, Useful for CBSE Exams 2024-25
Unit I - Relations & Functions
Relations & Functions, Inverse Trig. Functions
Q01. In two different societies, there are some school going students - including girls as well as boys.
Satish forms two sets with these students, as his college project.
Let A a1 , a 2 , a 3 , a 4 , a 5 and B b1 , b2 , b3 , b4
where a i ’s and bi ’s are the school going students of
first and second society respectively.
Satish decides to explore these sets for various types
of relations and functions.
Using the information given above, answer the following.
(i) Satish wishes to know the number of reflexive relations defined on set A. How many
such relations are possible?
(ii) Let R : A A , where R {(x, y) : x and y are students of same sex} . Is the relation R
an equivalence relation? Justify.
(iii) Satish and his friend Rajat are interested to know the number of symmetric relations
defined on both the sets A and B, separately. Satish decides to find the symmetric
relation on set A, while Rajat decides to find the symmetric relation on set B. What is
difference between their results?
(iv) Let R : A B , R {(a1 , b1 ), (a1 , b 2 ), (a 2 , b1 ), (a 3 , b 3 ), (a 4 , b 2 ), (a 5 , b 2 )} . Then, is R onto
or one-one or both or none? Justify.
(v) To help Satish in his project, Rajat decides to form onto function from set A to B. How
many such functions are possible?
Q06. Rahul and Priyam are students of class XII.
They are standing on either side of a light-house of 20 meters high.
Rahul is standing at A and Priyam is at C. They observe its top at the angles of elevation and
respectively (as shown in the figure below).
512 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics
, YouTube channel - Mathematicia By O.P. Gupta theopgupta.com
The distance between the two students is 30 meters and the distance between Rahul and the
light-house is 20 meters.
Based on the above information, answer the following.
(i) Find CAB.
(ii) Find the distance AB (as shown in the figure).
(iii) Find BCA.
(iv) Find ABC.
Q07. A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible
to vote and voter turnout was about 67%, the highest ever.
ONE - NATION
ONE - ELECTION
FESTIVAL OF DEMOCRACY
GENERAL ELECTION - 2019
Let I be the set of all citizens of India who were eligible to exercise their voting right in general
election held in 2019. A relation ‘R’ is defined on I as follows.
R (V1 , V2 ) : V1 , V2 I and both use their voting right in general election - 2019 .
Based on the above information, answer the following.
(i) Two friends X and Y I .
X and Y both exercised their voting right in the general election - 2019.
Then, state if (X, Y) R is true or not. Give reason.
(ii) Mr. ‘H’ and his wife ‘W’ both exercised their voting right in general election - 2019.
Then, state if the following statement is true or not. Give reason.
“If (H, W) R then, we may or may not have (W, H) R .”
(iii) Check if R is reflexive or, symmetric. Give reasons to support your answer.
(iv) Mr. Ghanshyam exercised his voting right in general election - 2019.
While his brother (having voting right), Mr. Radheshyam went to have fun at a nearby
mall. Can we have (Ghanshyam, Radheshyam) R ? Give reason.
If Miss. Radhika (having voting right) goes with Mr. Radheshyam to the mall skipping
the voting exercise, then is it correct to say (Radhika, Radheshyam) R ? Give reason.
Unit II - Algebra
Matrices, Determinants
Q01. Two farmers Ramkrishna and Hari Prasad cultivated three varieties of rice namely Basmati,
Permal and Naura.
MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics 513
Unit I - Relations & Functions
Relations & Functions, Inverse Trig. Functions
Q01. In two different societies, there are some school going students - including girls as well as boys.
Satish forms two sets with these students, as his college project.
Let A a1 , a 2 , a 3 , a 4 , a 5 and B b1 , b2 , b3 , b4
where a i ’s and bi ’s are the school going students of
first and second society respectively.
Satish decides to explore these sets for various types
of relations and functions.
Using the information given above, answer the following.
(i) Satish wishes to know the number of reflexive relations defined on set A. How many
such relations are possible?
(ii) Let R : A A , where R {(x, y) : x and y are students of same sex} . Is the relation R
an equivalence relation? Justify.
(iii) Satish and his friend Rajat are interested to know the number of symmetric relations
defined on both the sets A and B, separately. Satish decides to find the symmetric
relation on set A, while Rajat decides to find the symmetric relation on set B. What is
difference between their results?
(iv) Let R : A B , R {(a1 , b1 ), (a1 , b 2 ), (a 2 , b1 ), (a 3 , b 3 ), (a 4 , b 2 ), (a 5 , b 2 )} . Then, is R onto
or one-one or both or none? Justify.
(v) To help Satish in his project, Rajat decides to form onto function from set A to B. How
many such functions are possible?
Q06. Rahul and Priyam are students of class XII.
They are standing on either side of a light-house of 20 meters high.
Rahul is standing at A and Priyam is at C. They observe its top at the angles of elevation and
respectively (as shown in the figure below).
512 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics
, YouTube channel - Mathematicia By O.P. Gupta theopgupta.com
The distance between the two students is 30 meters and the distance between Rahul and the
light-house is 20 meters.
Based on the above information, answer the following.
(i) Find CAB.
(ii) Find the distance AB (as shown in the figure).
(iii) Find BCA.
(iv) Find ABC.
Q07. A general election of Lok Sabha is a gigantic exercise. About 911 million people were eligible
to vote and voter turnout was about 67%, the highest ever.
ONE - NATION
ONE - ELECTION
FESTIVAL OF DEMOCRACY
GENERAL ELECTION - 2019
Let I be the set of all citizens of India who were eligible to exercise their voting right in general
election held in 2019. A relation ‘R’ is defined on I as follows.
R (V1 , V2 ) : V1 , V2 I and both use their voting right in general election - 2019 .
Based on the above information, answer the following.
(i) Two friends X and Y I .
X and Y both exercised their voting right in the general election - 2019.
Then, state if (X, Y) R is true or not. Give reason.
(ii) Mr. ‘H’ and his wife ‘W’ both exercised their voting right in general election - 2019.
Then, state if the following statement is true or not. Give reason.
“If (H, W) R then, we may or may not have (W, H) R .”
(iii) Check if R is reflexive or, symmetric. Give reasons to support your answer.
(iv) Mr. Ghanshyam exercised his voting right in general election - 2019.
While his brother (having voting right), Mr. Radheshyam went to have fun at a nearby
mall. Can we have (Ghanshyam, Radheshyam) R ? Give reason.
If Miss. Radhika (having voting right) goes with Mr. Radheshyam to the mall skipping
the voting exercise, then is it correct to say (Radhika, Radheshyam) R ? Give reason.
Unit II - Algebra
Matrices, Determinants
Q01. Two farmers Ramkrishna and Hari Prasad cultivated three varieties of rice namely Basmati,
Permal and Naura.
MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics 513
