NCERT Practical Project Lab Manual Mathematics Class 12 with Viva-Voce - Latest Edition for Board Examinations 2025-26 | Complete Study Course | NCERT | CBSE Board | State Board Exam Book | School Textbook | Exam Preparations Book 2025-26 | Competitive Exam Books 1 Edition  (Paperback, Dr. R.D. Sharma, Er. Meera Goyal)

ACTIVITIES 1 : To verify that the relation R in the set L of all lines in a plane, defined by R = {(l,m) : ^ m} is symmetric but neither reflexive nor transitive 2 : To verify that the relation R in the set L of all lines in a plane, defined by R = {(l, m) : l || m} is an equivalence relation 3 : To demonstrate a function which is not one-one but is onto 4 : To demonstrate a function which is one-one but not onto 5 : To draw the graph of sin–1 x, using the graph of sin x and demonstrate the concept of mirror reflection (about the line y = x) 6 : To explore the principal value of the function sin–1 x using a unit circle 7 : To sketch the graph of ax and loga x, a > 0, a # 1 and to examine that they are mirror images of each other 8 : To establish a relationship between common logarithm (to the base 10) and natural logarithm (to the base e) of the number x 9 : To find analytically the limit of a function f (x) at x = c and also to check the continuity of the function at that point 10 : To verify that for a function f to be continuous at given point x0, Dy = | f (x0 + Dx) – f (x0)| is arbitrarily small, provided Dx is sufficiently small 11 : To verify Rolle’s Theorem 12 : To verify Lagrange’s Mean Value Theorem 13 : To understand the concepts of decreasing and increasing functions 14 : To understand the concepts of local maxima, local minima and point of inflection 15 : To understand the concepts of absolute maximum and minimum values of a function in a given closed interval through its graph 16 : To construct an open box of maximum volume from a given rectangular sheet by cutting equal squares from each corner 17 : To find the time when the area of a rectangle of given demensions become maximum, if the length is decreasing and the breadth increasing at given rates 18 : To verify that amongst all the rectangles of the same perimeter, the square has the maximum area 19 : To evaluate the definite integral òba Ö(1 – x2) dx as the limit of a sum and verify it by actual integration 20 : To verify geometrically that c × (a + b) = c × a + c × b 21 : To verify that angle in a semi-circle is a right angle, using vector method 22 : To locate the points to given coordinates in space, measure the distance between two points in space and then to verify the distance using distance formula 23 : To demonstrate the equation of a plane in normal form 24 : To verify that the angle between two planes is the same as the angle between their normal 25 : To find the distance of given point (in space) from a plane (passing through three non-collinear points) by actual measurement and also analytically 26 : To measure the shortest distance two skew-lines and verify it analytically 27 : To explain the computation of conditional probability of a given event A, when event B has already occurred, through an example of throwing a pair of dice PROJECTS 1 : To minimise the cost of the food, meeting the dietary requirements of the staple food of the adolescent students of your school 2 : Estimation of the population of a particular region/country under the assumptions that there is no migration in or out of the existing population in a particular year 3 : Finding the coordinates of different points identified in your classroom using the concepts of three dimensional geometry and also find the distances between the identified points 4 : Formation of differential equation to explain the process of cooling of boiled water to a given room temperature Log and Anti log