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XII (12) HSC

XI (11) FYJC
X (10) SSC

Question 1 :

Find the cardinal number of the following sets.

(i) M = {p, q, r, s, t, u}

Solution :

Number of elements in the set is 6. Hence n(M)  =  6.

(ii) P = {x : x = 3n + 2, n∈W and x < 15}

Solution :

Since n belongs to whole number, we have to start with 0.

By applying the values of n from 0 to 14, we get 15 different values for x. Hence n(P) is 15.

(iii) Q = { y : y = 4/3n, n ∈ N and 2 < n ≤ 5}

Solution :

The values of n are 3, 4, 5. By applying the above three values for n, we get different values of y. Hence n(Q) is 3.

(iv) R = {x : x is an integers, x ∈ Z and –5 ≤ x < 5}

Solution :

The elements of R are

R  =  {-5,-4, -3, -2, -1, 0, 1, 2, 3, 4}

n(R)  =   10

(v) S = The set of all leap years between 1882 and 1906.

Solution :

The leap years 1884, 1888, 1892, 1896, 1900, 1904.

Hence n(S)  =  6

## Finite Set and Infinite Set

Finite set :

A set with finite number of elements is called a finite set.

Infinite set :

A set which has infinite number of elements is called an infinite set.

Question 2 :

Identify the following sets as finite or infinite.

(i) X = The set of all districts in Tamilnadu.

Solution :

Districts in Tamilnadu is countable. Hence it is finite set.

(ii) Y = The set of all straight lines passing through a point.

Solution :

We may draw an infinite number of lines through a point.

Hence it is infinite set.

(iii) A = { x : x ∈ Z and x < 5}

Solution :

Z means integers. The elements of A are 1, 2, 3, 4.

Hence set A is finite.

(iv) B = {x : x2–5x+6 = 0, x ∈N}

Solution :

x2–5x+6 = 0

(x - 2) (x - 3)  =  0

x  =  2 and x  =  3

By solving the quadratic equation, we get two different values. Hence B is finite set.

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SUBJECTS

HINDI ENTIRE PAPER SOLUTION

MARATHI PAPER SOLUTION
SSC MATHS I PAPER SOLUTION
SSC MATHS II PAPER SOLUTION
SSC SCIENCE I PAPER SOLUTION
SSC SCIENCE II PAPER SOLUTION
SSC ENGLISH PAPER SOLUTION
SSC & HSC ENGLISH WRITING SKILL
HSC ACCOUNTS NOTES
HSC OCM NOTES
HSC ECONOMICS NOTES
HSC SECRETARIAL PRACTICE NOTES

2019 Board Paper Solution

HSC ENGLISH SET A 2019 21st February, 2019

HSC ENGLISH SET B 2019 21st February, 2019

HSC ENGLISH SET C 2019 21st February, 2019

HSC ENGLISH SET D 2019 21st February, 2019

SECRETARIAL PRACTICE (S.P) 2019 25th February, 2019

HSC XII PHYSICS 2019 25th February, 2019

CHEMISTRY XII HSC SOLUTION 27th, February, 2019

OCM PAPER SOLUTION 2019 27th, February, 2019

HSC MATHS PAPER SOLUTION COMMERCE, 2nd March, 2019

HSC MATHS PAPER SOLUTION SCIENCE 2nd, March, 2019

SSC ENGLISH STD 10 5TH MARCH, 2019.

HSC XII ACCOUNTS 2019 6th March, 2019

HSC XII BIOLOGY 2019 6TH March, 2019

HSC XII ECONOMICS 9Th March 2019

SSC Maths I March 2019 Solution 10th Standard11th, March, 2019

SSC MATHS II MARCH 2019 SOLUTION 10TH STD.13th March, 2019

SSC SCIENCE I MARCH 2019 SOLUTION 10TH STD. 15th March, 2019.

SSC SCIENCE II MARCH 2019 SOLUTION 10TH STD. 18th March, 2019.

SSC SOCIAL SCIENCE I MARCH 2019 SOLUTION20th March, 2019

SSC SOCIAL SCIENCE II MARCH 2019 SOLUTION, 22nd March, 2019

XII CBSE - BOARD - MARCH - 2019 ENGLISH - QP + SOLUTIONS, 2nd March, 2019

HSC Maharashtra Board Papers 2020

(Std 12th English Medium)

HSC ECONOMICS MARCH 2020

HSC OCM MARCH 2020

HSC ACCOUNTS MARCH 2020

HSC S.P. MARCH 2020

HSC ENGLISH MARCH 2020

HSC HINDI MARCH 2020

HSC MARATHI MARCH 2020

HSC MATHS MARCH 2020

SSC Maharashtra Board Papers 2020

(Std 10th English Medium)

English MARCH 2020

HindI MARCH 2020

Hindi (Composite) MARCH 2020

Marathi MARCH 2020

Mathematics (Paper 1) MARCH 2020

Mathematics (Paper 2) MARCH 2020

Sanskrit MARCH 2020

Important-formula

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