The students who are appearing for CBSE Class 12th Mathematics Examination 2020 on March 17, 2020, can go through the below-mentioned important questions for Chapter 1- Relations and Functions. These Questions are based on the latest syllabus prescribed by the CBSE Board.

**Question 1- **Let *A = *[-1,1] , then, discuss whether the following functions defined on *A* are one-one onto or bijective.

(i) *f(x) = x/2*

(ii) *g(x) *= |x|

(iii) *h(x) *= x |x|

(iv) *k(x) *= x^{2}

**Answer:**(i) *f(x)* is one-one but not bijective.

(ii) *g(x)* is neither one-one nor bijective.

(iii) *h(x) *is one-one as well as bijective.

(iv) *k(x)* is neither one-one nor bijective.

**Question 2-**

**Answer: **(i) *R* is neither reflexive nor symmetric. *R *is transitive.

(ii) *R *is neither reflexive nor transitive.*R *is symmetric.

(iii)*R *is reflexive, transitive and symmetric.

(iv) *R* is neither reflexive nor symmetric. *R *is transitive.

**Question 3-**

**Answer:** (ii), (iv) are commutative.

**Question 4-** Let* a *={1*, 2, *3, ...,9} and *R* be the relation in *A× a *defined by (*a *, *b*)* R *(*c , d*)* *if* a *+* d = b *+* c *for (*a , b*)*, *(*c *, *d*)* *in* a *×* a *Prove that *R* is an equivalence relation and also obtain the equivalent class [(2, 5)].

** Answer: **The equivalence class containing [(2, 5)] is given by {(1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)}.

**Question 5- **

**Answer: **Since,, f(x) is both injective and surjective function.

Hence, f(x)is a bijective function.

**Question 6- **Given, *A*= {2,3,4} ; *B*= {2,5,6,7} . Construct an example of each of the following:

(i) an injective mapping from *a* to B.

(ii) a mapping from *a* to *b* which is not injective.

(iii) a mapping from *b* to *A*.

**Answer: (i) ***f *= {(2,5), (3,6), (4,7)}

**(ii) ***g ***= **{(2,2), (3,5), (4,5)}

**(iii) ***h = {(2,2), (5,3), (6,4), (7,4)}*

**Question 7- **Let *R* be relation defined on the set of natural number *N. *Find the domain and range of the relation. Also verify whether *R* is reflexive, symmetric and transitive.

**Answer: **The domain of the relation *R* is {1,2,3…., 20}

The range of the relation is {1,3, 5, 7,.…., 39}*R* is neither reflexive nor symmetric and nor transitive.

**Question 8- ** If * be binary operation defined on R by:

What will the operation * be?

**Answer: **Operation * is communicative but not associative.

**Question 9- **Let * be the binary operation defined on Q. Find which of the following binary operations are commutative.

**Answer:** (i) * is not commutative.

(ii) * is commutative.

(iii) * is not commutative.

(iv) * is commutative.

**Question 10- **Functions f ,g :R →R are defined, respectively, by f(x) = x^{2} + 3x +1, g(x) = 2x − 3, find

(i) *fog*

(ii) *gof*

(iii) *fof*

(iv) *gog*

**Answer: **(i) *fog = 4x ^{2} - 6x + 1*

(ii) *gof = 2x ^{2} + 6x - 1*

(iii) *fof = x ^{4} + 6x^{3} + 14x^{2} + 15x + 5*

(iv) *gog = 4x - 9 *

The students will find the above-mentioned questions helpful for the last minute preparation for CBSE Class 12th Mathematics Examination 2020. These important questions are based on the NCERT textbook, previous year papers and sample papers. The students can also check the links mentioned below:

**CBSE 12th Maths Board Exam 2020: Important Multiple Choice Questions (MCQs) with Answers**

**CBSE 12th Maths Board Exam 2020: Chapter-wise Important Questions & Answers**

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