CBSE Maths Lab Manual Class 12 2026 Free PDF (Activities Observation Solutions)

Download CBSE Class 12 Maths Lab Manual 2026

There are a total of 20 experiments in the CBSE 12th maths lab manual. They can pick any 10 CBSE Class 12th maths experiments from these files and write them in their practical notebook. Students can directly click on the link to download the activity or experiment.

• CBSE Class 12 Maths Lab Manual Part 1: Download Now

• CBSE Class 12 Maths Lab Manual Part 2: Download Now

CBSE 12th Maths Lab Manual 2026: Experiments/Activity

The overall assessment for these activities is worth 10 marks. This is broken down into three components: 5 marks for the activities you perform and the upkeep of your record file; 3 marks for your performance on an end-of-year practical test; and 2 marks for the Viva-Voce, or oral examination.

CBSE 12th Maths Lab Manual: Activity 1

Objective: To demonstrate a function which is not one-one but is onto.

Material Required: Cardboard, nails, strings, adhesive and plastic strips.

Method of construction:

1. Paste a plastic strip on the left-hand side of the cardboard and fix three nails on it as shown in Fig.3.1. Name the nails on the strip as 1, 2 and 3.
2. Paste another strip on the right-hand side of the cardboard and fix two nails in the plastic strip as shown in Fig.3.2. Name the nails on the strip as a and b.
3. Join nails on the left strip to the nails on the right strip as shown in Fig. 3.3.

Demonstration:

1. Take the set X = {1, 2, 3}
2. Take the set Y = {a, b}
3. Join (correspondence) elements of X to the elements of Y as shown in Fig. 3.3

Observation:

1. The image of the element 1 of X in Y is __________. The image of the element 2 of X in Y is __________. 106 Laboratory Manual The image of the element 3 of X in Y is __________. So, Fig. 3.3 represents a __________ .
2. Every element in X has a _________ image in Y. So, the function is _________(one-one/not one-one).
3. The pre-image of each element of Y in X _________ (exists/does not exist). So, the function is ________ (onto/not onto).

Application: This activity can be used to demonstrate the concept of one-one and onto function.

CBSE 12th Maths Lab Manual: Activity 2

Objective: To verify Rolle’s Theorem

Material Required: A piece of plywood, wires of different lengths, white paper, sketch pen.

Method of construction:

1. Take a cardboard of a convenient size and paste a white paper on it.
2. Take two wires of convenient size and fix them on the white paper pasted on the plywood to represent x-axis and y-axis (see Fig. 11).
3. Take a piece of wire of 15 cm length and bend it in the shape of a curve and fix it on the plywood as shown in the figure.

4. Take two straight wires of the same length and fix them in such a way that they are perpendicular to the x-axis at the points A and B and meet the curve at the points C and D (see Fig.11).

Demonstration:

1. In the figure, let the curve represent the function y = f (x). Let OA = a units and OB = b units.
2. The coordinates of the points A and B are (a, 0) and (b, 0), respectively.
3. There is no break in the curve in the interval [a, b]. So, the function f is continuous on [a, b].
4. The curve is smooth between x = a and x = b which means that at each point, a tangent can be drawn which in turn gives that the function f is differentiable in the interval (a, b).
5. As the wires at A and B are of equal lengths, i.e., AC = BD, so f (a) = f (b).
6. In view of steps (3), (4) and (5), conditions of Rolle’s theorem are satisfied. From Fig.11, we observe that tangents at P as well as Q are parallel to the x-axis, therefore, f ′ (x) at P and also at Q are zero. Thus, there exists at least one value c of x in (a,b) such that f ′ (c) = 0. Hence, Rolle's theorem is verified.

Observation:

From Fig. 11. a = ______________, b = _____________ f (a) = ____________, f (b) = _________ Is f (a) = f (b) ? (Yes/No) Slope of tangent at P = __________, so, f (x) (at P) =

Application: This theorem may be used to find the roots of an equation.