Now in this topic, we will see a topic-wise introduction of all topics we are going to go through while framing Multiple-Choice Questions. The topics of class 12 maths include relations and sets, inverse trigonometric functions, matrices, etc. 

Class 12 Maths

Relations and Functions

 Now we will see some important points about Relations and Functions.

First, we will see what the relations is. To describe a relation, we take two sets A and B. Then we take the Cartesian product of these two sets which is denoted by A × B. Now the relation is the subset of this Cartesian Product. There are 8 types of Relations, Empty Relation, Universal Relation, Identity Relation, Inverse Relation, Reflexive Relation, Symmetric Relation, Transitive Relation, and Equivalence Relation.

Now we will see what a function is. Basically, a function is a relation in which one input gives only one output. That means that one value is related to only one other value.

Inverse Trigonometric Functions

As we know, there are six trigonometric functions, sin, cos, sec, cosec, tan and cotan. The inverse of these six trigonometric functions is known as Inverse Trigonometric Functions.

The Inverse Trigonometric Functions are represented by sin-1x, cos-1x, sec-1x, cosec-1x, tan-1x and cot-1x

Matrices: – 

A matrix may be described in simple words as an array that is written in a rectangular fashion. This rectangular array can consist of anything from numbers to variables and many other things. Now we will see a matrix to help us better understand this topic. 

[1    2

3    4]

The above matrix is a 2×2 matrix with four elements, 1, 2, 3, and 4

Determinants

Now that we know what a matrix is, we can move on to a determinant. A determinant may be described as a function of a particular square matrix. A square matrix is a matrix that has the same number of rows and columns.

A Particular Determinant A is represented by |A|. Now we will see how to find out the value of a Determinant.

Let’s consider a Determinant |A| =  | f         g

                                                                  h         i|

The value of such a Determinant |A|= (f*i)-(g*h)

Therefore |A|= fi-gh

Application of Derivatives

As we know that a Function is a special type of Relation that has only one output corresponding to one input. Now when we consider the change in the value of the output with respect to the change in the value of the input we get the derivative. A Derivative can be easily described as the change in the value of the output of a function with respect to the change in the value of the input of the function.

Application of Integrals

 Suppose when we draw a graph or a curve, the area under that curve or the graph is known as the Integral. The Integrals are of two types, Definite Integrals, and Indefinite Integrals.

Three-Dimensional Geometry

Geometry that happens in a three-dimensional space is known as Three-Dimensional Geometry. In three-dimensional geometry, the coordinates of a point are represented by three coordinates instead of two. These three coordinates are x, y, and z.

Linear Programming

When we have to find out the best-case scenario where the mathematical models are represented by linear relationships, we find that scenario by using linear programming.

Probability

In Mathematics, the Probability of an event describes the number of times that event will occur. The values of the probability of an event can range from 0 to 1.

Now we will see some multiple-choice questions related to the topics that we have discussed above.

Multiple-Choice Questions (MCQ) for class 12 maths

1. Consider a set A which has 8 elements and another set B which has 10 elements. Find out the one-one and onto mappings from A to B.

A. 80

B. 0

C. 256

D. 18

Soln. 

The answer will be B. This is because set A and set B have a different number of elements. What this means is that there will still be 2 elements left in set B. So it is not possible to have a one-one mapping from A to B.

2. Find the value of sin (x ) where |x|<1.

A. 1

B. 0

C. (x/ ((1+x2)) 

D. (x/ ((1- x2))

Soln. 

The answer is C. 

If we assume that x = a,

Then tan a = x =(x/1).

Writing the values for sin a and cos a,

sin a = (x/ ((1+x2)) 

cos a = (1/ ((1+x2))

So sin a = sin (x ) = (x/ ((1+x2))

3. If we consider a Matrix A. Let us assume that the matrix is skew-symmetric. Then the matrix A2 is?

A. Symmetric Matrix.

B. Skew-Symmetric Matrix

C. Null Matrix

D. None of the Above

Soln.

The answer is A. 

Given that matrix A is skew-symmetric. 

So applying the condition for skew-symmetry, A’=-A.

Now we try to find out the transpose of the Matrix A2.

(A2)’= (AA)’

(A2)’=A’A’

Now we already know that A’=-A, so substituting that,

(A2)’= (-A) (-A)

(A2)’=AA

(A2)’=A2

Therefore we infer that A2 is a Symmetric Matrix. 

Conclusion

We have discussed what we are really going to be doing on this topic. We discussed the topics in brief on which we are going to frame MCQs. We have talked about the topics of class 12 maths including the topic relations and sets, determinants, matrices, and many more. We have in brief talked about each topic to have a better understanding of what is covered in those topics. At last, we have given a few solved MCQs to understand the topics better.