9th Standard Syllabus & Materials
9th Standard
TN 9ஆம் வகுப்பு கணிதம் ஆயத்தொலை வடிவியல்,முக்கோணவியல் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Maths Coordinate Geometry,Trigonometry Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers
NEW9th Standard
TN 9ஆம் வகுப்பு கணிதம் அளவியல்,புள்ளியியல்&நிகழ்தகவு முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Maths Mensuration,Statistics&Probability Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - செவ்வியல் உலகம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Classical World Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - தொடக்ககாலத் தமிழ்ச் சமூகமும் பண்பாடும்முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Early Tamil Society and Culture Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - தொழிற்புரட்சி முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Industrial Revolution Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - நவீன யுகத்தின் தொடக்கம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Beginning of the Modern AgeImportant 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
Published on: 25/09/2019
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Download Tamil Nadu 9th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
State the formula to find \(n\left( A\cup B\cup C \right) \)
2.
State Associative property of sets.
3.
If A = {0, 2, 4, 6, 8}, B = {x : x is a prime number and x < 11} and C = {x : x ∈ N and 5 ≤ x < 9} then verify \(A\cup (B\cap C)=(A\cup B)\cap (A\cup C)\).
4.
If A = {p, q, r, s}, B = {m, n, q, s, t} and C = {m, n, p, q, s}, then verify the associative property of union of sets.
5.
If P = {1,2,5,7,9}, Q = {2, 3, 5, 9, 11}, R = {3, 4,5 7, 9} and S = {2, 3, 4, 5, 8}, then find
(i) \((P\cup Q)\cup R\)
(ii) \((P\cap Q)\cap S\)
(iii) \((Q\cap S)\cap R\)
6.
If A = {2, 3, 4, 5}, B = {2, 3, 5, 7} and C = {1, 3, 5}, then verify \(A\cup (B\cup C)=(A\cup B)\cup C\).
7.
If A = {2,5,6,7} and B = {3,5,7,8}, then verify the commutative property of union sets
8.
If A = {-2,0,1,3,5}, B = {-1,0,2,5,6} and C = {-1,2,5,6,7} then show that A-(BUC) = (A-B)∩(A-C).
9.
If P = {x : x\(\in \)W and 0 < x < 10} Q = {x : x = 2n+1, n\(\in \)W and n < 5} and R = {2, 3, 5, 7, 11, 13} then verify P −(Q ⋂ R) = (P − Q) U (P − R).
10.
Verify \((A\cap B)'=A'\cup B'\) using Venn diagrams.
11.
Verify \(A-(B\cap C)=(A-B)\cup (A-C)\)using Venn diagrams.
12.
If A = {11,13,14,15,16,18}, B = {11,12,15,16,17,19}, and C = {13,15,16,17,18,20}, then verify \(A\cap (B\cup C)=(A\cap B)\cup (A\cap C)\).
13.
Verify A∩(B∪C)=(A∩B)∪(A∩C) using Venn diagrams.
14.
A survey of 1000 farmers found that 600 grew paddy, 350 grew ragi, 280 grew corn, 120 grew paddy and ragi, 100 grew ragi and corn, 80 grew paddy and corn. If each farmer grew atleast any one of the above three, then find the number of farmers who grew all the three.
15.
If A = {x : x = 6n, n\(\in \)W and n < 6}, B = {x : x = 2n, n \(\in \)N and 2 < n ≤ 9} and C = {x : x = 3n, n\(\in \)N and 4n ≤ n < 10}, then show that \(A-(B\cap C)=(A-B)\cup (A-C)\).
16.
\(n(A\cup B\cup C)\)=________
n(A) + n(B) + n(C)
n(A) + n(b) + n(C) -\(n\left( A\cap B\cap C \right) \)
\(n\left( A\cap B\cap C \right) \)
n(A) + n(B) + n(C) -\(n\left( A\cap B \right) \)-\(n\left( B\cap A \right) -n\left( A\cap C \right) +n\left( A\cap B\cap C \right) \)
17.
If A,B,C are non-overlapping sets, then n \(\left( A\cap B\cap C \right) \) is ___________
n(A) + n(B) + n(C)
\(n\left( A\cup B\cup C \right) \)
0
\(n\left( A\cap B \right) \)
18.
For any three A, B and C, \(A-\left( B\cup C \right) \) ________
(A-B)\(\cup \)(A-C)
(A-B)\(\cap \)(A\(\cup \)C)
(A-B)\(\cup \)C
A\(\cup \)(B-C)
19.
If A and B are two non-empty sets, then (A-B)U(A⋂B) is _____________
A
B
ф
U
20.
If n(A U B U C) = 100, n(A) = 4x, n(B) = 6x, n(C) = 5x, n(A ∩ B) = 20, n(B ⋂C) = 15, n(A C) = 25 and n(A ⋂ B ⋂ C) = 10 , then the value of x is ________.
10
15
25
30
21.
Which of the following is true?
A-B = A\(\cap \)B
A−B = B −A
(A\(\cup \)B)' = A'\(\cup \)B'
(A\(\cap \)B)' = A'\(\cup \)B'
22.
If U = {x : x\(\in \)N and x<10}, A = {1, 2, 3, 5, 8} and B = {2, 5, 6, 7, 9}, then n[(A∪B)′] is ________.
1
2
4
8
1.
\(n\left( A\cup B\cup C \right) \)= n(A) + n(B) + n(C) - \(n\left( A\cap B \right) -\left( B\cap C \right) -n\left( A\cap C \right) +\left( A\cap B\cap B \right) \)
2.
For any three sets A, B and C
(i) \(A\cap \left( B\cap C \right) =\left( A\cap B \right) \cap C\)
(ii) \(A\cup \left( B\cup C \right) =\left( A\cup B \right) \cup C\)
3.
Given A = {0, 2, 4,6, 8} , B = {2, 3, 5, 7} and C = {5, 6, 7, 8}
First, we find \(B\cap C\) = {5, 7} ,\(A\cup (B\cap C)\) = {0, 2, 4, 5, 6, 7, 8} .......... (1)
Next, \(A\cup B\) = {0,2,3,4,5,6,7, 8}, \(A\cup C\) = {0, 2, 4, 5, 6, 7, 8}
Then, \((A\cup B)\cap (A\cup C)\) = {0, 2, 4, 5, 6, 7, 8} .............(2)
From (1) and (2), it is verified that \((A\cup \left( B\cap C \right) =(A\cup B)\cap (A\cup C)\).
4.
Associative Property of union of sets
AU(BUC) = (AUB)UC
BUC = {m, n, q, s, t} U {m, n, p, q, s} = {m, n, p, q, s, t}
AU(BUC) = {p, q, r, s} U {m, n, p, q, s, t} = {m, n, p, q, r, s, t} ...(1)
(AUB) = {p, q, r, s} U {m, n, q, s, t} = {p, q, r, s, m, n, t}
(AUB)UC = {p, q, r, s, m, n, t} U {m, n, p, q, s} = {p, q, r, s, m, n, t}...(2)
From (1) & (2)
It is verified that AU(BUC) =( AUB)UC
5.
(i) (P∪Q)∪R
(P∪Q) = {1, 2, 5, 7, 9} U {2, 3, 5, 9, 11} = {1,2,3,5,7,9,11}
(P∪Q)∪R = {1,2,3,5,7,9,11} U {3,4,5,7,9} = {1,2,3,4,5,7,9,11}
(ii) (P⋂Q)⋂S
(P⋂Q) = {1,2,5,7,9} ⋂ {2,3,5,9,11} = {2,5,9}
(P⋂Q)⋂S = {2,5,9} ⋂ {2,3,4,5,8} = {2,5}
(iii) (Q⋂S)⋂R
(Q⋂S) = {2,3,5,9,11} ⋂ {2,3,4,5,8} = {2,3,5}
(Q⋂S)⋂R = {2,3,5} ⋂ {3,4,5,7,9} = {3,5}
6.
Given, A = {2, 3, 4, 5},B = {2, 3, 5,7} and C = {1, 3, 5}
Now, \(B\cup C\) = {1,2, 3,5,7}
\(A\cup (B\cup C)\) ={1, 2, 3, 4, 5, 7} .....(1)
Then, \(A\cup B\) = {2, 3, 4,5,7}
\((A\cup B)\cup C\) = {1,2, 3, 4, 5, 7} ...(2)
From (1) and (2), it is verified that \(A\cup (B\cup C)\) = \((A\cup B)\cup C\).
7.
Given, A = {2,5,6,7} and B = {3,5,7,8}
\(A\cup B\) = {2,3,5,6,7,8} ...........(1)
\(B\cup A\) = {2,3,5,6,7,8} ..............(2)
8.
A = {-2,0,1,3,5}, B = {-1,0,2,5,6}
C = {-1,2,5,6,7}
BUC = {-1,0,2,5,6,7}
A-(BUC) = {-2,1,3}.............(1)
(A-B) = {-2,1,3}
(A-C) = {-2,0,1,3}
(A-B)∩(A-C) = {-2,1,3}............(2)
From (1) and (2), it is verified that
A-(BUC) = (A-B)⋂(A-C)
9.
The roster form of sets P, Q and R are
P = {1,2, 3, 4,5,6,7,8,9}, Q = {1, 3,5,7,9} and R = {2, 3, 5,7,11,13}
First, we find (Q ⋂ R) = {3, 5, 7}
Then, P −(Q ⋂ R) = {1, 2, 4 ,6, 8, 9}........ (1)
Next, P–Q = {2, 4, 6, 8} and P–R = {1, 4, 6, 8, 9}
and so, (P −Q) U (P −R) = {1,2, 4, 6, 8, 9}............ (2)
Hence from (1) and (2), it is verified that P −(Q ∩ R) = (P −Q) U (P −R).
Finding the elements of set Q
Given, x = 2n + 1
n = 0 ⟶ x = 2(0) + 1 = 0 + 1 = 1
n = 1 ⟶ x = 2(1) + 1 = 2 + 1 = 3
n = 2 ⟶ x = 2(2) + 1 = 4 + 1 = 5
n = 3 ⟶ x = 2(3) + 1 = 6 + 1 = 7
n = 4 ⟶ x = 2(4) + 1 = 8 + 1 = 9
Therefore, x takes values such as 1, 3, 5, 7 and 9.
10.
(2)=(5)
ஃ (A∩B)'=A'UB'
11.
ஃ A-(B∩C)=(A-B)U(A-C)
Hence it is proved.
12.
A = {11,13,14,15,16,18}
B = {11,12,15,16,17,19}, C = {13,15,16,17,18,20}
(BUC) = {11,12,13,15,16,17,18,19,20}
A⋂(BUC) = {11,13,14,15,16,18}⋂{11,12,13,15,16,17,18,19,20}
= {11,13,15,16,18}...(1)
A⋂B = {11,15,16}; A⋂C = {13,15,16,18}
(A⋂B)U(A⋂C) = {11,13,15,16,18}...(2)
From (1) and (2) it is verified that A⋂(BUC) = (A⋂B)U(A⋂C).
13.
From (1) and (2), \(A\cap (B\cup C)=(A\cap B)\cup (A\cap C)\) is verified.
14.
a = 600 - (120 -x + x + 80 -x)
= 600 - (200 -x)
= 600 - 200 + x = 400 + x
b = 350 - (120 -x + x + 100 -x)
= 350 - (220 - x)
= 350 - 230 + x = 130 + x
c = 280 - (80 - x + x + 100 - x)
2800 - (180 -x)
= 280 - 180 + x = 100 + x
Each farmer grew atleast one of the above three, the number of farmers who grew all the three is x.
= a + b + c + 120 - x + 100 - x + 80 - x + x = 1000
400 + x + 130 + x + 100 + x + 120 - x + 100 - x + 80 - x + x = 1000
ஃ 930 + x = 1000
x = 1000 - 930 = 70
ஃ 70 farmers grew all the three crops.
15.
A = {x : x = 6n, n ∈ W, n < 6}
x = 6n
n = {0,1,2,3,4,5}
x = 6 \(\times\) 0 = 0
x = 6 \(\times\) 1 = 6
x = 6 \(\times\) 2 =12
x = 6 \(\times\) 3 =18
x = 6 \(\times\) 4 = 24
x = 6 \(\times\) 5 = 30
ஃ A = {0,6,12,18,24,30}
B = {x : x = 2n, n∈N, 2
x = 2n
x = 2 \(\times \) 3 = 6;
2\(\times\)4 = 8;
2 \(\times\)5 = 10
2 \(\times\)6 = 12
2\(\times\) 7 = 14
2 \(\times\)8 = 16
2 \(\times\)9 = 18
ஃ B = {6,8,10,12,14,16,18}
C = {x : x = 3n, n∈N, 4 ≤ n < 10
N = {4,5,6,7,8,9}
x = 3\(\times\)4 = 12
x = 3 \(\times\) 5 = 15
x = 3 \(\times\) 6 = 18
x = 3 \(\times\) 7 = 21
x = 3 \(\times\) 8 = 24
x = 3 \(\times\) 9 = 27
x = 2 \(\times\) 9 = 18
ஃ C = {12,15,18,21,24,27}
A-(B⋂C) = (A-B)U(A-C)
L.H.S = R.H.S
B⋂C = {12,18}
A-(B⋂C) = {0,6,12,18,24,30} - {12,18}
= {0,6,24,30} .........(1)
(A-B) = {0,24,30}
(A-C) = {0,6,30}
(A-B)U(A-C) = {0,6,24,30} .........(2)
From (1) and (2), it is verified that
A-(B⋂C) = (A-B)U(A-C).
16.
(d)
n(A) + n(B) + n(C) -\(n\left( A\cap B \right) \)-\(n\left( B\cap A \right) -n\left( A\cap C \right) +n\left( A\cap B\cap C \right) \)
17.
(c)
0
18.
(b)
(A-B)\(\cap \)(A\(\cup \)C)
19.
(a)
A
20.
(a)
10
21.
(d)
(A\(\cap \)B)' = A'\(\cup \)B'
22.
(a)
1
9th Standard Syllabus & Materials
9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - பண்டைய நாகரிகங்கள் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Ancient . Civilisations Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - புரட்சிகளின் காலம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - The Age of Revolutions Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - இடைக்கால இந்தியாவில் அரசும் சமூகமும் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - State and Society in Medieval India Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
NEW9th Standard
TN 9ஆம் வகுப்பு சமூக அறிவியல் வரலாறு - ஆசிய ஆப்பிரிக்க நாடுகளில் காலனியாதிக்கம் முக்கியமான 2,3,&5 மதிப்பெண் வினாக்கள் விடைகளுடன் TN 9th Social Science HIS - Colonialism in Asia and Africa Important 1 Mark Questions with Answers 2,3,&5 Marks Questions with Answers.
Tamilnadu Stateboard 9th Standard Subjects
Tamilnadu Stateboard Standards
