10th Standard Syllabus & Materials
10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Population, Transport, Communication and Trade Important Questions And Answers Study Material - QB365 Set C
NEW10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Population, Transport, Communication and Trade Important Questions And Answers Study Material - QB365 Set B
NEW10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Population, Transport, Communication and Trade Important Questions And Answers Study Material - QB365 Set A
NEW10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Resources and Industries Important Questions And Answers Study Material - QB365 Set C
NEW10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Resources and Industries Important Questions And Answers Study Material - QB365 Set B
NEW10th Standard
Tamilnadu 10th Standard Social Science GEO - India - Resources and Industries Important Questions And Answers Study Material - QB365 Set A
Published on: 13/05/2022
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Questions + Answers key
Take MCQ Maths Test1.
If A = {1,3,5} and B = {2,3} then
(i) find A x B and B x A
(ii) Is A x B = B x A? If not why?
(iii) Show that n(A x B) = n(B x A) = n(A) x n(B)
2.
If A x B = {(3,2), (3, 4), (5,2), (5, 4)} then find A and B.
3.
Find A x B, A x A and B x A
A = {2, -2, 3} and B = {1,-4}
4.
Let A = {3,4,7,8} and B = {1,7,10}. Which of the following sets are relations from A to B?
R1 = {(3,7), (4,7), (7,10), (8,1)}
5.
The arrow diagram shows a relationship between the sets P and Q. Write the relation in
(i) Set builder form
(ii) Roster form
(iii) What is the domain and range of R.
6.
Let X = {3, 4, 6, 8}. Determine whether the relation R = {(x, f(x)) | x \(\in \) X, f(x) = x2 + 1}. is a function from X to N?
7.
Let f(x) = 2x + 5. If x ≠ 0 then find \(\frac { f(x+2)-f(2) }{ x } \).
8.
A function f is defined by f(x) = 3 - 2x. Find x such that f(x2) = (f(x))2.
9.
A plane is flying at a speed of 500 km per hour. Express the distanced travelled by the plane as function of time t in hours.
10.
Using vertical line test, determine which of the following curves (Fig.1.18(a), 1.18(b), 1.18(c), 1.18(d)) represent a function?
1.
Given that A = {1,3,5} and B = {2,3}
(i) A x B = {1,3,5} x {2,3} = {(1,2), (1,3), (3,2), (3,3), (5,2), (5,3)} ...(1)
B x A = {2,3} x {1,3,5} = {(2,1), (2,3), (2,5), (3,1), (3,3), (3,5)} ...(2)
(ii) From (1) and (2) we conclude that A x B ≠ B x A as (1,2) ≠ (2,1) and (1,3) ≠) (3,1). etc
(iii) n(A) = 3; n (B) = 2.
From (1) and (2) we observe that, n (A x B) = n (B x A) = 6;
we see that, n(A) x n(B) = 3 x 2 = 6 and n (B) x n (A) = 2 x 3 = 6
Hence, n (A x B) = n (B x A) = n(A) x n(B) = 6.
Thus, n(A x B) = n (B x A) = n(A) x n(B).
2.
A x B = {(3,2), (3,4), (5,2), (5,4)}
We have A = {set of all first coordinates of elements of A x B}. Therefore, A = {3,5}
B = {set of all second coordinates of elements of A x B}. Therefore, B = {2,4}
Thus A = {3,5} and B = {2,4}.
3.
Given A = {2, – 2, 3}, B = {1, – 4}.
A x B = {2,-2,3) x {1 ,-4}
= {(2, 1), (2, - 4), (- 2, 1), (- 2, - 4), (3, 1), (3, - 4)}
A x A = {2,-2,3} x {2,-2,3}
= {(2,2), (2, - 2), (2,3), (-2,2), (- 2, - 2), (- 2,3),(3,2),(3, - 2), (3, 3)}
B x A = {1, -4} x {2, -2, 3}
= {(1,2),(1, -2 ),(1, 3)}, (- 4, 2), (- 4, - 2), (- 4, 3)}
4.
A x B = {(3,1), (3,7), (3,10), (4,1), (4,7), (4,10), (7,1), (7,7), (7,10), (8,1), (8,7), (8,10)}
We note that, R1 ⊆ A x B. Thus, R1 is a relation from A to B.
5.
(i) Set builder form of R = ((x, y) | y = x - 2, x \(\in \) P, y \(\in \) Q}
(ii) Roster form R = {(5 , 3),(6 , 4)(7 , 5)}
(iii) Domain of R = {5, 6, 7} and range of R = {3, 4, 5}
6.
Given X = {3, 4, 6, 8}
Relation R = {(x, f(x)) | x \(\in \) X, f(x) = x2 + 1}
When x = 3 ⇒ f(x) = f(3)2 = 9 + 1 = 10 \(\in \) N
When x = 4 ⇒ f(x) = f(4)2 = 16 + 1 = 17 \(\in \) N
When x = 6 ⇒ f(x) = f(6)2 = 36 + 1 = 37 \(\in \) N
When x = 8 ⇒ f(x) = f(8)2 = 64 + 1 = 65 \(\in \) N
R = {(3, 10), (4, 17), (6, 37), (8, 65)}
Since, all the elements of X are having natural numbers as images, it is a function from X to N.
7.
f(x) = 2x + 5, x ≠ 0.
\(\frac{f(x+2)-f(2)}{x} =\frac{[2(x+2)+5]-[2(2)+5]}{x} \)
\(=\frac{2 x+4+5-9}{x}=\frac{2 x+9-9}{x} \)
\(=\frac{2 x}{x}=2\)
8.
f(x) = 3 - 2x
Given f (x2) = [f (x)]2
3 - 2x2 = (3 - 2x)2
3 - 2x2 = 9 - 12x + 4x2
6x2 - 12x + 6 = 0
6(x2 - 2x + 1) = 0
(x - 1)2 = 0
x = 1
9.
Let the distance be 'd'
Speed = 500 km/hr
Time = 't' hours
Distance = Time x Speed
d(t) = 500 t
10.
The curves in Fig.1.18(a) and Fig.1.18(c) do not represent a function as the vertical lines meet the curves in two points P and Q.
The curves in Fig.1.18(b) and Fig.1.18(d) represent a function as the vertical lines meet the curve in at most one point.
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Tamilnadu 10th Standard Social Science GEO - Climate and Natural Vegetation of India Important Questions And Answers Study Material - QB365 Set B
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Tamilnadu 10th Standard Social Science GEO - Climate and Natural Vegetation of India Important Questions And Answers Study Material - QB365 Set A
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Tamilnadu Stateboard 10th Standard Subjects
Tamilnadu Stateboard Standards
