Ncert Solutions Maths class 12th

We have,

R= $\{\left(a,b\right):a\le b^2\}$ is a relation in R.

For $a\in R$ then is $b=a,a\le a^2$ is not true for all real number less than 1.

Hence, R is not reflexive.

Let $\left(a,b\right)\in R$ and a=1 and b=2

Then, $a\le b^2$ = $1\le 2^2$ = $1\le 4$ so, $\left(1,2\right)\in R$

But $\left(b,a\right)=\left(2,1\right)$

i.e., $2\le 1^2$ = $2\le 1$ is not true

so, $\left(2,1\right)\notin R$

hence, R is no

(i) We have, $R=\{\left(x,y\right):3x-y=0\}$ a relation in set A= $\{1,2,3..........14\}$

For $x\in A,y=3x$ or $y\ne x$ i.e.,

$\left(x,x\right)$ does not exist in R

$\therefore$ R is not reflexive.

For $\left(x,y\right)\in R,y=3x$

Then $\left(y,x\right)x\ne 3y$

So $\left(y,x\right)\notin R$

$\therefore$ R is not symmetric

For $\left(x,y\right)\in R$ and $\left(y,z\right)\in R$ . We have

$y=3x$ and $z=3y$

Then $z=3\left(3x\right)=9x$

i.e., $\left(x,z\right)\notin R$

$\therefore$ R is not Transitive

(ii) We have,

R=

students can check the table for the principal values for all ITFs below;

To understand this, Assume you have a bucket that has infinite number of apples and if your mother asks "give me the apple". How will you figure out which one is "The Apple", she is asking for.

Similarly any inversre trigonometric functions behaves like a Many-one Function; which means,

For Exam

The Class 12 Relations and Functions explores various types of Functions, Students can check main types dicussed in this chapter below;

• One-One Function (Injective)

• Onto Function (Surjective)

• One-One and Onto Function (Bijective)

• Identity Function

• Constant Function

• Inverse of a Function

• Composite Functions

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NCERT Class 12 Determinants Solutions provide complete step-by-step solutions for all the questions of the chapter. Since NCERT Textbooks cover all types of questions commonly asked in board exams, So the NCERT Solution for Determinats also include all types of questions. Questions are asked in

Determinats and Matrices are generally combined as a unit in class 12 syllaus, Determinats and Matrices unit carries in general 10-12 marks weightage in the CBSE 12th boards. Specifically Determinant chapter carries weightage of around 6 marks in the actual exams.

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