Mathematics Questions
Browse 1,240 Mathematics questions with expert-verified, step-by-step solutions — NCERT, exemplar and previous-year questions, organised by chapter.
Chapters
Ch01 Real NumbersCh01 Real NumbersCh02 PolynomialsCh02 PolynomialsCh03 Pair of Linear EquationsCh03 Pair of Linear Equations in Two VariablesCh04 Quadratic EquationsCh04 Quadratic EquationsCh05 Arithmetic ProgressionsCh05 Arithmetic ProgressionsCh06 TrianglesCh06 TrianglesCh07 Coordinate GeometryCh07 Coordinate GeometryCh08 Introduction to Trigonometry and its ApplicationsCh08 TrigonometryCh09 Applications of TrigonometryCh09 CirclesCh10 CirclesCh10 ConstructionsCh11 Areas Related to CirclesCh11 Areas Related to CirclesCh12 Surface Areas and VolumesCh12 Surface Areas and VolumesCh13 StatisticsCh13 Statistics and ProbabilityCh14 ProbabilityA1 Proofs in MathematicsA2 Mathematical Modelling
- Q181A wooden article was made by scooping out a hemisphere from each end of a solid cylinder, as shown in Fig. 12.11. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the total surface area of the article.
- Q182A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of .
- Q183Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)
- Q184A gulab jamun contains sugar syrup up to about 30% of its volume. Find approximately how much syrup would be found in 45 gulab jamuns, each shaped like a cylinder with two hemispherical ends, with length 5 cm and diameter 2.8 cm (see Fig. 12.15).
- Q185A pen stand made of wood is in the shape of a cuboid with four conical depressions to hold pens. The dimensions of the cuboid are 15 cm by 10 cm by 3.5 cm. The radius of each of the depressions is 0.5 cm and the depth is 1.4 cm. Find the volume of wood in the entire stand (see Fig. 12.16).
- Q186A vessel is in the form of an inverted cone. Its height is cm and the radius of its top, which is open, is cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius cm are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.
- Q187A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm of iron has approximately 8 g mass. (Use )
- Q188A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.
- Q189A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 cm^3. Check whether she is correct, taking the above as the inside measurements, and .
- Q190A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in houses in a locality. Find the mean number of plants per house. Which method did you use for finding the mean, and why?
- Q191Consider the following distribution of daily wages of 50 workers of a factory. Find the mean daily wages of the workers of the factory by using an appropriate method.
- Q192The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs 18. Find the missing frequency .
- Q193Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised in the table below. Find the mean heartbeats per minute for these women, choosing a suitable method.
- Q194In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
- Q195The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.
- (i)Find the modal monthly expenditure of the families.
- (ii)Find the mean monthly expenditure of the families.
- Q196To find out the concentration of in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below. Find the mean concentration of in the air.
- Q197A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.
- Q198The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
- Q199The following table shows the ages of the patients admitted in a hospital during a year. Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.
- Q200The following data gives the information on the observed lifetimes (in hours) of 225 electrical components. Determine the modal lifetimes of the components.