Given:The heights of 50 students, measured to the nearest centimetres.To do:We have to (i) Represent the data given above by a grouped frequency distribution table, taking the class intervals as \( 160-165, 165-170 \), etc.(ii) Find the conclusion about their heights from the table.Solution:(i) The given data is large, so we ... Read More

Given:The relative humidity (in \( \% \) ) of a certain city for a month of 30 days is given.To do:We have to (i) Construct a grouped frequency distribution table with classes 84 - 86, 86 - 88, etc. (ii) Find the month or season the data is about.(iii) Find the range ... Read More

Given: Two congruent circles intersect each other at points \( \mathrm{A} \) and \( \mathrm{B} \). Through \( \mathrm{A} \) any line segment \( \mathrm{PAQ} \) is drawn so that \( \mathrm{P}, \mathrm{Q} \) lie on the two circles.To do: We have to prove that \( \mathrm{BP}=\mathrm{BQ} \).Solution:Let two circles intersect each ... Read More

Given: In a triangle \( \mathrm{ABC} \), the angle bisector of \( \angle \mathrm{A} \) and perpendicular bisector of \( \mathrm{BC} \) intersect.To do: We have to prove that they intersect on the circumcircle of the triangle \( \mathrm{ABC} \).Solution:Let $ABC$ be a triangle in which the angle bisector of \( \angle ... Read More

To do: We have to give five examples of data that we can collect from our day-to-day life.Solution:Five examples from day-to-day life that are examples of data are:1. Number of pens in our box.2. Number of teachers in our school.3. Number of apples in a shop4. Number of hospitals in our ... Read More

To do: We have to classify the data in Q.1 above as primary or secondary data.Solution:(i) Primary Data - The data collected by the person for a definite purpose is known as primary data. Primary data in Q.1 - 1, 2, 3, 4(ii) Secondary Data - The data collected from a source, which already had that ... Read More

Given:The blood groups of $30$ students of class VIII are recorded as follows:$A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O, A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O$.To do:We have to represent this data in the ... Read More

 Given:The distance (in \( \mathrm{km} \) ) of 40 engineers from their residence to their place of workTo do:We have to construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as \( 0-5 \) ( 5 not included). Solution:The given data is ... Read More

Given:Bisectors of angles \( \mathrm{A}, \mathrm{B} \) and \( \mathrm{C} \) of a triangle \( \mathrm{ABC} \) intersect its circumcircle at \( \mathrm{D}, \mathrm{E} \) and $F$ respectively.To do:We have to prove that the angles of the triangle \( \mathrm{DEF} \) are \( 90^{\circ}-\frac{1}{2} \mathrm{~A}, 90^{\circ}-\frac{1}{2} \mathrm{~B} \) and \( ... Read More

Given:\( \mathrm{AC} \) and \( \mathrm{BD} \) are chords of a circle which bisect each other. To do:We have to prove that (i) \( \mathrm{AC} \) and \( \mathrm{BD} \) are diameters (ii) \( \mathrm{ABCD} \) is a rectangle.Solution:(i) Let $AC$ and $BD$ be two chords of a circle which bisect each ... Read More