Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Students can download Maths Chapter 1 Relations and Functions Unit Exercise 1 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Unit Exercise 1

Question 1.
If the ordered pairs (x2 – 3x, y2 + 4y) and (-2, 5) are equal, then find x and y.
Answer:
(x2 – 3x, y2 + 4y) = (-2, 5)
x2 – 3x = -2
x2 – 3x + 2 = 0
(x – 2) (x – 1) = 0
x – 2 = 0 or x – 1 = 0
x = 2 or 1
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 1
y2 + 4y = 5
y2 + 4y – 5 = 0
(y + 5) (y – 1) = 0
y + 5 = 0 or y – 1 = 0
y = -5 or y = 1
The value of x = 2, 1
and 7 = -5, 1
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 2

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 2.
The Cartesian product A × A has 9 elements among which (-1, 0) and (0, 1) are found. Find the set A and the remaining elements of A × A.
Solution:
A = {-1, 0, 1}, B = {1, 0, -1}
A × B = {(-1, 1), (-1, 0), (-1, -1), (0, 1), (0, 0), (0, -1), (1, 1), (1, 0), (1, -1)}

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 3.
Given that f(x) = \(\left\{\begin{array}{rl}
{\sqrt{x-1}} & {x \geq 1} \\
{4} & {x<1}
\end{array}\right.\).
Find
(i) f(0) (ii)f (3) (iii) f(a + 1) in terms of a.(Given that a > 0)
Answer:
f(x) = \(\sqrt { x-1 }\) ; f(x) = 4
(i) f(0) = 4
(ii) f(3) = \(\sqrt { 3-1 }\) = \(\sqrt { 2 }\)
(iii) f(a + 1) = \(\sqrt { a+1-1 }\) = \(\sqrt { a }\)

Question 4.
Let A = {9, 10, 11, 12, 13, 14, 15, 16, 17} and let f: A → N be defined by f(n) = the highest prime factor of n ∈ A. Write f as a set of ordered pairs and find the range of f.
Solution:
A = {9, 10, 11, 12, 13, 14, 15, 16, 17}
f: A → N
f(n) = the highest prime factor of n ∈ A
f = {(9, 3), (10, 5), (11, 11), (12, 3), (13, 13), (14, 7), (15, 5), (16, 2), (17, 17)}
Range = {3, 5, 11, 13, 7, 2, 17}
= {2, 3, 5, 7, 11, 13, 17}

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 5.
Find the domain of the function
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 3
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 4
Domain of f(x) = {-1, 0, 1}

Question 6.
If f(x)= x2, g(x) = 3x and h(x) = x – 2 Prove that (fog)oh = fo(goh).
Solution:
f(x) = x2
g(x) = 3x
h(x) = x – 2
(fog)oh = x – 2
LHS = fo(goh)
fog = f(g(x)) = f(3x) = (3x)2 = 9x2
(fog)oh = (fog) h(x) = (fog) (x – 2)
= 9(x – 2)2 = 9(x2 – 4x + 4)
= 9x2 – 36x + 36 ……………. (1)
RHS = fo(goh)
(goh) = g(h(x)) = g(x – 2)
= 3(x – 2) = 3x – 6
fo(goh) = f(3x – 6) = (3x – 6)2
= 9x2 – 36x + 36 ………….. (2)
(1) = (2)
LHS = RHS
(fog)oh = fo(goh) is proved.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 7.
Let A= {1,2} and B = {1,2,3,4}, C = {5,6} and D = {5,6,7,8}. Verify whether A × C is a subset of B × D?
Answer:
Given A = {1, 2}
B = {1, 2, 3, 4}
C = {5,6}
D = {5,6, 7,8}
A × C = {1,2} × {5,6}
= {(1,5) (1,6) (2, 5) (2, 6)}
B × D = {1,2, 3, 4} × {5, 6, 7, 8}
= {(1,5) (1,6) (1,7) (1,8)
(2, 5) (2, 6) (2,7) (2, 8)
(3, 5) (3, 6) (3, 7) (3, 8)
(4, 5) (4, 6) (4, 7) (4, 8)}
∴ A × C ⊂ B × D
Hence it is verified

Question 8.
If f(x) = \(\frac{x-1}{x+1}, x \neq 1\) Show that
f(f(x)) = – \(\frac { 1 }{ x } \), Provided x ≠ 0.
Answer:
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 5
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 6

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 9.
The functions f and g are defined by f{x) = 6x + 8; g(x) = \(\frac { x-2 }{ 3 } \)
(i) Calculate the value of gg [latex]\frac { 1 }{ 2 } [/latex]
(a) Write an expression for gf (x) in its simplest form.
Answer:
f(x) = 6x + 8 ; g(x) = \(\frac { x-2 }{ 3 } \)
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 7
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 8
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 88

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1

Question 10.
Write the domain of the following real functions
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Unit Exercise 1 9
Answer:
(i) f (x) = \(\frac { 2x+1 }{ x-9 } \)
If the denominator vanishes when x = 9
So f(x) is not defined at x = 9
∴ Domain is x ∈ [R – {9}]

(ii) if p(x) = \(=\frac{-5}{4 x^{2}+1}\)
p(x) is defined for all values of x. So domain is x ∈ R.

(iii) g(x) = \(\sqrt { x-2 }\)
When x < 2 g(x) becomes complex. But given “g” is real valued function.
So x > 2
Domain x ∈ (2, α)

(iv) h (x) = x + 6
For all values of x, h(x) is defined. Hence domain is x ∈ R.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Students can download Maths Chapter 1 Relations and Functions Ex 1.3 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Ex 1.3

Question 1.
Let f = {(x, y) |x,y; ∈ N and y = 2x} be a relation on N. Find the domain, co-domain and range. Is this relation a function?
Answer:
X = {1,2,3,….}
Y = {1,2,3,….}
f = {(1,2) (2, 4) (3, 6) (4, 8) ….}
Domain = {1, 2, 3, 4 ….}
Co – Domain = {1, 2, 3, 4 ….}
Range = {2, 4, 6, 8 }
Yes this relation is a function.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 2.
Let X = {3, 4, 6, 8}. Determine whether the relation
R = {(x,f(x)) |x ∈ X, f(x) = x2 + 1}
is a function from X to N?
Answer:
f(x) = x2 + 1
f(3) = 32 + 1 = 9 + 1 = 10
f(4) = 42 + 1 = 16 + 1 = 17
f(6) = 62 + 1 = 36 + 1 = 37
f(8) = 82 + 1 = 64 + 1 = 65
yes, R is a function from X to N

Question 3.
Given the function f: x → x2 – 5x + 6, evaluate
(i) f(-1)
(ii) f(2a)
(iii) f(2)
(iv) f(x – 1)
Solution:
Give the function f: x → x2 – 5x + 6.
(i) f(-1) = (-1)2 – 5(1) + 6 = 1 + 5 + 6 = 12
(ii) f(2a) = (2a)2 – 5(2a) + 6 = 4a2 – 10a + 6
(iii) f(2) = 22 – 5(2) + 6 = 4 – 10 + 6 = 0
(iv) f(x – 1) = (x – 1)2 – 5(x – 1) + 6
= x2 – 2x + 1 – 5x + 5 + 6
= x2 – 7x + 12

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 4.
A graph representing the function f(x) is given in it is clear that f(9) = 2.
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 1

(i) Find the following values of the function
(a) f(0)
(b) f(7)
(c) f(2)
(d) f(10)
Answer:
(a) f (0) = 9
(b) f (7) = 6
(c) f (2) = 6
(d) f(10) = 0

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

(ii) For what value of x is f(x) = 1 ?
Answer:
When f(x) = 1 the value of x is 9.5

(iii) Describe the following
(i) Domain
(ii) Range.
Answer:
Domain = {0, 1, 2, 3,… .10}
= {x / 0 < x < 10, x ∈ R}
Range = {0,1,2,3,4,5,6,7,8,9}
= {x / 0 < x < 9, x ∈ R}

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

(iv) What is the image of 6 under f?
Answer:
The image of 6 under f is 5.

Question 5.
Let f (x) = 2x + 5. If x ≠ 0 then find
\(\frac{f(x+2)-f(2)}{x}\)
Answer:
f(x) = 2x + 5
f(x + 2) = 2(x + 2) + 5
= 2x + 4 + 5
= 2x + 9
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 2

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 6.
A function/is defined by f(x) = 2x – 3
(i) find \(\frac{f(0)+f(1)}{2}\)
(ii) find x such that f(x) = 0.
(iii) find x such that/ (A:) = x.
(iv) find x such that fix) =/(l – x).
Answer:
(i) f(x) = 2x – 3
f(0) = 2(0) – 3 = -3
f(1) = 2(1) – 3 = 2 – 3 = -1
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 3

(ii) f(x) = 0
2x – 3 = 0
2x = 3
x = \(\frac { 3 }{ 2 } \)

(iii) f(x) = x
2x – 3 = x
2x – x = 3
x = 3

(iv) f(1 – x) = 2(1 – x) – 3
= 2 – 2x – 3
= – 2x – 1
f(x) = f(1 – x)
2x – 3 = – 2x – 1
2x + 2x = 3 – 1
4x = 2
x = \(\frac { 2 }{ 4 } \) = \(\frac { 1 }{ 2 } \)

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 7.
square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown. Express the volume V of the box as a function of x.
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 4
Solution:
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 44
After cutting squares we will get a cuboid,
length of the cuboid (l) = 24 – 2x
breadth of the cuboid (b) = 24 – 2x
height of the cuboid (h) = 2x
Volume of the box = Volume of the cuboid
V = (24 – 2x)(24 – 2x) (x)
= (24 – 2x)2 (x)
= (576 + 4x2 – 96x) x
= 576x + 4x3 – 96x2
V = 4x3 – 96x2 + 576x
V(x) = 4x3 – 96x2 + 576x

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 8.
A function f is defined by f(x) = 3 – 2x. Find x such that f(x2) = (f (x))2.
Answer:
f(x) = 3 – 2x
f(x2) = 3 – 2 (x2)
= 3 – 2x2
(f (x))2 = (3 – 2x)2
= 9 + 4x2 – 12x
But f(x2) = (f(x))2
3 – 2 x2 = 9 + 4x2 – 12x
-2x2 – 4x2 + 12x + 3 – 9 = 0
-6x2 + 12x – 6 = 0
(÷ by – 6) ⇒ x2 – 2x + 1 = 0
(x – 1) (x – 1) = 0
x – 1 = 0 or x – 1 = 0
x = 1
The value of x = 1

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 9.
A plane is flying at a speed of 500 km per hour. Express the distance d travelled by the plane as function of time t in hours.
Solution:
Speed = \(\frac{\text { distance covered }}{\text { time taken }}\)
⇒ distance = Speed × time
⇒ d = 500 × t [ ∵ time = t hrs]
⇒ d = 500 t

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Question 10.
The data in the adjacent table depicts the length of a woman’s forehand and her corresponding height. Based on this data, a student finds a relationship between the height (y) and the forehand length (x) as y = ax + b , where a, b are constants.
(i) Check if this relation is a function.
(ii) Find a and b.
(iii) Find the height of a woman whose forehand length is 40 cm.
(iv) Find the length of forehand of a woman if her height is 53.3 inches.

Length ‘x’ of forehand (in cm) Height y (in inches)
35 56
45 65
50 69.5
55 74

Answer:
The relation is y = 0.9x + 24.5
(i) Yes the relation is a function.
(ii) When compare with y = ax + b
a = 0.9, b = 24.5
(iii) When the forehand length is 40 cm, then height is 60.5 inches.
Hint: y = 0.9x + 24.5
= 0.9 × 40 + 24.5
= 36 + 24.5
= 60.5 feet

(iv) When the height is 53.3 inches, her forehand length is 32 cm
Hint: y = 0.9x + 24.5
53.3 = 0.9x + 24.5
53.3 – 24.5 = 0.9 x
28.8 = 0.9 x
x = \(\frac { 28.8 }{ 0.9 } \)
x = 32 cm

Representation of functions

A function may be represented by

(a) Set of ordered pairs
(b) Table form
(c) Arrow diagram
(d) Graphical form

Vertical line test
A curve drawn in a graph represents a function, if every vertical line intersects the curve in at most one point.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Types of function

1. One – One function (injection)
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 5
A function f: A → B is called one-one function if distinct elements of A have a distinct image in B.

2. Many – One function
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 6
A function f: A → B is called many-on function if two or more elements of A have same image in B.

3. Onto function (surjection)
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 7
A function f: A → B is said to be on to function if the range of f is equal to the co-domain of f.

4. Into function
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 8
A function f: A → B is called an into function if there exists at least one element in B which is not the image of any element of A.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

5. Bijection
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 9
A function f: A → B is both one – one and onto, then f is called a bijection from A to B.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

Horizontal line test
A function represented in a graph is one – one, if every horizontal line intersects the curve in at most one point.

Special cases of function

1. Constant function
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 10
A function f: A → B is called a constant function if the range of f contains only one element.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3

2. Identity function
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.3 11
A function f : A → A defined by f(x) = x for all x ∈ A is called an identity function on A and is denoted by IA.

3. Real valued function
A function f: A → B is called a real valued function if the range of f is a subset of the set of all real numbers R.

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Students can download Maths Chapter 1 Relations and Functions Ex 1.6 Questions and Answers, Notes, Samacheer Kalvi 10th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 1 Relations and Functions Ex 1.6

Multiple Choice Questions

Question 1.
If n(A × B) = 6 and A= {1, 3} then n (B) is ………….
(1) 1
(2) 2
(3) 3
(4) 6
Answer:
(3) 3
Hint: n(A × B) = 6
n(A) = 2
n(A × B) = n(A) × n(B)
6 = 2 × n(B)
n(B) = \(\frac { 6 }{ 2 } \) = 3

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 2.
A = {a, b, p}, B = {2, 3}, C = {p, q, r, s} then n[(A ∪ C) × B] is
(1) 8
(2) 20
(3) 12
(4) 16
Answer:
(3) 12
Hint:
A = {a, b, p}, B = {2, 3}, C = {p, q, r, s}
n (A ∪ C) × B
A ∪ C = {a, b, p, q, r, s}
(A ∪ C) × B = {{a, 2), (a, 3), (b, 2), (b, 3), (p, 2), (p, 3), (q, 2), (q, 3), (r, 2), (r, 3), (s, 2), (s, 3)
n [(A ∪ C) × B] = 12

Question 3.
If A = {1,2}, B = {1,2, 3, 4}, C = {5,6} and D = {5, 6, 7, 8} then state which of the following statement is true ……………….
(1) (A × C) ⊂ (B × D)
(2) (B × D) ⊂ (A × C)
(3) (A × B) ⊂ (A × D)
(4) (D × A) ⊂ (B × A)
Answer:
(1) (A × C) ⊂ (B × D)
Hint: n(A × B) = 2 × 4 = 8
(A × C) = 2 × 2 = 4
n(B × C) = 4 × 2 = 8
n(C × D) = 2 × 4 = 8
n(A × C) = 2 × 2 = 4
n(A × D) = 2 × 4 = 8
n(B × D) = 4 × 4 = 16
∴ (A × C) ⊂ (B × D)
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 4.
If there are 1024 relations from a set A = {1, 2, 3, 4, 5} to a set B, then the number of elements in B is
(1) 3
(2) 2
(3) 4
(4) 6
Answer:
(2) 2
Hint:
n(A) = 5
n(B) = x
n(A × B) = 1024 = 210
25x = 210
⇒ 5x = 10
⇒ x =2

Question 5.
The range of the relation R = {(x, x2) a prime number less than 13} is ……………………
(1) {2, 3, 5, 7}
(2) {2, 3, 5, 7, 11}
(3) {4, 9, 25, 49, 121}
(4) {1, 4, 9, 25, 49, 121}
Answer:
(3) {4, 9, 25, 49, 121}
Hint:
Prime number less than 13 = {2, 3, 5, 7, 11}
Range (R) = {(x, x2)}
Range = {4, 9, 25, 49, 121} (square of x)

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 6.
If the ordered pairs (a + 2, 4) and (5, 2a + b)are equal then (a, b) is
(1) (2, -2)
(2) (5, 1)
(3) (2, 3)
(4) (3, -2)
Answer:
(4) (3, -2)
Hint:
(a + 2, 4), (5, 2a + b)
a + 2 = 5
a = 3
2a + b = 4
6 + b = 4
b = -2

Question 7.
Let n(A) = m and n(B) = n then the total number of non-empty relations that can be defined from A to B is ……………..
(1) mn
(2) nm
(3) 2mn – 1
(4) 2mn
Answer:
(4) 2mn

Question 8.
If {(a, 8),(6, b)}represents an identity function, then the value of a and b are respectively
(1) (8, 6)
(2) (8, 8)
(3) (6, 8)
(4) (6, 6)
Answer:
(1) (8, 6)
Hint:
{{a, 8), (6, b)}
a = 8
b = 6

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 9.
Let A = {1, 2, 3, 4} and B = {4, 8, 9, 10}.
A function f: A → B given by f = {(1, 4), (2, 8),(3,9),(4,10)} is a ……………
(1) Many-one function
(2) Identity function
(3) One-to-one function
(4) Into function
Answer:
(3) One-to-one function
Hint:
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6 2
Different elements of A has different images in B.
∴ It is one-to-one function.

Question 10.
If f (x) = 2x2 and g(x) = \(\frac { 1 }{ 3x } \), then fog is …………..
(1) \(\frac{3}{2 x^{2}}\)
(2) \(\frac{2}{3 x^{2}}\)
(3) \(\frac{2}{9 x^{2}}\)
(4) \(\frac{1}{6 x^{2}}\)
Answer:
(3) \(\frac{2}{9 x^{2}}\)
Hint:
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6 3

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 11.
If f: A → B is a bijective function and if n(B) = 7, then n(A) is equal to
(1) 7
(2) 49
(3) 1
(4) 14
Answer:
(1) 7
Hint:
In a bijective function, n(A) = n(B)
⇒ n(A) = 7

Question 12.
Let f and g be two functions given by
f = {(0,1),(2, 0),(3-4),(4,2),(5,7)}
g = {(0,2),(1,0),(2, 4),(-4,2),(7,0)}
then the range of f o g is …………………
(1) {0,2,3,4,5}
(2) {-4,1,0,2,7}
(3) {1,2,3,4,5}
(4) {0,1,2}
Answer:
(4) {0,1,2}
Hint: f = {(0, 1)(2, 0)(3, -4) (4, 2) (5, 7)}
g = {(0,2)(l,0)(2,4)(-4,2)(7,0)}
Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6 4
fog = f[g(x)]
f [g(0)] = f(2) = 0
f [g(1)] = f(0) = 1
f [g(2)] = f(4) = 2
f[g(-4)] = f(2) = 0
f[g(7)] = f(0) = 1
Range of fog = {0,1,2}

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 13.
Let f(x) = \(\sqrt{1+x^{2}}\) then
(1) f(xy) = f(x),f(y)
(2) f(xy) ≥ f(x),f(y)
(3) f(xy) ≤ f(x).f(y)
(4) None of these
Answer:
(3) f(xy) ≤ f(x).f(y)
Hint:
\(\sqrt{1+x^{2} y^{2}} \leq \sqrt{\left(1+x^{2}\right)} \sqrt{\left(1+y^{2}\right)}\)
⇒ f(xy) ≤ f(x) . f(y)

Question 14.
If g= {(1,1),(2,3),(3,5),(4,7)} is a function given by g(x) = αx + β then the values of α and β are
(1) (-1,2)
(2) (2,-1)
(3) (-1,-2)
(4) (1,2)
Answer:
(2) (2, -1)
Hint: g (x) = αx + β
g(1) = α(1) + β
1 = α + β ….(1)
g (2) = α (2) + β
3 = 2α + β ….(2)
Solve the two equations we get
α = 2, β = -1

Samacheer Kalvi 10th Maths Guide Chapter 1 Relations and Functions Ex 1.6

Question 15.
f(x) = (x + 1)3 – (x – 1)3 represents a function which is
(1) linear
(2) cubic
(3) reciprocal
(4) quadratic
Answer:
(4) quadratic
Hint:
f(x) = (x + 1)3 – (x – 1)3
= x3 + 3x2 + 3x + 1 -[x3 – 3x2 + 3x – 1]
= x3 + 3x2 + 3x + 1 – x3 + 3x2 – 3x + 1 = 6x2 + 2
It is a quadratic function.

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Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

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10th English Guide Supplementary Zigzag Textbook Questions and Answers

A. Identify the speaker / character.

Question 1.
Even though I clearly said “no”!
Answer:
Dr. Krishnan

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 2.
The one that spits deadly poison straight into its opponent’s eyes.
Answer:
Maya

Question 3.
Remember the tiny penknife he gave me last year.
Answer:
Maya

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 4.
It’s Somu’s thoughtless ways that reduce me to tears.
Answer:
Mrs. Krishnan

Question 5.
‘Come in, zigzag, come in dear!’
Answer:
Visu, the old cook

B. Read the story again and write how these characters reacted in these situations.

Question 1.
“You’re both quite mistaken”.
Answer:
Dr. Krishnan hastened to explain
Mrs. Krishnan was horrified on hearing about zigzag.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 2.
“It’s Somu’s thoughtless ways that reduce me to tears”.
Answer:
Mrs. Krishnan spoke irritably.
Dr. Krishnan was hurrying to his clinic.

Question 3.
“Just wait till zigzag settles down in this new home”.
Answer:
Visu comforted everyone.
Aravind and Maya were disappointed as the bird didn’t talk.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 4.
“Zigzag hardly ever sleeps”.
Answer:
Somu sent an e-mail to Dr.Krishnan about Zigzag.
Dr.Krishnan predicted it as ridiculously simple.

Question 5.
“You are an absolute treasure…”
Answer:
Dr. Krishnan sighed and spoke to zigzag Zigzag didn’t bother to reply.

C. Complete the given tabular columns.


Answer:

D. Answer the following questions in one or two sentences.

Question 1.
Why did Dr. Ashok’s cousin call him?
Answer:
Dr. Ashok Krishnans cousin Somu called him to shelter Zigzag, his pet bird, when he left for Alaska.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 2.
Mention atleast …. zigzag at home?
Answer:

  1. I’m going crazy with the sound of zigzag snoring, plus all these telephone calls.
  2. “And my beautiful painting…”

Question 3.
What are pets did Somu have?
Answer:
Somu had a giant green and gold fighting beetle and an African snake.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 4.
What was Mrs. Krishnan busy with?
Answer:
Mrs. Krishnan was busy with her paintings to be displayed for sale the following week.

Question 5.
What commotion did the boomerang cause in the neighbourhood?
Answer:
Boomerang sliced through all the TV aerials in the neighborhood. It caused permanent damage to several cars in the parking lot. It also knocked out their watchman cold with the force thrown by Arvind.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 6.
What happened when Somu left zigzag with the Krishnan’s?
Answer:
Zigzag deposited the walnuts and fruits to the Chandelier and transferred them all the blades of the ceiling fan. Then it perched on the curtain rod and went off to sleep.

Question 7.
How did zigzag communicate with the Krishnan’s?
Answer:
Zigzag did not communicate with the Krishnan’s although everyone tried several times and in several languages to speak to him, he only slept and snored.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 8.
What was the e-mail message sent to Somu by Dr. Krishnan?
Answer:
Dr. Krishnan sent an email to Somu, asking for instructions on how to stop zigzag from snoring.

Question 9.
What did Aravind confess?
Answer:
Arvind confessed that for the first time in his life, he was actually looking forward to go to school. The school was as calm as a monastery compared to their house.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 10.
Why did Mrs. Jhunjhunwala buy the painting?
Answer:
Mrs. jhunjhunwala bought the painting because she liked the new technique of- painting.

E. Answer the following questions in about 100-150 words:

Question 1.
Write a passage in your own words the various commotions caused by zigzag at Dr. Krishnan’s
Answer:
When Visu, the old cook of Dr. Somu brought Zigzag to Dr. Krishnan’s house, all were surprised to see such a strange and weird bird. It was a foot and a half tall. It was a multilingual talking- singing bird. It could talk and sing in twenty-one languages.

When it refused to say a word, Arvind brought some juicy fruits and nuts for the bird. It did not eat them but transferred one ‘ by one to the chandelier and on to the blades of the ceiling fan. Then it perched on a curtain rod, it sank his beak into plumpy guava and then went off to sleep. Then he began to snore. The snore became louder and very louder.

His snoring pounded their eardrums till their heads ached. When the fan was switched on by their maid, the painting of Mrs. Krishnan got spoilt by streaks of orange pulp spreading on it. His snoring troubled all the neighbors and they were complaining about it.

(OR)

Title: Zigzag
Author: Asha Nehemiah
Characters: Zigzag, Dr. Krishnan, Mrs. Krishnan, Dr. Somu, Aravind, the old-cook Visu and Lakshmi.
Theme: Things are not always as we think.

Dr. Somu left for Alaska. He had a pet bird. He sent it to Dr. Krishnan’s house through his old cook Visu. His name was Zigzag. All were surprised to see the strange bird. He was one and a half foot tall. He could talk and sing in 21 languages. But he did not speak a word. Aravind brought juicy fruits and nuts for zigzag.

He transferred them to the chandelier and on to the fan plates. He perched on the curtain rod and started sleeping and snoring. The snore became louder. It pounded their eardrums causing headaches. When the fan was switched on, the streaks of orange pulp spread on Mrs. Krishnan’s painting. It was spoilt. His snoring troubled all the neighbours and they were complaining about it.

(OR)

  1. The cook of Dr. Somu brought Zigzag to Dr. Krishnan’s house.
  2. All were surprised to see him
  3. He was a strange and wierd bird
  4. He could talk and sing in 21 languages
  5. But he did not say a word
  6. Aravind gave juicy fruits and nuts to him
  7. He did not eat but transferred them to the chandelier and fan plate
  8. He perched on the curtain rod and slept with snoring.
  9. When the maid Lakshmi switched on the fan the painting of Mrs. Krishnan got spoilt by the streaks of orange pulp
  10. The neighbours complained about the loud snoring of the bird as they were troubled.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 2.
What happened when zigzag was taken to the clinic?
Answer:
Introduction:
Zigzag created lot of misunderstandings in Dr. Krishnan’S house. So he wanted to take zigzag to his clinic. Let us see below what happens in the clinic.

Zigzag’s arrival to clinic:
Dr. Krishnan took zigzag to the clinic. He warned him not to sleep. Zigzag went to the clinic and perched on the reception table. Dr. Krishnan heard some strange sound in the clinic.

Zigzag’s behaviour:
The strange sound was zigzag’s clear and commanding voice. There was complete silence in the clinic. Dr, Krishnan was amazed. Zigzag’s bored and grumpy expression was gone. He went about the job.

Conclusion:
Thus zigzag made the clinic completely silent. Zigzag efficiently comforted the frightened y patients. Dr. Krishnan thought that zigzag was an absolute treasure.

(OR)

Title: Zigzag
Author: Asha Nehemiah
Characters: Dr. Krishnan and Zigzag.
Theme: Change is the law of life.

Dr. Krishnan took Zigzag to the clinic. He asked him to wait in the car. He warned him not to sleep. But he was not used to being kept waiting. So he went into the clinic and perched on the reception table. Dr. Krishnan heard a voice when he hardly walked into his clinic. It was Zigzag’s clear and commanding voice.

There was silence in the room. Everyone waited, open mouth for his next sentence. Dr. Krishnan was amazed. Zigzag’s bored and grumpy expression was gone. Instead he looked happy and alert. He went about the job. He had been trained for the job with the doctors. The clinic became a calm and orderly place without any confusion. Zigzag efficiently comforted the frightened patients.

(OR)

  1. Dr. Krishnan took Zigzag to the clinic.
  2. He asked zigzag to wait in the car.
  3. But he went into the clinic and perched on the reception table.
  4. Dr. Krishnan heard a voice even before he went into his room
  5. There was a silence and everyone waited for Zigzag’s next sentence.
  6. Dr. Krishnan was amazed
  7. Zigzag’s bored and grumpy expression was gone
  8. Instead Zigzag looked happy and alert to do his job
  9. He comforted the frightened patients.
  10. Dr. Krishnan’s clinic became a calm place without confusion.

Samacheer Kalvi 10th English Guide Supplementary Chapter 2 Zigzag

Question 3.
Narrate the story zigzag in your own words.
Answer:
This story is about a multilingual weird bird, named Zigzag. Dr. Krishnan’s clinic usually sounded noisy because of the shouting and crying of children. His friend Dr. Somu requested him to shelter Zigzag, his pet as he was about to leave for Alaska.

When Zigzag was brought to his house, it did not speak to anyone. It could sing and talk in 21 different languages. But it did not speak any word to them. Instead, he transferred the fruits and nuts given to him to a Chandelier and to the blades of the ceiling fan. It perched on a curtain rod and went off to sleep. When the fan was switched on, all the fruits and nuts fell down.

The papaya slice splattered on the painting of Mrs. Krishnan and spoiled it. Mrs. Krishnan was irritated and persuaded Dr. Krishnan to send the bird away to Visu s house. So Dr. Krishnan took the bird to his clinic. There it commanded everyone in an orderly way. He brought peace, calmness and a disciplined atmosphere in the clinic. The painting which had been spoilt by Zigzag was sold out for ₹ 5,000. It was bought because the new technique in painting was liked by the buyer. Thus Mr. Krishnan’s family invited Zigzag to stay with them for another week.

(OR)

This is a story about Zigzag, a multilingual bird. Dr. Somu who left for Alaska asked Dr. Krishnan to shelter him. Visu brought him to Dr. Krishnan’s house. He did not speak to anyone though he could talk and sing in 21 languages. Instead, he transferred the fruits and nuts to a chandelier and the fan plates.

Then he perched on a curtain rod and went to sleep. When the fan was switched on the fruit slices fell off spoiling the painting of Mrs. Krishnan. She got irritated and told her husband to send Zigzag to Visu’s house. Dr. Krishnan took him to his clinic.

Zigzag commanded the patients and the clinic became a calm and orderly place. The spoilt painting was sold for Rs. 5000. The buyer considered it as a new technique of painting. Mrs. Krishnan wanted to keep Zigzag for another week.

(OR)

  1. Zigzag was a bird.
  2. Dr. Krishnan was a child specialist.
  3. Vishu brought zigzag to Dr. Krishnan’s house.
  4. Zigzag could speak 21 languages.
  5. But the bird didn’t speak a word.
  6. Zigzag fell asleep and began to snore.
  7. Its loud snore disturbed everyone.
  8. Mrs. Krishnan’s painting was spoiled
  9. Mrs. Krishnan was very angry.
  10. Dr. Krishnan took zigzag to the clinic.
  11. At the clinic it helped to maintain calmness.
  12. It made the children laugh.
  13. It recited the French poetry.
  14. So the family decided to keep him with them.
  15. Everyone is happy now.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Tamilnadu State Board New Syllabus Samacheer Kalvi 10th English Guide Pdf Supplementary Chapter 7 A Dilemma Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 10th English Solutions Supplementary Chapter 7 A Dilemma

10th English Guide Supplementary A Dilemma Textbook Questions and Answers

A. Read the given lines carefully and identify the character / speaker:

Question 1.
I suppose you think me queer. I will explain?
Answer:
Uncle Philip

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
Don’t come back. I won’t hasten things?
Answer:
Uncle Philip

Question 3.
He thought it simply a cruel jest?
Answer:
Tom’s Father Confessor.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 4.
He did not desire to do so?
Answer:
Professor Clinch

Question 5.
He would think it over and come back later?
Answer:
The collector

B. Based on your understanding of the story, answer the following briefly.

Question 1.
What did the uncle do as soon as he bought a stone?
Answer:
As soon the uncle bought a stone, he carried it in his pocket for a month and now and then he took it out and looked at it.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
What did the uncle bequeath to the narrator?
Answer:
The uncle bequeathed an iron safe containing gems and a dynamite that would explode in his safe.

Question 3.
What was the condition laid by the uncle to inherit his property?
Answer:
The uncle asked Tom to open the box with belief and trust which increase his expectation and desire. If he doubted and opened the dynamite would explode.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 4.
Why do you think Tom happily looked forward to the expenditure for his uncle’s funeral?
Answer:
Tom thought he would become a very rich man after his uncle died when he inherited the box of gems.

Question 5.
Write a few words about the mechanism used in the iron box?
Answer:
The box contained an interesting mechanism. It will act with certainty as one unlocks it, and explode 9 1/2 ounces of his improved, super sensitive dynamite one must open without doubting to desire a fortune. If they doubt, the person will be blown to atoms.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 6.
What was the counsel offered to the narrator?
Answer:
The narrator was counselled to give up thinking about the box and its contents

Question 7.
Why and when was the narrator shocked?
Answer:
The narrator was shocked when he read the letter that the box contained sensitive dynamite.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 8.
What was the doctor’s warning to Tom?
Answer:
The doctor warned Tom not to lose his mind thinking a lot about the rubies.

Question 9.
Why didn’t Tom dare to assign the task of unlocking the box to someone?
Answer:
Tom felt a stranger had no right to be subjected to the trial that he dare not face. So he did not want a stranger to open the box.

C. Answer the questions given below in a paragraph of 150 words.

Question 1.
Describe briefly the contents of the letter written by Tom’s uncle.
Answer:
Title: A Dilemma
Character: Tom and Uncle Philip
Author: Silas Weir Mitchell
Theme: ‘A Bird in hand is worth two in the bush’

In his letter Uncle Philip wrote that the box contained a large number of fine pigeon – blood rubies and a lot of diamonds of which one was a beautiful blue diamond. There were hundreds of pearls, a famous green pearl and a necklace of blue pearls. Regarding Susan, he insisted Tom to continue to have expectations and remember his dear uncle.

He gave the stones to Tom instead of leaving them to a charity. The letter instructed Tom about the mechanism of unlocking it. It would explode 9 1/2 ounces of improved, super sensitive diamond. The letter added that if he opened it doubtfully it would rain him to atoms. If he opened it with faith and care, he would nourish hopes and expectations. He asked Tom to be very careful.

(OR)

Uncle Philip wrote that there were plenty of pigeon – blood rubies, diamonds, pearls and a necklace of blue pearls. Among them there was a beautiful blue diamond and a famous green pearl.

He thought of Susan and said he must have expectations and remembrance of his dear uncle. He gave the stones to him instead of a charity. He told about the mechanism of unlocking it. If he opened it doubtfully, 9 1/2 ounces of quality dynamite would turn to atoms. With faith, if he opened it carefully, he would nourish hopes and expectations. Tom was warned to be careful.

(OR)

  1. Uncle Philip wrote about plenty of rubies, diamonds, pearls and a blue pearls necklace in the box.
  2. There was a beautiful blue diamond and a famous green pearl.
  3. Uncle gave him the stones instead of a charity
  4. He told about the mechanism of unlocking the box
  5. Opening the box doubtfully, 9 1/2 ounces of dynamite would explode
  6. Opening it with faith and care, Tom would nourish hopes and expectations
  7. Uncle philip asked Tom to be careful

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
Explain the efforts taken by Tom to open the iron box. Did he succeed? Why?
Answer:
Title: A Dilemma
Author: Silas Weir Mitchell
Characters: Tom, Prof. Clinch, Father Confessor and the Collector.
Theme: ‘Take the risk or lose the chance’

After getting the box, Tom went on thinking about it. He went after people for their advice. He spent his spare times in the libraries. He imagined wild plans like dropping the box from a height to open it. He wanted to get the gems after the explosion. In all his attempts, he could not succeed.

He thought very hard in vain over weeks and months. His father confessor dismissed it that it was a cruel joke of his uncle. His doctor advised him to stop thinking about the box with precious gems as it would make him mad.

He tried to deposit it in the bank, but withdrew it because he was afraid of burglary. He consulted Professor Clinch about his dilemma. He dismissed it as an incredible story. Thus Tom had to leave the box to the society for Preservation of Human Vivisection.

“Take the risk and drop the fear”

(OR)

Tom inherited the iron box. He constantly thought about it. He went after people for their advice. He ransacked libraries. He imagined wild plans like dropping the box from a height to open it.

He wanted to get the gems after the explosion. He thought hard in vain for weeks and months. His father dismissed it as a cruel joke of his uncle. His doctor advised him to stop thinking about it. He tried to deposit it in the bank. He consulted Prof. Clinch about his dilemma. He dismissed it as an incredible story. Finally, Tom had to leave the box to the society for Preservation of Human Vivisection.

(OR)

  1. Tom always thought about the box
  2. He asked many people to advise him
  3. He imagined wild plans to open the box
  4. He thought of getting the gems after the box’s explosion
  5. Nothing worked out for his success
  6. His father dismissed it
  7. His doctor advised him to stop thinking about the box
  8. He was afraid of deposit
  9. His Professor Clinch dismissed it
  10. Thus Tom left the box to the society for the Preservation of Human Vivisection

D. Fill in the blanks with the right options and write down the summary of the story ‘A dilemma’.

Question 1.
The narrator was sent for, by his uncle when we was ……………….. (on his death bad / on his travels / in his work place)
Answer:
on his death bed

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
The uncle had collected precious ……………….. (jewels / stones / articles)
Answer:
stones

Question 3.
His uncle announced Tom as his heir and wanted him to pay for his …………………. (rented house / marriage / funeral)
Answer:
funeral

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 4.
Leaving an iron box for Tom, his uncle instructed him not to …………………… the box. (throw / carry / shake)
Answer:
shake

Question 5.
The letter read that the box contained ……………….. (a sensitive dynamite / jewels / money)
Answer:
a sensitive dynamite

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 6.
He started thinking of all possible ways to open the box without being …………………. (wounded / killed / maimed)
Answer:
killed

Question 7.
He planned to explode the box at but dropped the plant in fear of losing the rubies (home / a safe distance / a waste land)
Answer:
a safe distance

Question 8.
His consultation with …………………. did not yield him any fruitful solution. (Uncle Philip / Professor Clinch / Susan)
Answer:
Professor Clinch

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 9.
He failed in his attempts to open the box. His efforts to read about explosives led to ……………….. (hopes / confusions / suspicious) and he had to change his (name and occupation / lodgings / appearance)
Answer:
confusion, name and occupation

Question 10.
At last, he bequeathed the box to ………………… (his offspring / his friends / the society)
Answer:
the society

Read the following passage and answer the questions that follow.

1. I was just thirty-seven when my Uncle Philip died. A week before that event he sent for me; and here let me say that I had never set eyes on him. He hated my mother, but I do not know why. She told me long before his last illness that I need expect nothing from my father’s brother. He was an inventor, an able and ingenious mechanical engineer, and had much money by his improvement in turbine-wheels.

He was a bachelor; lived alone, cooked his own meals, and collected precious stones, especially rubies and pearls. From the time he made his first money he had this mania. As he grew richer, the desire to possess rare and costly gems became stronger. When he bought a new stone, he carried it in his pocket for a month and now and then took it out and looked at it. Then it was added to the collection in his safe at the trust company.

Question 1.
How old was the narrator when his uncle died?
Answer:
The narrator was just thirty-seven, when his Uncle Philip died.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
Had the narrator seen his uncle before? Give lines from the passage that support your answer?
Answer:
No, the narrator had not seen his uncle before, “A week before that even he sent for me; and here let me say that I had never set eyes on him”.

Question 3.
What had the narrator’s mother told him of his father’s brother?
Answer:
He was an inventor, an able and ingenious mechanical engineer and had much money by his improvement in turbine wheels.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 4.
What do you know about Uncle Philip?
Answer:
He was a bachelor lived alone cooked his own meals and collected precious stones, especially rubies and pearls. From the time he made his first money, he had this mania.

Question 5.
What did the uncle do, when he bought a new stone?
Answer:
He carried the new stonein his pocket for a month and now and then took it out and looked at it. Then it was added to the collection in his safe at the trust company.

2. Now I repent of my wickedness to you all, and desire to live in the memory of at least one of my family. You think I am poor and have only my annuity. You will be profitably surprised. I have never parted with my precious stones; they will be yours. You are my sole heir. I shall carry with me to the other world the satisfaction of making one man.

Question 1.
What did he repent of?
Answer:
He repented of his wickedness to all.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 2.
What didn’t he part with?
Answer:
He did not part with his precious stones.

Question 3.
Who would be his sole heir?
Answer:
Tom would be his sole heir.

Samacheer Kalvi 10th English Guide Supplementary Chapter 7 A Dilemma

Question 4.
What kind of satisfaction was he going to have?
Answer:
By announcing Tom his sole heir, he makes Tom happy. This kind of satisfaction was he going to have.

Question 5.
Was he a poor man?
Answer:
No, Tom’s uncle was not a poor man.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Tamilnadu State Board New Syllabus Samacheer Kalvi 10th English Guide Pdf Supplementary Chapter 6 The Little Hero of Holland Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 10th English Solutions Supplementary Chapter 6 The Little Hero of Holland

10th English Guide Supplementary The Little Hero of Holland Textbook Questions and Answers

A. Based on the understanding of the story, complete the Graphic Organiser suitably.


Answer:
Title: The Little Hero of Holland
Setting: A dike above the sea water
Characters: Peter, Peter’s mother and father, Peter’s blind friend, people of Holland.
Theme: Sacrifice to save the country
Plots: Father works in the dike as a gate keeper.
Mother sends Peter with cakes to visit his blind filend.
Peter notices a leak ¡n the dike while returning.
He plucks the hole with his finger the whole night to save his people of Holland.
Brave little hero Peter saves Holland from drowning.
Climax: Peter stays at the dike with his finger In the whole night in cold weather with his finger stuffed and numbed. Next morning passers by saved him and mended the hole. Peter saved Holland.

Values
Highlighted: Love and concern for the nation. Determination to save the people. Dedication towards the mother land.

B. Based on your understanding of the story answer the following questions in one or two sentences:

Question 1.
What are the little children of Holland, aware of?
Answer:
The little children of Holland are aware the dikes must be watched every moment and that even a small hole can be very dangerous. It would bring the sea to Holland.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 2.
What is the work assigned to Peter’s father?
Answer:
Tending the gates of the dike was the work assigned to Peter’s father. He opened and closed the gates when ships entered the sea from Holland.

Question 3.
Why did Peter’s mother call him?
Answer:
Peter’s mother called him to go and give cakes to his friend who was blind.

Question 4.
How did Peter spend his time with his blind friend?
Answer:
Peter’s stayed with his poor blind man a little while to tell him about his walk along the dike and the sun and the flowers and the ships far out at sea.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 5.
Why did the father always say angry waters’?
Answer:
The father always said angry waters because the seawater lashed on the dikes always.

Question 6.
What did Peter see when he stopped near the dikes?
Answer:
When Peter stopped near the dikes he saw a small hole in the dike through which a tiny stream was flowing.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 7.
What were the thoughts of the mother when Peter did not return home?
Answer:
Peter’s mother thought that she was spending that night with his friend and that she would scold him next morning for staying away from home without permission.

Question 8.
How did Peter spend his night at the dikes?
Answer:
Peter put his finger in the hole. He crouched on a stone bending his head. He did not sleep, though his eyes were closed. He rubbed his hand thinking that he could stay throughout the night.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 9.
Who found Peter in the dikes and what did he do?
Answer:
A man who went for his work heard Peter moaning and found him clinging to the side of the great wall.

Question 10.
How did the villagers mend the hole?
Answer:
The villagers brought shovels and mended the hole after hearing the alarm.

C. Based on your understanding of the story answer the following question in about 100-150 words.

Question 1.
Narrate in your own words the circumstances that led Peter to be a brief little hero.
Answer:
Introduction:
This story is about a little boy who saved his country from flooding.

Across the dikes:
Peter was a little boy who lived in Holland. Peter’s mother wanted him to go across the dikes to meet his blind friend. Peter went there and stayed till evening. When returning he heard some sound of trickling water. He found a small hole in the dikes. He put his finger into the hole and stopped the water.

Little hero:
He stayed there putting his finger in that hole. His finger became numb. He slept there the whole night. In the morning, a villager saw Peter sitting there. He called the villagers. The villagers arrived with shovels and mended the hole.

Conclusion:
Thus, Peter saved his country, from flooding and was called as the “Hero of Holland”.

(OR)

Peter was a little boy in Holland. One day his mother sent him to give a cake to his blind friend. He walked along the dike. He spent sometime and wanted to return home early. On his way he saw water streaming through a small hole in the dike. He wanted to save Holland.

He climbed down and put his finger into the hole and stopped the leakage. He stayed outside in cold without sleeping. He shouted for help but in vain. Next day a passer by heard his groan and came to rescue him. He spread the alarm. The villagers came runnng with shovels and mended the dike. Thus Peter became a great hero who saved Holland.

(OR)

  1. Peter was a little boy in Holland
  2. His mother asked him to visit his blind friend
  3. He stayed with him for a while and returned home
  4. On his way he saw a small hole in the dike and water was gushing out.
  5. He wanted to save Holland
  6. He climbed down the dike and closed the hole with his little finger
  7. The water leakage was stopped
  8. He stayed outside at night in cold weather without sleeping
  9. Next morning a passer by heard his groan and went nearer him
  10. He alarmed and the villagers came running and mended the dike
  11. Peter became a great little hero of Holland

D. Identify the character / speaker:

Question 1.
‘I want you to go across the dike and take these cakes to your friend, the blind man’
Answer:
Peter’s Mother

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 2.
I am glad they are so strong?
Answer:
Peter

Question 3.
‘Holland shall not be drowned while I am here’.
Answer:
Peter

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 4.
‘What’s the matter?” he called. “Are you hurt?’
Answer:
Passer by

Question 5.
‘Tell them to come quickly!’
Answer:
Peter

E. Read the following passage and answer the questions that follow.

1. One afternoon the early fall when Peter was eight years old his mother called him from his play, “Come, Peter,” she said. “I want you to go across the dike and take these cakes to your friend, the blind man. If you go quickly, and do not stop to play, you will be home again before dark.” The little boy was glad to go on such an errand, and started off with a light heart.

He stayed with the poor blind man a little while to tell him about his walk along the dike and about the sun and the flowers and the ships far out at sea. Then he remembered his mother’s wish that he should return before dark and, bidding his friend goodbye, he set out for home.

Question 1.
What did Peter’s mother want him to do?
Answer:
Peter’s mother wanted him to go across the dike and take those cakes to his blind friend.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 2.
What did Peter’s mother advise him to do?
Answer:
Peter’s mother advised him not to indulge in playing and to return home before dark.

Question 3.
Why was the little boy glad?
Answer:
The little boy was glad to go on such an errand to meet the blind man.

Samacheer Kalvi 10th English Guide Supplementary Chapter 6 The Little Hero of Holland

Question 4.
What did the little boy tell his friend?
Answer:
The little boy told his friend about his walk along the dike and about the sun and the flowers and the ships far out at sea.

Question 5.
What did the little boy remember?
Answer:
The little boy remembered his mother’s wish that he should return before dark.