JEE  >  Maths 35 Years JEE Main & Advanced Past year Papers  >  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Document Description: Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced for JEE 2022 is part of Maths 35 Years JEE Main & Advanced Past year Papers preparation. The notes and questions for Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced have been prepared according to the JEE exam syllabus. Information about Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced covers topics like and Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Example, for JEE 2022 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced.

Introduction of Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced in English is available as part of our Maths 35 Years JEE Main & Advanced Past year Papers for JEE & Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced in Hindi for Maths 35 Years JEE Main & Advanced Past year Papers course. Download more important topics related with notes, lectures and mock test series for JEE Exam by signing up for free. JEE: Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
1 Crore+ students have signed up on EduRev. Have you?

Q.1. An investigator interviewed 100 students to determine their preferences for the three drinks : milk (M), coffee (C) and tea (T). He reported the following : 10 students had all the three drinks M, C and T; 20 had M and C; 30 had C and T; 25 had M and T; 12 had M only; 5 had C only; and 8 had T only.
 Using a Venn diagram find  how many did not take any of the three drinks. (1978)

Ans. Sol. We have
n (U) = 100, where U stands for universal set
n (M ∩ C ∩ T) = 10; n (M ∩ C) = 20;.
n (C ∩ T) = 30; n (M ∩ T) = 25;
n (M only) = 12; n (only C) = 5;
n (only T) = 8
Filling all the entries we obtain the Venn diagram as shown :

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ n (M ∩ C ∪ T) = 12 + 10 + 5 + 15 + 10 + 20 + 8  = 80

∴ n (M ∪ C ∪ T)' = 100 – 80 = 20

 

 

Q.2. (a) Construct a triangle with base 9 cm and altitude 4 cm, the ratio of the other two sides being 2 : 1.
 (b) Construct a triangle in which the sum of the three sides is 15 cm with base angles 60° and 45°. Justify your steps.
 (1979)
 Ans. Sol. 
(a) To construct a Δ with base = 9 cm, altitude = 4 cm and ratio of the other two sides as  2 : 1.
Steps of Construction : 1. Draw BC = 9 cm
2. Divide BC internally at P and externally at Q in the ratio 2 : 1.

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

3. Draw a semicircle on PQ.
4. Draw a line || BQ at a distance of 4 cm from intersecting semicircle at A and A'.
5. ABC and A'BC are the required Δ's.
(b) To construct a Δ with perimeter = 15 cm, base angles 60° and 45°.
Steps of Construction :
1. Draw PQ = 15 cm

2. At P draw ∠RPQ = 60° and Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

and at Q draw ∠SQP = 45° and ∠YQP =Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

3. PX and QY meet each other at A.
4. Through A draw AB || PR and AC || QS.
5. ABC is the required Δ.
Justification: Q AB || PR and PA  transversal

∴∠PAB = ∠RPA = Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEx 60° = 30°

∠APB = ∠BAP = 30° ⇒ AB = PB

Similarly AC = CQ

∴ AB + BC + CA = PB + BC + CQ = 15 cm

Also ∠ABC = ∠RPB = 60°  and  ∠ACB = ∠SQS = 45°

 

 

Q.3. A tent is made in the form of a frustrum A of a right circular cone surmounted by another right circular cone B. The diameter of the ends of the frustrum A are 8 m and 4 m, its height is 3 m and the height of the cone B is 2 m. Find the area of the canvas required. (1979) 

Ans. Sol. Slant height of frustum Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Curved surface area of frustum =Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Also slant height of cone Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Curved surface area of cone  = Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ Area of canvas required = Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

 

 

Q.4. In calculating the mean and variance of 10 readings, a student wrongly used the figure 52 for the correct figure of 25. He obtained the mean and variance as 45.0 and 16.0 respectively. Determine the correct mean and variance. (1979)
 Ans. Sol. 
Let the remaining 9 readings be x1, x2, x3 ..... x9 and tenth is taken by the student as 52.

∴ Incorrect mean Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒ x+ x2 + ....+ x9 = 450 – 52 = 398

∴ Correct mean Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒ Correct mean = 42.3

Incorrect variance Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

= 111 + 90 × 398 – 9 × (45)2 = 17706 ...(2)

Correct variance  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEESubjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE= 43.81

 

 

Q.5. The diameter PQ of a semicircle is 6 cm. Construct a square ABCD with points A, B on the circumference, and the side CD on the diameter PQ. Describe briefly the method of con struction. (1980) 

Ans. Sol. The rough figure is as shown, let 2x be the side of square.
In ΔOBC r2 = x2 + 4x2

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Now on number line we locate M such that OM = Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Divide OM in five equal parts and take a point C on it such that OC : CM = 3 : 2. So, that Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Now, draw a line segment PQ = 6 cm whose mid-point is O.
From this cut a line segment Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE on opposite sides of O.

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

At C and B draw perpendiculars to PQ. With O as centre and OP as radius, draw a semicircle intersecting the perpendiculars draw at C & D at A and P respectively. Join AB. ABCD is the required square.

 

 

Q.6. C and D are any two points on the same side of a line L.
 Show how to find a point P on the line L such that PC and PD are equally inclined to the line L. Justify your steps. (1980)
 Ans. Sol. 
Here we are given two points C and D on the same side of line L. To find a point P on L such that PC and PD are equally inclined to L.
Steps of Construction : 1. From C draw CE ⊥ L  and produce it to C ' such that EC ' = EC.
2. Join C ' D intersecting L at P. Also join CP.
3. By simple geometry ∠1 = ∠2 and ∠2 = ∠3 ⇒ ∠1 = ∠3
∴ PC and PD are the required lines inclined equally to L.

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

 

 

Q.7. (i) Set A has 3 elements, and set B has 6 elements. What can be the minimum number of elements in the set A ∪ B? (1980) (ii) P, Q, R are subsets of a set A. Is the following equality true ?
 R × (Pc ∪ Qc)c = (R × P) ∩ (R × Q)? (1980)

(iii) For any two subset X and Y of a set A define X o Y = (Xc ∩ Y) ∪ (X ∩Yc) Then for any three subsets X, Y and Z of the set A, is the following equality true. (X o Y) o Z = X o (Y o Z)? (1980) 

Ans. Sol. (i) n (A) = 3, n (B)  = 6
We know that n (A ∪ B) ≥ max (n (A), n (B)) ⇒ n (A ∪ B) ≥ 6
∴ Min number of element that A ∪ B can have is 6.
(ii) Here R × (Pc ∪ Qc)c = R × (P ∩ Q) = (R × P) ∩ (R × Q)

∴ Given equality is true.

(iii) Yes

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE
Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

From (1) and (2) (X o Y) o Z = X o (Y o Z)

 

Q.8. Suppose A1, A2, ........ A30 are thirty sets each with five elements and B1, B2, ....... Bn  are n sets each with three elements. Let   Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE Assume that each element of S belongs to exactly ten of the Ai’ s and to exactly nine of the Bj’ s. Find n. (1981 - 2 Marks) 

Ans. Sol. We are given that  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE....(1)

Each A'is contain 5 elements, so Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE contains 5 × 30 = 150 elements (with repetition) out of which each element is repeated 10 times, (as given that each element of S belongs to 10 A'is)

∴ Number of different elements in Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE 

∴ From eqn (1) we can say S contains 15 elements...(2) Again each B'js contains 3 elements, so Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEcontains 3 × n = 3n elements (with repetition), out of which each element is repeated 9 times (as each element of S belongs to 9 B'js)

∴ No. of different elements in Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

∴ From eqn (1) we can say S contain n/3 elements....(3) From  (2) and (3) we get Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE=15 ⇒ n = 45

 

 

Q.9. The mean square deviations of a set of observations x1, x2, ....., xn about a points c is defined to be

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE The mean suqare deviations about –1 and +1 of a set of observatons are 7 and 3 respectively. Find the standard deviation of this set  of observations. (1981 - 2 Marks) 

Ans. Sol. Given that : Mean square deviation for the observations x1, x2, .... xn, about a point. c is given by  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE Also given that mean square deviations about – 1 and + 1 are 7 and 3 for a particular set of observations.

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE and  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEand  NOTE THIS STEP

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE...(1)

and Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE...(2)

Subtracting (2) from (1), we get

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Now standard deviation for same set of observations

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEESubjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

{using the given value}

 

 

Q.10. The marks obtained by 40 students are grouped in a frequency table in class intervals of 10 maks each. The mean and the variance obtained from this distribution are found to be 40 and 49 respectively. It was later discovered that two observations belonging to the class interval (21–30) were included in the class interval (31–40) by mistake. Find the mean and the variance after correcting the error. (1982 - 3 Marks) 

Ans. Sol. n = 40 Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE ....(1)

Also Var. = 49 =Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE 

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE2 x 1600 x 40 x 40

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE...(2)

Let 21 – 30 and 31 – 40 denote the kth and (k + 1)th class intervals respectively.
Then if before correction fk and fk+1 are the frequencies of these intervals then after correction (2 observations are shifted from 31 – 40 to 21 – 30), frequency of kth intervals becomes fk + 2 and frequency of (k + 1)th interval becomes fk+1 – 2.
Then, we get

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE= 40 – 0.5 = 39.5

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEESubjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

= 1649 – 3160 + 1560.25 = 49.25      [Using eqn. (1) and (2)]

 

 

Q.11. A relation R on the set of complex numbers is defined by z1 R z2 if and only if

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is real. Show that R is an equivalence relation. (1982 - 2 Marks)

Ans. Sol.  Given that Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is real.

To show that R is an equivalence relation.
Reflexivity : For z= z2 = z (say)

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE0 which is real

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE     ∴  R is reflexive.

Symmetric : Let z1 R z2Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is real Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEalso real

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEis real ⇒ z2 R z1 ⇒ R is symmetric.

Transitivity : Let z1 R z2 and z2 R z3

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEis real and  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE  is also real

Now, Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEEis real ⇒ Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE...(1)

Similarly,Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE...(2)

From (1) and (2) we get Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

⇒ Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE = 0 ⇒  Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is real
⇒ z1R z3 ∴ R is transitive.
Thus R is reflexive, symmetric and transitive.
Hence R is an equivalence relation.

The document Subjective Type Questions: Miscellaneous (Sets, Relations, Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE is a part of the JEE Course Maths 35 Years JEE Main & Advanced Past year Papers.
All you need of JEE at this link: JEE

Related Searches

Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

Sample Paper

,

Semester Notes

,

Free

,

MCQs

,

Extra Questions

,

past year papers

,

Exam

,

ppt

,

Relations

,

Summary

,

mock tests for examination

,

Objective type Questions

,

Subjective Type Questions: Miscellaneous (Sets

,

Previous Year Questions with Solutions

,

Viva Questions

,

Subjective Type Questions: Miscellaneous (Sets

,

study material

,

Relations

,

Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

Subjective Type Questions: Miscellaneous (Sets

,

Statistics & Mathematical | JEE Advanced Notes | Study Maths 35 Years JEE Main & Advanced Past year Papers - JEE

,

video lectures

,

Relations

,

pdf

,

practice quizzes

,

Important questions

,

shortcuts and tricks

;