48, find the value of x. Hence, find the mode of the given data. Here the number of observations i. So, the given data is 13, 35, 43, 46, 46, 50, 55, 61, 71, In the given data, 46 occurs most frequently. The daily wages of 80 workers in a project are given below.
Use a graph paper to draw an ogive for the above distribution. Use your ogive to estimate. The cumulative frequency table of the given distribution is as follows:. Wages Rs. Upper limit. Draw vertical line parallel to y axis from A to meet x axis at B. The value of point B is Thus, the number of workers that earn more than Rs.
The histogram below represents the scores obtained by 25 students in a Mathematics mental test. Use the data to:. Frame a frequency distribution table. To calculate mean. To determine the Modal class. The frequency distribution table is as follows:. Class interval. Mean value x. Here the maximum frequency is 8 which is corresponding to class 20 - Hence, the modal class is 20 - Enter the OTP sent to your number Change. Resend OTP. Starting early can help you score better!
Avail Offer. Find the mean of the following set of numbers: i 6, 9, 11, 12 and 7 ii 11, 14, 23, 26, 10, 12, 18 and 6. Question 2. Marks obtained in mathematics by 9 student are given below: 60, 67, 52, 76, 50, 51, 74, 45 and 56 a find the arithmetic mean b if marks of each student be increased by 4; what will be the new value of arithmetic mean. Question 3. Question 4. Question 5. Question 6. Question 7. The ages of 40 students are given in the following table: Age in yrs 12 13 14 15 16 17 18 Frequency 2 4 6 9 8 7 4 Find the arithmetic mean.
Question 8. Question 9. Height cm 50 55 58 60 65 70 71 No. Height cm x i No. Question Age - Years 16 - 18 18 - 20 20 - 22 24 No. Age in years C. Weekly Wages Rs No. The following are the marks obtained by 70 boys in a class test: Marks No.
Find mean by step - deviation method: C. I Frequency 5 20 10 10 9 6 12 8. Frequency Mid value x fx 10 20 20 30 25 40 15 50 5 60 Total 75 Class Freq 5 f 1 10 f 2 7 8.
Calculate the mean of the distribution, given below, using the short cut method : Mark No. Arranging the given data in descending order: 8, 7, 6, 5, 4, 3, 3, 1, 0 The middle term is 4 which is the 5 th term. The weights in kg of 10 students of a class are given below: 21, Arranging the given data in descending order: The marks obtained by 19 students of a class are given below: 27, 36, 22, 31, 25, 26, 33, 24, 37, 32, 29, 28, 36, 35, 27, 26, 32, 35 and Find: i median ii lower quartile iii upper quartile iv interquartile range.
Arranging in ascending order: 22, 24, 25, 26, 26, 27, 27, 28, 28, 29, 21, 32, 32, 33, 35, 35, 36, 36, 37 i Middle term is 10 th term i. From the following data, find: i Median ii Upper quartile iii Inter-quartile range 25, 10, 40, 88, 45, 60, 77, 36, 18, 95, 56, 65, 7, 0, 38 and The ages of 37 students in a class are given in the following table: Age in years 11 12 13 14 15 16 Frequency 2 4 6 10 8 7 Find the median.
The weight of 60 boys are given in the following distribution table: Weight kg 37 38 39 40 41 No. Weight kg x no. Estimate the median for the given data by drawing an ogive: Class frequency 4 9 15 14 8. By drawing an ogive, estimate the median for the following frequency distribution: Weight kg No.
Weight kg No. From the following cumulative frequency table, find: i median ii lower quartile iii upper quartile Marks less than 10 20 30 40 50 60 70 80 90 Cumulative frequency 5 24 37 40 42 48 70 77 79 In a school, pupils have heights as tabulated below: Height in cm No. Height in cm No. Find the mode of the following data: i 7, 9, 8, 7, 7, 6, 8, 10, 7 and 6 ii 9, 11, 8, 11, 16, 9, 11, 5, 3, 11, 17 and 8.
The following table shows the frequency distribution of heights of 50 boys: Height cm Frequency 5 8 18 10 9 Find the mode of heights. Find the mode of following data, using a histogram: Class Frequency 5 12 20 9 4. Find the mode of their expenditure: Expenditure Rs No. Find the median and mode for the set of numbers: 2, 2, 3, 5, 5, 5, 6, 8 and 9.
At a shooting competition the score of a competitor were as given below: Score 0 1 2 3 4 5 No. Score x No. Using the graph, determine: The median height. The interquartile range. Marks No.
The numbers 3, 2, 4, 2, 3, 3 and p have mean m-1 and median q. Find p and q. In a malaria epidemic, the number of cases diagnosed were as follows: Date July 1 2 3 4 5 6 7 8 9 10 11 12 Num 5 12 20 27 46 30 31 18 11 5 0 1 On what days do the mode and upper and lower quartiles occur? Date Number C. Income in thousand Rs No. The marks of 20 students in a test were as follows: 2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19 and Calculate: i the mean ii the median iii the mode.
The marks obtained by students in a mathematics test is given below: Marks No. Weight Frequency C. Marks obtained 5 6 7 8 9 10 No. Marks obtained x No. I Freq 5 3 f 7 2 6 The monthly income of a group of employees in a company is given below: Monthly Income thousands No. From the graph determine : i the median wage. Monthly Income thousands No.
A mathematics aptitude test of 50 students was recorded as follows: Marks No. Marks obtained by students in an examination are given below: Marks No. Using the graph: i the median marks. The daily pocket expenses of students in a school are given below : Pocket expenses in Rs No.
Histogram is as follows: In the highest rectangle which represents modal class draw two lines AC and BD intersecting at E. The marks obtained by students in a mathematics test are given below : Marks No.
Marks Number of students Frequency Cumulative Frequency 3 3 7 10 12 22 17 39 23 62 14 76 9 85 6 91 5 96 4 The ogive is as follows:.
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