# Class 10

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.8

Question 1.
Find the square root of the following polynomials by division method
(i) x4 – 12x3 + 42x2 – 36x + 9
(ii) 37x2 – 28x3 + 4x4 + 42x + 9
(iii) 16x4 + 8x2 + 1
(iv) 121x4 – 198x3 – 183x2 + 216x + 144
Solution:
The long division method in finding the square root of a polynomial is useful when the degrees of a polynomial is higher.

Synthetic Division Calculator. The calculator will divide the polynomial by the binomial using synthetic division, with steps shown.

Question 2.
Find the square root of the expression $$\frac{x^{2}}{y^{2}}-10 \frac{x}{y}+27-10 \frac{y}{x}+\frac{y^{2}}{x^{2}}$$
Solution:

Question 3.
Find the values of a and b if the following polynomials are perfect squares
(i) 4x4 – 12x3 + 37x2 + bx + a
(ii) ax4 + bx3 + 361ax2 + 220x + 100
Solution:
(i)

Since it is a perfect square.
Remainder = 0
⇒ b + 42 = 0, a – 49 = 0
b = -42, a = 49

(ii) ax4 + bx3 + 361ax2 + 220x + 100

Since remainder is 0
a = 144
b = 264

Question 4.
Find the values of m and n if the following expressions are perfect squares
(i) $$\frac{1}{x^{4}}-\frac{6}{x^{3}}+\frac{13}{x^{2}}+\frac{m}{x}+n$$
(ii) x4 – 8x3 + mx2 + nx + 16
Solution:
(i)

(ii)

Since remainder is 0,
m = 24, n = -32

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 6 Trigonometry Ex 6.2

Question 1.
Find the angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of a tower of height 10$$\sqrt{3}$$ m.
Solution:

Question 2.
A road is flanked on either side by continuous rows of houses of height 4$$\sqrt{3}$$ m with no space in between them. A pedestrian is standing on the median of the road facing a row house. The angle of elevation from the pedestrian to the top of the house is 30°. Find the width of the road.
Solution:

Question 3.
To a man standing outside his house, the angles of elevation of the top and bottom of a window are 60° and 45° respectively. If the height of the man is 180 cm and if he is 5 m away from the wall, what is the height of the window? ($$\sqrt{3}$$ = 1.732)
Solution:

Let ‘H’ be the fit of the window. Given that elevation of top of the window is 60°.

Given that elevation of bottom of the window is 45°.

∴ Height of the window = 3.66 m

Question 4.
A statue 1.6 m tall stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 40°. Find the height of the pedestal. (tan 40° = 0.8391, $$\sqrt{3}$$ = 1.732)
Solution:

Let ‘p’ be the fit of the pedestal and d be the distance of statue from point of cabs, on the ground.
Given the elevation of top of the statue from pf on ground is 60°.

Question 5.
A flag pole ‘h’ metres is on the top of the hemispherical dome of radius V metres. A man is standing 7 m away from the dome. Seeing the top of the pole at an angle 45° and moving 5 m away from the dome and seeing the bottom of the pole at an angle 30°. Find
(i) the height of the pole
Solution:

Question 6.
The top of a 15 m high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
Solution:

Let BD be tower of height = 15 m
AE be pole of height = ‘p’

Question 7.
A vertical pole fixed to the ground is divided in the ratio 1 : 9 by a mark on it with lower part shorter than the upper part. If the two parts subtend equal angles at a place on the ground, 25 m away from the base of the pole, what is the height of the pole?
Solution:

This mile calculator estimates the number of driving miles between two locations in the United States.

Question 8.
A traveler approaches a mountain on highway. He measures the angle of elevation to the peak at each milestone. At two consecutive milestones the angles measured are 4° and 8°. What is the height of the peak if the distance between consecutive milestones is 1 mile, (tan 4° = 0.0699, tan 8° = 0.1405).
Solution:

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 4 Geometry Ex 4.3

Question 1.
A man goes 18 m due east and then 24 m due north. Find the distance of his current position from the starting point?
Solution:
Using Pythagoras theorem

AC2 = AB2 + BC2
= (18)2 + (24)2
= 324 + 576
= 900
AC = $$\sqrt{900}$$ = 30 m
∴ The distance from the starting point is 30 m.

Question 2.
There are two paths that one can choose to go from Sarah’s house to James house. One way is to take C street, and the other way requires to take A street and then B street. How much shorter is the direct path along C street? (Using figure).

Solution:
By using Pythagoras theorem
AC2 = AB2 + BC2
= 22 + (1.5)2
= 4 + 2.25
= 6.25
AC = 2.5 miles.
If one chooses C street the distance from James house to Sarah’s house is 2.5 miles
If one chooses A street and B street he has to go 2 + 1.5 = 3.5 miles.
2.5 < 3.5, 3.5 – 2.5 = 1 Through C street is shorter by 1.0 miles.
∴ The direct path along C street is shorter by 1 mile.

To round to the nearest tenth, look at the tenth’s place (right after the decimal).

Question 3.
To get from point A to point B you must avoid walking through a pond. You must walk 34 m south and 41 m east. To the nearest meter, how many meters would be saved if it were possible to make a way through the pond?
Solution:
By using Pythagoras

AC2 = AB2 + BC2
= 342 + 412
= 1156+ 1681
= 2837
AC = 53.26 m
Through B one must walk 34 + 41 = 75 m walking through a pond one must comes only 53.2 m
∴ The difference is (75 – 53.26) m = 21.74 m
∴ To the nearest, one can save 21.74 m.

Question 4.
In the rectangle WXYZ, XY + YZ = 17 cm, and XZ + YW = 26 cm. Calculate the length and breadth of the rectangle?

Solution:
XY + YZ = 17 cm …………. (1)
XZ + YW = 26 cm ………… (2)
(2) ⇒ XZ = 13, YW = 13
(∵ In rectangle diagonals are equal).
(1) ⇒ XY = 5, YZ = 12 XY + YZ = 17
⇒ Using Pythagoras theorem
52 + 122 = 25 + 144 = 169 = 132
∴ In ∆XYZ = 132 = 52 + 122 it is verified
∴ The length is 12 cm and the breadth is 5 cm.

Question 5.
The hypotenuse of a right triangle is 6 m more than twice of the shortest side. If the third side is 2 m less than the hypotenuse, find the sides of the triangle?
Solution:
Let a is the shortest side.
c is the hypotenuse
b is the third side.

∴ The sides of the triangle are 10m, 24m, 26m.
Verification 262 = 102 + 242
676 = 100 + 576 = 676

Question 6.
5 m long ladder is placed leaning towards a vertical wall such that it reaches the wall at a point 4m high. If the foot of the ladder is moved 1.6 m towards the wall, then find the distance by which the top of the ladder would slide upwards on the wall.
Solution:
Let the distance by which top of the slide moves upwards be assumed as ‘x’.

From the diagram, DB = AB – AD
= 3 – 1.6 ⇒ DB = 1.4 m
also BE = BC + CE
= 4 + x
∴ DBE is a right angled triangle
DB2 + BE2 = DE2 ⇒ (1.4)2 + (4 + x)2= 52
⇒ (4 + x)2 = 25 – 1.96 ⇒ (4 + x)2 = 23.04
⇒ 4 + x = $$\sqrt{23.04}$$ = 4.8
⇒ x = 4.8 – 4 ⇒ x = 0.8 m

Question 7.
The perpendicular PS on the base QR of ∆PQR intersects QR at S, such that QS = 3 SR. Prove that 2PQ2 = 2PR2 + QR2.
Solution:

In ∆PQS,
PQ2 = PS2 + QS2 ………… (1)
In ∆PSR,
PR2 = PS2 + SR2 ……….. (2)
(1) – (2) ⇒ PQ2 – PR2 = QS2 – SR2 …………. (3)

Hence it proved.

Question 8.
In the adjacent figure, ABC is a right-angled triangle with right angle at B and points D, E trisect BC. Prove that 8AE2 = 3AC2 + 5AD2.

Solution:
Since D and E are the points of trisection of BC,
therefore BD = DE = CE
Let BD = DE = CE = x
Then BE = 2x and BC = 3x
In right triangles ABD, ABE and ABC, (using Pythagoras theorem)
We have AD2 = AB2 + BD2
⇒ AD2 = AB2 + x2 ……………. (1)
AE2 = AB2 + BE2
⇒ AB2 + (2x)2
⇒ AE2 = AB2 + 4x2 ………… (2)
and AC2 = AB2 + BC2 = AB2 + (3x)2
AC2 = AB2 + 9x2
Now 8 AE2 – 3 AC2 – 5 AD2 = 8 (AB2 + 4x2) – 3 (AB2 + 9x2) – 5 (AB2 + x2)
= 8AB2 + 32x2 – 3AB2 – 27x2 – 5AB2 – 5x2
= 0
∴ 8 AE2 – 3 AC2 – 5 AD2 = 0
8 AE2 = 3 AC2 + 5 AD2.
Hence it is proved.

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Additional Questions

Question 1.
Use Euclid’s algorithm to find the HCF of 4052 and 12756.
Solution:
Since 12576 > 4052 we apply the division lemma to 12576 and 4052, to get HCF
12576 = 4052 × 3 + 420.
Since the remainder 420 ≠ 0, we apply the division lemma to 4052
4052 = 420 × 9 + 272.
We consider the new divisor 420 and the new remainder 272 and apply the division lemma to get
420 = 272 × 1 + 148, 148 ≠ 0.
∴ Again by division lemma
272 = 148 × 1 + 124, here 124 ≠ 0.
∴ Again by division lemma
148 = 124 × 1 + 24, Here 24 ≠ 0.
∴ Again by division lemma
124 = 24 × 5 + 4, Here 4 ≠ 0.
∴ Again by division lemma
24 = 4 × 6 + 0.
The remainder has now become zero. So our procedure stops. Since the divisor at this stage is 4.
∴ The HCF of 12576 and 4052 is 4.

Question 2.
If the HCF of 65 and 117 is in the form (65m – 117) then find the value of m.
By Euclid’s algorithm 117 > 65
117 = 65 × 1 + 52
52 = 13 × 4 × 0
65 = 52 × 1 + 13
H.C.F. of 65 and 117 is 13
65m – 117 = 13
65 m = 130
m = $$\frac { 130 }{ 65 }$$ = 2
The value of m = 2

The smallest number to appear on both lists is 60, so 60 is the least common of 15 and 20.

Question 3.
Find the LCM and HCF of 6 and 20 by the prime factorisation method.
Solution:
We have 6 = 21 × 31 and
20 = 2 × 2 × 5 = 22 × 51
You can find HCF (6, 20) = 2 and LCM (6, 20) = 2 × 2 × 3 × 5 = 60. As done in your earlier classes. Note that HCF (6, 20) = 21 = product of the smallest power of each common prime factor in the numbers.
LCM (6, 20) = 22 × 31 × 51 = 60.
= Product of the greatest power of each prime factor, involved in the numbers.

Common Multiples of 16: 16, 32, 48, 64, 80,… Hence the Least common multiple of 12 and 16 is 48. The LCM of 12 and 16 is 48.

Question 4.
Prove that $$\sqrt { 3 }$$ is irrational.
Let us assume the opposite, (1) $$\sqrt { 3 }$$ is irrational.
Hence $$\sqrt { 3 }$$ = $$\frac { p }{ q }$$
Where p and q(q ≠ 0) are co-prime (no common factor other than 1)

Hence, 3 divides p2
So 3 divides p also …………….. (1)
Hence we can say
$$\frac { p }{ 3 }$$ = c where c is some integer
p = 3c
Now we know that
3q2 = p2
Putting = 3c
3q2 = (3c)2
3q2 = 9c2
q2 = $$\frac { 1 }{ 3 }$$ × 9c2
q2 = 3c2
$$\frac{q^{2}}{3}$$ = C2
Hence 3 divides q2
So, 3 divides q also ……………. (2)
By (1) and (2) 3 divides both p and q
By contradiction $$\sqrt { 3 }$$ is irrational.

Question 5.
Which of the following list of numbers form an AP? If they form an AP, write the next two terms:
(i) 4, 10, 16, 22, …
(ii) 1, -1,-3, -5,…
(iii) -2, 2, -2, 2, -2, …
(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3,…
Solution:
(i) 4, 10, 16, 22, …….
We have a2 – a1 = 10 – 4 = 6
a3 – a2 = 16 – 10 = 6
a4 – a3 = 22 – 16 = 6
∴ It is an A.P. with common difference 6.
∴ The next two terms are, 28, 34

(ii) 1, -1, -3, -5
t2 – t1 = -1 – 1 = -2
t3 – t2 = -3 – (-1) = -2
t4 – t3 = -5 – (-3) = -2
The given list of numbers form an A.P with the common difference -2.
The next two terms are (-5 + (-2)) = -7, -7 + (-2) = -9.

(iii) -2, 2,-2, 2,-2
t2 – t1 = 2-(-2) = 4
t3 – t2 = -2 -2 = -4
t4 – t3 = 2 – (-2) = 4
It is not an A.P.

(iv) 1, 1, 1, 2, 2, 2, 3, 3, 3
t2 – t1 = 1 – 1 = 0
t3 – t2 = 1 – 1 = 0
t4 – t3 = 2 – 1 = 1
Here t2 – t1 ≠ t3 – t2
∴ It is not an A.P.

Question 6.
Find n so that the nth terms of the following two A.P.’s are the same.
1, 7,13,19,… and 100, 95,90,…
The given A.P. is 1, 7, 13, 19,….
a = 1, d = 7 – 1 = 6
tn1 = a + (n – 1)d
tn1 = 1 + (n – 1) 6
= 1 + 6n – 6 = 6n – 5 … (1)
The given A.P. is 100, 95, 90,….
a = 100, d = 95 – 100 = – 5
tn2 = 100 + (n – 1) (-5)
= 100 – 5n + 5
= 105 – 5n …..(2)
Given that, tn1 = tn2
6n – 5 = 105 – 5n
6n + 5n = 105 + 5
11 n = 110
n = 10
∴ 10th term are same for both the A.P’s.

Question 7.
In a flower bed, there are 23 rose plants in the first row, 21 in the second, 19 is the third, and so on. There are 5 rose plants in the last row. How many rows are there in the flower bed?
The number of rose plants in the 1st, 2nd, 3rd,… rows are
23, 21, 19,………….. 5
It forms an A.P.
Let the number of rows in the flower bed be n.
Then a = 23, d = 21 – 23 = -2, l = 5.
As, an = a + (n – 1)d i.e. tn = a + (n – 1)d
We have 5 = 23 + (n – 1)(-2)
i.e. -18 = (n – 1)(-2)
n = 10
∴ There are 10 rows in the flower bed.

Question 8.
Find the sum of the first 30 terms of an A.P. whose nth term is 3 + 2n.
Given,
tn = 3 + 2n
t1 = 3 + 2 (1) = 3 + 2 = 5
t2 = 3 + 2 (2) = 3 + 4 = 7
t3 = 3 + 2 (3) = 3 + 6 = 9
Here a = 5,d = 7 – 5 = 2, n = 30
Sn = $$\frac { n }{ 2 }$$ [2a + (n – 1)d]
S30 = $$\frac { 30 }{ 2 }$$ [10 + 29(2)]
= 15 [10 + 58] = 15 × 68 = 1020
∴ Sum of first 30 terms = 1020

Question 9.
How many terms of the AP: 24, 21, 18, . must be taken so that their sum is 78?
Solution:
Here a = 24, d = 21 – 24 = -3, Sn = 78. We need to find n.
We know that,
Sn = $$\frac { n }{ 2 }$$ (2a + (n – 1)d)
78 = $$\frac { n}{ 2 }$$ (48 + 13(-3))
78 = $$\frac { n}{ 2 }$$ (51 – 3n)
or 3n2 – 51n + 156 = 0
n2 – 17n + 52 = 0
(n – 4) (n – 13) = 0
n = 4 or 13
The number of terms are 4 or 13.

Question 10.
The sum of first n terms of a certain series is given as 3n2 – 2n. Show that the series is an arithmetic series.
Solution:
Given, Sn = 3n2 – 2n
S1 = 3 (1)2 – 2(1)
= 3 – 2 = 1
ie; t1 = 1 (∴ S1 = t1)
S2 = 3(2)2 – 2(2) = 12 – 4 = 8
ie; t1 + t2 = 8 (∴ S2 = t1 + t2)
∴ t2 = 8 – 1 = 7
S3 = 3(3)2 – 2(3) = 27 – 6 = 21
t1 + t2 + t3 = 21 (∴ S3 = t1 + t2 + t3)
8 + t3 = 21 (Substitute t1 + t2 = 8)
t3 = 21 – 8 ⇒ t3 = 13
∴ The series is 1,7,13, …………. and this series is an A.P. with common difference 6.

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 2 Numbers and Sequences Ex 2.1

Question 1.
Find all positive integers which when divided by 3 leaves remainder 2.
The positive integers when divided by 3 leaves remainder 2.
By Euclid’s division lemma a = bq + r, 0 ≤ r < b.
Here a = 3q + 2, where 0 ≤ q < 3, a leaves remainder 2 when divided by 3.
∴ 2, 5, 8, 11 ……………..

Question 2.
A man has 532 flower pots. He wants to arrange them in rows such that each row contains 21 flower pots. Find the number of completed rows and how many flower pots are left over?
Here a = 532, b = 21
Using Euclid’s division algorithm
a = bq + r
532 = 21 × 25 + 7
Number of completed rows = 21
Number of flower pots left over = 7

Question 3.
Prove that the product of two consecutive positive integers is divisible by 2.
Solution:
Let n – 1 and n be two consecutive positive integers. Then their product is (n – 1)n.
(n – 1)(n) = n2 – n.
We know that any positive integer is of the form 2q or 2q + 1 for some integer q. So, following cases arise.
Case I. When n = 2q.
In this case, we have
n2 – n = (2q)2 – 2q = 4q2 – 2q = 2q(2q – 1)
⇒ n2 – n = 2r, where r = q(2q – 1)
⇒ n2 – n is divisible by 2.

Case II. When n = 2q + 1
In this case, we have
n2 – n = (2q + 1)2 – (2q + 1)
= (2q + 1)(2q + 1 – 1) = 2q(2q + 1)
⇒ n2 – n = 2r, where r = q (2q + 1).
⇒ n2 – n is divisible by 2.
Hence, n2 – n is divisible by 2 for every positive integer n.
Hence it is Proved

Question 4.
When the positive integers a, b and c are divided by 13, the respective remainders are 9,7 and 10. Show that a + b + c is divisible by 13.
Let the positive integer be a, b, and c
We know that by Euclid’s division lemma
a = bq + r
a = 13q + 9 ….(1)
b = 13q + 7 ….(2)
c = 13q + 10 ….(3)
a + b + c = 13q + 9 + 13q + 7 + 13q + 10
= 39q + 26
a + b + c = 13 (3q + 2)
This expansion will be divisible by 13
∴ a + b + c is divisible by 13

Question 5.
Prove that square of any integer leaves the remainder either 0 or 1 when divided by 4.
Solution:
Let x be any integer.
The square of x is x2.
Let x be an even integer.
x = 2q + 0
then x2 = 4q2 + 0
When x be an odd integer
When x = 2k + 1 for some interger k.
x2 = (2k + 1 )2
= 4k2 + 4k + 1
= 4k (k + 1) + 1
= 4q + 1
where q = k(k + 1) is some integer.
Hence it is proved.

Again, all the prime numbers you used to divide above are the Prime Factors of 84.

Question 6.
Use Euclid’s Division Algorithm to find the Highest Common Factor (H.C.F) of
(i) 340 and 412
To find the HCF of 340 and 412 using Euclid’s division algorithm. We get
412 = 340 × 1 + 72
The remainder 72 ≠ 0
Again applying Euclid’s division algorithm to the division of 340
340 = 72 × 4 + 52
The remainder 52 ≠ 0
Again applying Euclid’s division algorithm to the division 72 and remainder 52 we get
72 = 52 × 1 + 20
The remainder 20 ≠ 0
Again applying Euclid’s division algorithm
52 = 20 × 2 + 12
The remainder 12 ≠ 0
Again applying Euclid’s division algorithm
20 = 12 × 1 + 8
The remainder 8 ≠ 0
Again applying Euclid’s division algorithm
12 = 8 × 1 + 4
The remainder 4 ≠ 0
Again applying Euclid’s division algorithm
8 = 4 × 2 + 0
The remainder is zero
∴ HCF of 340 and 412 is 4

(ii) 867 and 255
To find the HCF of 867 and 255 using
Euclid’s division algorithm. We get
867 = 255 × 3 + 102
The remainder 102 ≠ 0
Using Euclid’s division algorithm
255 = 102 × 2 + 51
The remainder 51 ≠ 0
Again using Euclid’s division algorithm
102 = 51 × 2 + 0
The remainder is zero
∴ HCF = 51
∴ HCF of 867 and 255 is 51

(iii) 10224 and 9648
Find the HCF of 10224 and 9648 using Euclid’s division algorithm. We get
10224 = 9648 × 1 + 576
The remainder 576 ≠ 0
Again using Euclid’s division algorithm
9648 = 576 × 16 + 432
The remainder 432 ≠ 0
Using Euclid’s division algorithm
576 = 432 × 1 + 144
The remainder 144 ≠ 0
Again using Euclid’s division algorithm
432 = 144 × 3 + 0
The remainder is 0
∴ HCF = 144
The HCF of 10224 and 9648 is 144

(iv) 84,90 and 120
Find the HCF of 84, 90 and 120 using Euclid’s division algorithm
90 = 84 × 1 + 6
The remainder 6 ≠ 0
Using Euclid’s division algorithm
4 = 14 × 6 + 0
The remainder is 0
∴ HCF = 6
The HCF of 84 and 90 is 6
Find the HCF of 6 and 120
120 = 6 × 20 + 0
The remainder is 0
∴ HCF of 120 and 6 is 6
∴ HCF of 84, 90 and 120 is 6

Question 7.
Find the largest number which divides 1230 and 1926 leaving remainder 12 in each case.
Solution:
The required number is the H.C.F. of the numbers.
1230 – 12 = 1218,
1926 – 12 = 1914
First we find the H.C.F. of 1218 & 1914 by Euclid’s division algorithm.
1914 = 1218 × 1 + 696
The remainder 696 ≠ 0.
Again using Euclid’s algorithm
1218 = 696 × 1 + 522
The remainder 522 ≠ 0.
Again using Euclid’s algorithm.
696 = 522 × 1 + 174
The remainder 174 ≠ 0.
Again by Euclid’s algorithm
522 = 174 × 3 + 0
The remainder is zero.
∴ The H.C.F. of 1218 and 1914 is 174.
∴ The required number is 174.

Question 8.
If d is the Highest Common Factor of 32 and 60, find x and y satisfying d = 32x + 60y.
Find the HCF of 32 and 60
60 = 32 × 1 + 28 ….(1)
The remainder 28 ≠ 0
By applying Euclid’s division lemma
32 = 28 × 1 + 4 ….(2)
The remainder 4 ≠ 0
Again by applying Euclid’s division lemma
28 = 4 × 7 + 0….(3)
The remainder is 0
HCF of 32 and 60 is 4
From (2) we get
32 = 28 × 1 + 4
4 = 32 – 28
= 32 – (60 – 32)
4 = 32 – 60 + 32
4 = 32 × 2 -60
4 = 32 x 2 + (-1) 60
When compare with d = 32x + 60 y
x = 2 and y = -1
The value of x = 2 and y = -1

Question 9.
A positive integer when divided by 88 gives the remainder 61. What will be the remainder when the same number is divided by 11?
Solution:
Let a (+ve) integer be x.
x = 88 × y + 61
61 = 11 × 5 + 6 (∵ 88 is multiple of 11)
∴ 6 is the remainder. (When the number is divided by 88 giving the remainder 61 and when divided by 11 giving the remainder 6).

Question 10.
Prove that two consecutive positive integers are always coprime.

1. Let the consecutive positive integers be x and x + 1.
2. The two number are co – prime both the numbers are divided by 1.
3. If the two terms are x and x + 1 one is odd and the other one is even.
4. HCF of two consecutive number is always 1.
5. Two consecutive positive integer are always coprime.

Fundamental Theorem of Arithmetic
Every composite number can be written uniquely as the product of power of prime is called fundamental theorem of Arithmetic.

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.4

Question 1.
Reduce each of the following rational expressions to its lowest form.

Solution:

Question 2.
Find the excluded values, if any of the following expressions.

Solution:
(i) $$\frac{y}{y^{2}-25}=\frac{y}{(y+5)(y-5)}$$ is undefined when (y + 5) (y – 5) = 0 that is y = -5, 5
∴ The excluded values are -5, 5

(ii) $$\frac{t}{t^{2}-5 t+6}$$ is undefined when t2 – 5t + 6 = 0 i.e.
(t – 3) (t – 2) = 0 ⇒ t = 3, 2
∴ The excluded values are 3, 2

(iii) $$\frac{x^{2}+6 x+8}{x^{2}+x-2}$$ is undefined when x2 + x – 2 = 0 i.e.
(x + 2) (x + 1) = 0
∴ The excluded values are 2, 1

(iv) $$\frac{x^{3}-27}{x^{3}+x^{2}-6 x}$$ is undefined when x3 + x2 – 6x = 0, i.e
x(x2 + x – 6) = 0
x(x + 3) (x – 2) = 0
∴ The excluded values are -3, 2

## Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.1

The class 10 maths formulas include formulas related to real numbers, polynomials, quadratic equations, triangles, circles, statistics, probability, etc.

## Tamilnadu Samacheer Kalvi 10th Maths Solutions Chapter 3 Algebra Ex 3.1

Question 1.
Solve the following system of linear equations in three variables
(i) x + y + z = 5; 2x – y + z = 9; x – 2y + 3z = 16
(ii) $$\frac { 1 }{ x }$$ – $$\frac { 2 }{ y }$$ + 4 = 0; $$\frac { 1 }{ y }$$ – $$\frac { 1 }{ z }$$ + 1 = 0; $$\frac { 2 }{ z }$$ + $$\frac { 3 }{ x }$$ = 14
(iii) x + 20 = $$\frac { 3y }{ 2 }$$ + 10 = 2z + 5 = 110 – (y + z)
Solutions:
(i) x + y + z = 5 ………….. (1)
2x – y + z = 9 …………. (2)
x – 2y + 3z = 16 …………. (3)

Substitute z = 4 in (4)
3x + 2(4) = 14
3x + 8 = 14
3x = 6
x = 2
Substitute x = 2, z = 4 in (1)
2 + y + 4 = 5 ⇒ y = -1
x = 2, y = -1, z = 4

$$\frac{1}{y}$$ = b
$$\frac{1}{z}$$ = c in (1), (2) & (3)
a – 2b + 4 = 0 ⇒ a – 2b = -4 …………. (1)
b – c + 1 = 0 ⇒ b – c = -1 ……….. (2)
2c + 3a = 14 ⇒ 2c + 3a = 14 …………. (3)

(iii) x + 20 = $$\frac { 3y }{ 2 }$$ + 10 = 2z + 5 = 110 – (y + z)
x = $$\frac { 3y }{ 2 }$$ – 10 …………. (1)
2z + 5 = 110 – (y + z)
2z = 105 – y – z
y = 105 – 3z ………….. (2)
Substitute (2) in (1), x = $$\frac { 315 }{ 2 }$$ – $$\frac { 9z }{ 2 }$$ – 10
= 2z + 5 – 20
∴ 315 – 9z – 20 = 4z – 30
13 z = 315 – 20 + 30
= 325
z = $$\frac { 325 }{ 13 }$$ = 25
x + 20 = 2z + 5
x + 20 = 50 + 5
x = 35
Substitute z = 25 in (2)
y = 105 – 3z = 105 – 75 = 30
y = 30
x = 35, y = 30, z = 25
The system has unique solutions.

Question 2.
Discuss the nature of solutions of the following system of equations
(i) x + 2y – z = 6 ; -3x – 2y + 5z = -12 ; x – 2z = 3
(ii) 2y + z = 3 (-x + 1); -x + 3y -z = -4 3x + 2y + z = – $$\frac { 1 }{ 2 }$$
(iii) $$\frac { y+z }{ 4 }$$ = $$\frac { z+x }{ 3 }$$ = $$\frac { x+y }{ 2 }$$; x + y + z = 27
Solution:
(i) x + 2y – z = 6 …………. (1)
-3x – 2y + 5z = -12 ……… (2)
x – 2z = 3 …………… (3)

We see that the system has an infinite number of solutions.
(ii) 2y + z = 3(-x + 1);
-x + 3y – z = -4;
3x + 2y + z = –$$\frac { 1 }{ 2 }$$
2y + z + 3x = 3 ⇒ 3x + 2y + z = 3 ………….. (1)
-x + 3y – z = -4 …………. (2)
3x + 2y + z = –$$\frac { 1 }{ 2 }$$ ………………. (3)

This is a contradiction. This means the system is inconsistent and has no solutions.

Sub. x = 3 in (4) ⇒ 5(3) – z = 0
15 – z = 0
-z = -15
z = 15
Sub, x = 3, z = 15 in (3)
x + y + z = 27
3 + y + 15 = 27
y = 27 – 18 = 9
x = 3, y = 9, z = 15
∴ The system has unique solutions.

Question 3.
Vani, her father and her grand father have an average age of 53. One-half of her grand father’s age plus one-third of her father’s age plus one fourth of Vani’s age is 65. Four years ago if Vani’s grandfather was four times as old as Vani then how old are they all now?
Solution:
Let Vani’s age be x
Let Vani’s father’s age be y
Let Vani’s grand father’s age be z.

Sub, z = 84 in (3), we get
4x – 84 = 12
4x = 96
x = 24
Sub, x = 24, z = 84 in (1) we get
24 + y + 84 = 159
y = 159 – 108
= 51
∴ Vani’s age = 24 years
Her father’s age =51 years
Her grand father’s age = 84 years.

Question 4.
The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than five times the former number. If the hundreds digit plus twice the tens digit is equal to the units digit, then find the original three digit number?
Solution:
Let the number be 100x + 10y + z.
Reversed number be 100z + 10y + x.
x + y + z = 11 …………… (1)
100z + 10y + x = 5(100x + 10y + z) + 46
100z + 10y + x = 500x + 50y + 5z + 46
499x + 40y – 95z -46 ………….. (2)
x + 2y = z
x + 2y – z = 0 ……………. (3)

Question 5.
There are 12 pieces of five, ten and twenty rupee currencies whose total value is ₹105. When first 2 sorts are interchanged in their numbers its value will be increased by ₹20. Find the number of currencies in each sort.
Solution:
Let x, y and z be number of currency pieces of 5,10,20 rupees
x + y + z = 12 ………. (1)
5x + 10y + 20z = 105 ………… (2)
10x + 5y + 20z = 125 …………. (3)

Sub, z = 2 in (5), we get
15y + 20 × 2 = 85
15y = 45
y = 3
Sub; y = 3, z = 2 in (1)
x + y + z = 12
x = 7
∴ The solutions are
the number of ₹ 5 are 7
the number of ₹ 10 are 3
the number of ₹ 20 are 2

## Samacheer Kalvi 10th English Solutions Poem Chapter 6 No Men Are Foreign

You can Download No Men Are Foreign Questions and Answers, Summary, Activity, Notes, Samacheer Kalvi 10th English Book Solutions Guide Pdf Poem Chapter 6 help you to revise complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

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## Tamilnadu Samacheer Kalvi 10th English Solutions Poem Chapter 6 No Men Are Foreign

### No Men Are Foreign Textual Questions

A. Based on the understanding of the poem, read the following lines, and answer the questions given below.

(i) Beneath all uniforms, a single body breathes
Like ours: the land our brothers walk upon
Is earth like this, in which we all shall lie.

(a) What is found beneath all uniforms?
Though the outward appearance of people may change because of the difference in their attire, there is an inherent similarity between all human beings. All people live and breathe in a similar fashion. Militaries in the world may don different uniforms but they comprise of human beings who essentially are the same anywhere in the world.

(b) What is the same for every one of us?
When we die, we all shall meet this same earth in the end where we shall be buried in it the same way.

(c) Where are we all going to lie finally?
The poet says that at the end of our respective lives, we all shall lie buried in the same earth. He means to draw our attention to the common fate that awaits us regardless of our nationality.

(a) What makes men strange and countries foreign?
(b) Who is referred to as ‘our brothers’ in this stanza?
(c) What lesson can we learn from these lines?
(d) What should we remember?
(e) What uniforms is the poet talking about?
(f) Where do our brothers walk?
(g) Name the poem and the poet.
(h) What is the figure of speech in the first line?
(i) Explain the metaphor in the first line.
(j) What breathes beneath all uniforms?
(a) Geographical boundaries in segregate countries. We consider countries other than ours to be ‘foreign’ and the people living in these countries to be ‘strange’.
(b) The people who live in countries other than ours have been referred to as our brothers.
(c) These lines teach us the lesson of peace, universal brotherhood and harmony.
(d) We should remember that no men are strange and no country is foreign.
(e) The poet is talking about the different uniforms worn by different people in different countries.
(f) Our brothers walk on this earth which is the same for all.
(g) The name of the poem is ‘No Men Are Foreign’ and the name of the poet is ‘James Kirkup’.
(h) Beneath all uniforms, a single body breathes – Metaphor is the figure of speech employed here. Beneath all uniforms, a single body breathes.
(i) ‘Uniforms’ here basically stand for militaries that different countries in the world have. These uniforms may be different in colour, design, shape and culture, but people donning them are the same anywhere in the world. So the word uniform is indirectly compared to the militaries of different countries.
(j) A single type of body breathes beneath all uniforms.

(ii) They, too, aware of sun and air and water,
Are fed by peaceful harvests, by war’s long winter started.
(a) What is common for all of us?
(b) How are we fed?
(c) Mention the season referred to here?
(a) Sun, air and water is common for all of us.
(b) We the people of the world are nourished and nurtured equally by the elements of Nature like sun, air and water, enjoying the harvests in peaceful times and dreading starvation caused by long-drawn wars.
(c) The season mentioned here is winter.

(a) Who does ‘they’ refer to in the first line?
(b) What are they aware of?
(c) What are all men fed by?
(d) What do you mean by peaceful harvest?
(e) What do you mean by ‘wars’ long winter?
(f) What are they starved by?
(g) Which poetic device has been used in “war’s long winter starv’d”?
(h) Why has war’s winter been called long?
(i) What is the figure of speech in the line, war’s long winter starv’d?
(j) Explain war’s long winter starv’d?
(a) ‘They’ refers to the people of countries other than ours, whom we consider as strangers.
(b) They are aware of the benefits of sun, air and water drawing sustenance from these elements of nature.
(c) All men are fed by peaceful harvests.
(d) By peaceful harvests, we mean the crops grown during the period of peace.
(e) It means the painful days of the war when we are kept indoors.
(f) They are starved by long winter.
(g) The poetic device used in “war’s long winter starv’d” is a ‘metaphor’.
(h) The winter of war has been called ‘long’ because unlike the naturalness it is self-inflicted trouble that not only robs the warmth of peace but also never ending.
(i) The starvation caused by the harsh winter has been compared indirectly to the wartime destruction. So it is a Metaphor. The poetic device can also be Alliteration where the initial consonants in war and winter are repeated.
(j) Here the starvation experienced during unproductive and harsh winter describes the want and hunger faced during war-time. Both these conditions lead to ultimate destruction.

(iii) Their hands are ours, and in their lines we read
A labour not different from our own. –
(a) Who does ‘their’ refer to?
(b) What does the poet mean by ‘lines we read’?
(c) What does not differ?
(d) “Are fed by peaceful harvest, by war’s long winter starved” What is the figure of speech
(a) Their refers to men from different countries.
(b) Lines that show hard work done by the hands.
(c) Labour does not differ.
(d) in this line transferred epithet

(а) Explain the expression: ‘Their hands are ours’.
(b) Explain: ‘A labour not different from our own’.
(a) ‘Their hands are ours’ means that they too work hard like us with their hands to earn their livelihood.
(b) This expression means that the hard work done by the people who live in other countries is not different in any way from the one that we do. All of us have to toil and work hard in a similar way for survival.

(iv) Let us remember, whenever we are told To hate our brothers, it is ourselves That we shall dispossess, betray, condemn
(а) Who tells us to hate our brothers?
(b) What happens when we hate our brothers?
(c) What do we do to ourselves?
(a) The opportunist and leaders and politicians craving for power and authority, in short the selfish people, who control all wartime affairs, tell us to hate our brothers.
(b) When we hate our brothers, we hate ourselves unknowingly.
(c) We dispose and be disloyal to ourselves expressing complete disapproval to our deeds.

(a) What are we doing to our fellow beings?
(b) Why do we sometimes hate our brothers?
(c) How shall we dispossess ourselves?
(d) Whom do we harm by going to war?
(e) What are the aftermaths of hatred?
(f) Why does the poet call all strangers and foreigners ‘brothers’?
(a) We are disposing of; betraying and criticising our fellow beings.
(b) We sometimes hate our brothers because we allow vested and unscrupulous politicians and religious leaders to instigate us. We are taken in by their lies about our differences and begin to consider our brothers as strange and foreign.
(c) We shall dispossess ourselves by disliking our brothers in other parts of the world when we are told by the politically driven people to do so. These brothers cannot become foreign or strange just because they belong to different countries, races and cultures.
(d) By going to war, we harm ourselves as much as we harm the enemy. The environmental pollution makes this earth an equally unhealthy place to live in for both sides that go to war.
(e) The aftermaths of hatred are violence, communal disharmony and inhuman behaviour.
(f) All of them are bound by the common bond of humanity. Hence the poet calls all the , strangers and foreigners as brothers.

(v) Our hells of fire and dust outrage the innocence
Of air that is everywhere our own,
Remember, no men are foreign, and no countries strange.
(a) What outrages the innocence?
(b) Who is not foreign?
(c) What is not strange?
(a) The fire and the dust during a war outrage the innocence.
(b) The people of this earth are not foreign.
(c) Every country on this earth is not strange.

(a) Explain: ‘hells of fire and dust’.
(b) Explain: ‘the innocence of air’.
(a) ‘Hells of fire and dust’ stands for the devastation created and caused by the arms and ammunition used in wars. The dust and smoke thus caused pollute the very air we breathe.
(b) ‘Innocence of air’ means the freshness and purity of air that nature has blessed us with. It also indicates the innocence of the human mind.

(i) Remember they have eyes like ours that wake
Or sleep, and strength that can be won
By love. In every land is a common life
That all can recognise and understand.”
(a) What do all people have in common?
(b) Who does the word, ‘they’ refer to?
(c) Who do the words, ‘ours’ refer to?
(d) What do the eyes do?
(e) How can strength be won?
(f) What is common in every land?
(g) What can all recognize and understand?
(h) Explain: ‘they have eyes like ours that wake or sleep’.
(i) According to the poet, how can we win other people?
(j) What do you understand by ‘common life’?
(k) What should we remember about men?
(l) What should we remember about countries?
(m) What advice does the poet give us in these lines?
(a) All people have eyes, sleep and strength in common.
(b) ‘They’ refers to people whom we discriminate and all the people of different countries whom we consider to be strange.
(c) ‘Ours’ refers to the people living in our own country whom we consider to be like us.
(d) The eyes wake and sleep.
(e) Strength can be won by love.
(f) Life is common in every land.
(g) All can recognise and understand that life is common in every land.
(h) The poet is trying to bring home the idea that those people whom we consider strange m or foreign are similar to us in every way. They sleep and wake up each new day just ’ like us. Even though the colour and shape of their eyes is different from ours, they perform a similar function.
(i) The poet says that the strength of other people can be won by love and kindness, not by force or war.
(j) ‘Common life’ means life anywhere in the world that has similar patterns and features – birth and death, joys and sorrows, youth and old age, and so on and so forth. This commonness of ‘common life’ is experienced by all the people of the world regardless of the country in which they live.
(k) We should remember that no men are strange.
(l) We should remember that no countries are foreign.
(m) The poet advises us to ignore the orders of those who incite us to hate and abuse others because by doing so we harm ourselves.

(ii) “It is the human earth that we defile
Our hells of fire and dust outrage the innocence
Of air that is everywhere our own,
Remember, no men are foreign, and no countries strange”
(a) What are we doing to the earth?
(b) What is outraging this earth?
(c) How do we outrage the innocence of air?
(d) What do you mean by ‘hells of fire and dust’?
(e) What can we call our own?
(f) Is there any strange country?
(g) What is ‘human earth’?
(h) What does the poet want to convey by telling us that “It is the human earth that we defile”?
(i) How do we defile human earth?
(j) How do we humiliate the mother earth?
(k) What should a man remember?
(a) We are polluting this earth.
(b) Hells of fire and dust are outraging this earth.
(c) We outrage the innocence of air by our poisonous ideas and deeds.
(d) ‘Hells of fire and dust’ means the wars that cause a lot of destruction.
(e) We can call the air our own.
(f) No, there isn’t any strange country.
(g) ‘Human earth’ is the human world that is comprised of all countries, races, cultures and creeds.
(h) The poet wants to convey that wars cause enormous destruction of life and possessions. They ruin the clean and green surroundings of the earth and breed disgust and hostility. Hence, no one profits from war because the damage caused to earth is to be tolerated similarly, for we all share the same earth.
(i) We defile or pollute the human earth by using arms and ammunition to cause extensive , death and destruction. Contemporary weapons cause irreparable damage to the environment. So, we defile the earth by our polluted ideas and hellish deeds.
(j) We humiliate the mother earth by fighting and killing one another.
(k) A man should remember that no men are foreign and no countries are strange.

NCERT Class 9 English Poem 6 No Men Are Foreign MCQ Question Answers.

B. Based on your understanding of the poem, complete the summary using the phrases given below.

This poem is about the ……………… (a) ……………… of all men. The subject of the poem is the …………… (b) …………. race, despite of the difference in colour, caste, creed, religion, country, etc. All human beings are the same. We walk on the …………….. (c) ………….. and we will be buried under it. Each and every one of us is related to the other. We all are born the same and die in the same way. We may wear different uniforms like ………………… (d) ………….. during wars the opposing side will also have the same …………… (e) …………….. like ours. We as human do the same labour with ……………. (f) …………… and look at the world with the …………… (g) ……………… Waging war against others as they belong to a different country is like attacking our own selves. It is the ………………(h) ……………. we impair. We all share the same ……………… (i) …………… We are similar to each other. So the poet concludes that we shouldn’t have wars as it is ……………. (j) ……………… to fight against us.
(unity of human, dreams and aspirations, same land, our hands, unnatural, breathing body, same eyes, brotherhood, language, human-earth)
(a) brotherhood
(b) unity of human
(c) same land
(d) language
(e) breathing body
(f) our hands
(g) same eyes
(h) dreams and aspirations
(i) human earth
(j) unnatural

C. Based on your understanding of the poem answer the following questions in a ‘paragraph of about 100-150 words.

Question 1.
‘What is the central theme of the poem ‘No men are foreign’?
Introduction:
In this poem “No men are foreign” James Falconer Kirkup discusses the dreams and aspirations of all men.

The theme of the poem:
The theme of the poem ¡s the unity of the human race, despite the differences in colour, caste, creed, religion, country, etc.

All are equal:
All human beings are the same. We walk on the human earth and we will be buried under it. Breathing, walking and lying are the same for every one of us.

Life is common:
We can read and understand the hard work of everyone through their palm lines. We can understand that life is common in every land.

Never hate our brothers:
When we hate our brothers. We hate ourselves. We deprive, deceive, and condemn ourselves when we hate them. The men who fight only pollute the earth waging war against others is like attacking ourselves.

Conclusion:
The poem concludes that we shouldn’t have war, since it is unnatural to fight against ourselves. The poet asks us to remember the people of other countries are not foreign and the other countries are not strange.

Question 2.
The poem ‘No men are foreign ’ has greater relevance in today’s world. Elucidate. The poet, James Kirkup, quotes various instances to prove that no men are foreign. The very title of the poem is thought-provoking and forces the reader to think about the issue of people living in other countries as foreigners and strangers.

As the poem advances, the poet recurrently emphasises that all human beings are indistinguishable in their nature and tactics. All live on the same earth; enjoy air, sun, and water; love peace, and are opposed to war. They all have mutual experiences and toil in a similar manner to earn the living. The realistic reasoning put forth by the poet and the numerous reminders fully satisfy the reader that no men are foreign. He gets the message that alienation from fellow brethren is equally damaging to himself.

He also understands that by treating other men as foreign, the world stands exposed to the risk of war which can lead to permanent destruction and pollution of mother earth. It is true that many people have been telling us to live harmoniously for since long. We never follow their message. We also know that our greed to get more wealth and power cannot give us a peaceful life.

But some deep-rooted evils in our society make us draw a distinction between people. We know that all customs and conventions have been made by people. We start to hate even our family members due to our ego to be more powerful. By doing so, we at last harm ourselves. In society, people dislike selfish people. So before going to hurt other’s feelings, first of all we should think whether doing such act with others are justified by other people or society.

‘Smile at strangers and you just might change a life. ’

Question 1.
How are we alike? Explain in context with the poem, ‘No Men Are Foreign’.
All human beings are the same. We have a similar body structure. All of us need air to breathe, sunlight and warmth to live and water for our survival. Our daily routine is also similar. We wake up in the morning, bathe, and have breakfast before going on with our daily chores. All of us long for love and affection. We all sleep at night and wake up in the morning. When our needs and feelings are the same, then isn’t it right to treat all men alike? We should not look down upon anybody on the basis of his/her colour, caste, region, or gender.

We should treat everyone as our brother and sister. Unfortunately, some self-centered people fight with others and hurt them. They think that others have harmed them. We should not think that other people are ‘others’. They are also our brothers. If they make one mistake, we should forgive them or compromise with them.

‘Acceptance for one another is the key to living.’

Question 2.
‘ The land our brothers walk upon
Is earth like this, in which we all shall lie.’
What does the poet mean to say in the above lines? Explain.
The poet means to say in these lines that it is the same land on which we walk and tread. After our death, we would be buried in the same earth. Through these lines the poet tells us that we do all our activities on this same land. We get food for our survival from this same land. We make our houses on this land and we get many other things from the same land. Therefore, why should we consider some as strangers? No one is foreign or strange. We live in the same house or universe as a family.

Then why do we create discrimination against some people? Why do we fight with our brothers? It is all because of our greed to get more wealth and power. We want to have more wealth and power than others. In our quest to fulfil this desire, we fight with others and hurt them. The poet also tells us that one day all of us will die. Nothing would remain ours. We cannot take any of our possessions with us. We will have to leave all things on this same earth. Finally when we die, all of us will be buried in this same earth.

‘All are alike. ’

Question 3.
In what way do we dispossess, betray and condemn ourselves by hating our brothers and taking up arms against them?
By hating our brothers and taking up arms against them, we ‘dispossess’ ourselves as we rob ourselves of their love. When we hate them, they too react destructively and stop loving us. Mutually, we deprive each other of the noble emotion of love. We deceive ourselves as our hatred leads to wars, and wars cause widespread death and devastation. This leads to the piling up of waste that pollutes our own mother earth. The dust and smoke from war obstruct the air that we breathe.

So, hatred of fellow beings, in fact, leads to betrayal of our own selves. Further, this earns us condemnation as we disrupt the purity of the elements of nature. We threaten our own existence by ruining the systems that sustain us. Hence, hating our brothers and taking up arms against them does more damage to us.

‘The universal brotherhood of man is our most precious possession. ‘

No Men Are Foreign (James Falconer Kirkup)
Literary Devices At A Glance (Figures of Speech)

No Men Are Foreign by James Falconer Kirkup about the poet:
James Falconer Kirkup was born on April 23, 1918, in South Shields, Durham, England to James Harold Joseph and Mary Virginia. He attended Westoe Secondary School before studying Modem Languages at Armstrong College where he co-produced the poetry magazines Dint and Fulcrum, which featured his earliest verse. James Kirkup, who died on Sunday 10 May, aged 91, at his Andorran home, was an internationally celebrated English poet, travel writer, memoirist, novelist, playwright and translator. Dining the Second World War, Kirkup secured conscientious objector status, working as a farm labourer and for the Forestry Commission.

No Men Are Foreign summary:

Introduction:
In the poem ‘No men are foreign’ the poet stresses the fact that all human beings are equal. He is requesting his countrymen to not treat people unequally. Moreover, the poet conveys that we are scarring the earth by shedding the blood of our brethren in wars. Therefore the poet is putting forth a request to people to live their lives in harmony on this beautiful earth that God has given us.

World fraternity:
Emphasising the value of universal brotherhood, the poet draws our attention to the absence of any differences amongst the people of different countries. He asks us never to forget that people living in other countries are not strange or unfamiliar. The uniforms worn by people in different parts of the world may be different, but the bodies beneath them are the same. All human bodies live and breathe in a similar fashion. We are all brothers because we walk upon the same earth that we have divided into countries. Also, we shall all meet this same earth when we die and be buried in it.

All men are our friends:
All the people of the world are nourished and nurtured equally by the elements of Nature like sun, air and water. We are all human beings. We have a common soul. Everyone is united by the sameness of spirit. Therefore wars and the bloodshed that takes place in the name of caste, class, creed and country are futile and must be condemned. They too prosper during peace but have to suffer poverty, hunger and even dread starvation caused by long-drawn wars. They too toil to earn the livelihood and their destiny is similar to ours.

We should remember that our eyes that wake, sleep and love are similar to eyes all over the world. The poet asks us to remember that the so-called ‘strange’ and ‘foreign’ people experience sleep and wakefulness like us. It is a fact that wherever we may be, we can win powerful strength with love. Their experiences of life are similar to those of ours. Hence, we all find something familiar in each other’s life and realise a common identity with one another.

Hate others and hate yourself:
The poet says whenever we are asked by our leaders or rulers to hate and exploit the people of other countries, we must remember that this hatred would have a negative effect on us. We should keep in mind that if we hate others it means that we hate ourselves. We would find ourselves cheated as it would deprive us of the bliss of universal brotherhood. We would condemn ourselves to a life of enmity and strangeness.

Mother Earth’s mercy:
The poet again retells us in the end that people are contaminating this earth by their deeds. The fatal weapons emit fire and ashes that spread all over and pollute the environment. War is futile as it spoils the very earth for which we take up arms against each other. We should protect our atmosphere and keep in mind that this universe is the creation of God and we all are one. All will one day or the other die and return to earth only. This robs the air of its pureness and the world becomes a more difficult place to live in. The earth that one walks upon is the same for all people from diverse countries. People in every part of the world get the sunshine, air and water in equal methods. It is, therefore, imperative not to consider any human being as foreign and any country as strange. We must build common respect and trust.

Conclusion:
The poet tries to convey that one must shed the difference of opinion and be united and make this earth a haven. To treat anybody as a foreigner is an insult to the one who cultivates.

No Men Are Foreign Glossary:
Textual:

## Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium

Students can Download Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium Pdf, Samacheer Kalvi 10th Social Science Model Question Papers helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations.

This discussion on I want class 10th sst MCQ of all chapter? is done on CBSE Study Group by Class 10 Students.

## Tamil Nadu Samacheer Kalvi 10th Social Science Model Question Paper 1 English Medium

General Instructions:

1. The question paper comprises of four parts
2. You are to attempt all the questions in each part. An internal choice of questions is provided wherever applicable.
3. All questions of Part I, II, III and IV are to be attempted separately.
4. Question numbers 1 to 14 in Part I are Multiple Choice Questions of one mark each.
These are to be answered by writing the correct answer along with the corresponding option code and the corresponding answer
5. Question numbers 15 to 28 in Part II are of two marks each. Any one question should be answered compulsorily.
6. Question numbers 29 to 42 in Part III are of five marks each. Any one question should be answered compulsorily.
7. Question numbers 43 to 44 in Part IV are of Eight marks each. Draw diagrams wherever necessary.

Time: 3 Hours
Maximum Marks: 100

Part – I

Answer all the questions. Choose the correct answer [14 × 1 = 14]

Question 1.
Where did the Ethiopian army defeat the Italian army?
(a) Delville
(b) Orange State
(d) Algiers

Question 2.
With whose conquest did the Mexican civilization collapse?
(a) Hernan Cortes
(b) Francisco Pizarro
(c) Toussaint Louverture
(d) Pedro I
(a) Hernan Cortes

Question 3.
In which year was Sati abolished?
(a) 1827
(b) 1829
(c) 1826
(d) 1927
(b) 1829

Question 4.
Who was the first Palayakkarar to resist the East India Company’s policy of territorial aggrandizement?
(a) Marudhu brothers
(b) Puli Thevar
(c) Velunachiyar
(d) Veera Pandya Kattabomman
(b) Puli Thevar

Question 5.
established a full-fledged printing press in 1709, at Tranquebar.
(a) Caldwell
(b) F.W.Ellis
(c) Ziegenbalg
(d) Meenakshisundaram
(c) Ziegenbalg

Question 6.
The North-South extent of India is
(a) 2,500 km
(b) 2,933 km
(c) 3,214 km
(d) 2,814 km
(c) 3,214 km

Question 7.
Pick the odd one out.
(a) Cotton
(b) rice
(c) Wheat
(d) Maize
(a) Cotton

Question 8.
The city which is called as the Manchester of South India is
(a) Chennai
(b) Salem
(d) Coimbatore
(d) Coimbatore

Question 9.
The highest peak in Tamil Nadu is
(a) Anaimudi
(b) Doddabetta
(c) Mahendragiri
(d) Servarayar
(b) Doddabetta

Question 10.
The delta which is known as Granary of South India is
(a) Cauvery delta
(c) Godavari delta
(d) Krishna delta
(a) Cauvery delta

Question 11.
How many times has the preamble to the constitution of India amended?
(a) Once
(b) Twice
(c) Thrice
(d) Never
(a) Once

Question 12.
Which is not related to our foreign policy?
(a) World co-operation
(b) World peace
(c) Racial equality
(d) Colonialism
(d) Colonialism

Question 13.
Which one is a trade policy?
(a) irrigation policy
(b) import and export policy
(c) land-reform policy
(d) Wage policy
(b) import and export policy

Question 14.
Tiruppur is known for ………………
(a) Leather tanning
(b) lock making
(c) knit wear
(d) Agro – Processing
(c) knit wear

Part – II

Answer any 10 questions. Question No. 28 is compulsory. [10 × 2 = 20]

Question 15.
How did Great Depression impact on the Indian agriculture?

• The Great Depression had a deep impact on the Indian agriculture. The value of farm produce, declined by half, while the land rent to be paid by the peasant, remained unchanged.
• In terms of prices of agricultural commodities, the obligation of the farmers to the state doubled.

Question 16.
How was the Cuban Missile crisis defused?

• The Cuban Missile crisis was a confrontation between the United States and the Soviet Union which initiated by the American discovery of Soviet Ballistic missile deployment in Cuba.
• Finally, the Soviet President Nikita Khrushchev agreed to withdraw the missiles and thus the missile crisis was defused.

Question 17.
Explain the concept of constructive swadeshi?
Under Constructive Swadeshi the self-defeating modest approach of moderates was rejected and self-help was focused on through swadeshi industries, national schools, arbitration courts and constructive programmes in the village. It was totally non-political in nature.

Question 18.
What do you know of the Cheranmahadevi Gurukulam incident?
A Gurukulam was established in Cheranmahadevi by V. V. S. Iyer with the financial support of the Tamil Nadu Congress Committee. However, students were discriminated on the basis of caste. Brahmin and non-Brahmin students were made to dine separately.

Periyar was disturbed to see the discrimination. He questioned the practice, and severely criticised it. Despite his objections the Congress continued to support the iniquitous practice in the Gurukulam. This disappointed Periyar.

Question 19.
Write a brief note on the island group of Lakshaweep.

• It lies close to the Malabar coast of Kerala.
• This group of islands is composed of small coral islands.
• Earlier they were known as Laccadive, Minicoy and Amindive. In 1973, these were named as Lakshadweep.
• This island group has great diversity of flora and fauna. The Pitti island which is uninhabited, has a bird sanctuary.

Question 20.
State the major Inland waterways of India.
The major inland water ways of India are:

• National Waterway 1: It extends between Haldia and Allahabad, measures 1620 km and includes the stretches of the Ganga – Bhagirathi – Hooghly river system.
• National Waterway 2: This waterway includes the stretch of the Brahmaputra river between Dhubri and Sadiya a distance of 891 km.
• National Waterway 3: This waterway extends between Kollam and Kottappuram in the state of Kerala. It is the first national waterway in the country with 24 hour navigation facilities along its entire stretch of 205 km.

Question 21.
Name the major Islands of Tamil Nadu.
Pamban, Hare, Krusadai, Nallathanni Theevu, Pullivasal, Srirangam, Upputanni, Island Grounds, Kattupalli Island, Quibble Island and Vivekananda Rock Memorial are some major islands of Tamil Nadu.

Question 22.
List out the air ports and sea ports of Tamil Nadu.
Airports:

• Chennai International Airport
• Coimbatore International Airport
• Tiruchirapalli International Airport

Domestic Airports:

• Tuticorin and Salem

Sea Port: Major Sea Ports are:

• Chennai
• Ennore
• Tuticorin

Intermediate port at Nagapattinam and 15 minor ports.

Question 23.
What are the classical languages in India?
There are six classical languages namely – Tamil, Sanskrit, Telugu, Kannada, Malayalam and Odia.

Question 24.
List any four guiding principles of Panchsheel.
Guiding principles of Panchsheel are:

1. Mutual Respect for each other’s territorial integrity and sovereignty
2. Mutual non-interference
3. Equality and co-operation for mutual benefit
4. Peaceful co-existence.

Question 25.
Define National Income.
National Income is a measure of the total value of goods and services produced by an economy over a period of time, normally a year. National Income is also known as Gross National Product or GNP or National Dividend.

Question 26.
What is globalization?
Globalization is the process of integrating various economies of the world without creating any barriers in the free flow of goods and services, technology, capital and even labour or human capital.

Question 27.
Define tax.
Tax is levied by government for the development of the state’s economy. The revenue of the government depends upon direct and indirect taxes.

Question 28.
Define the resource and state its types.
Any matter or energy derived from the environment that is used by living things including humans is called a natural resource.
Types of Natural Resources are:

1. Renewable and
2. Non – renewable resources.

Part – III

Answer any 10 questions. Question No. 42 is compulsory. [10 × 5 = 50]

Question 29.
Fill in the blanks
(i) …………..was humiliated by the Treaty of Versailles.
(ii) …………………..makes our toothpaste white.
(iii) The Dutch captured pondicherry in ………………..
(iv) ………………are very important in the modem economic activities of man.
(v) Sathanur dam is constructed across the river………….
(i) Germany
(ii) Titanium Oxide
(iii) 1693
(iv) Industries
(v)Thenpennai

Question 30.
Match the following

Question 31.
Match the following

Question 32.
(a) Distinguish between
(i) GMT and 1ST.
(ii) Weather and Climate,
(a) (i) GMT and IST:
GMT :

• It means Greenwich Mean Time.
• GMT is calculated at 0° longitude.
• It passes through Greenwich.
• It is the World Standard Time.

IST:

• It means Indian Standard Time.
• India’s central meridian is 82° 30’ E longitude.
• It passes through Mirzapur.
• It is the Indian Standard Time.

(ii) Weather and Climate:
Weather:

• Weather is a day to day conditions of the atmosphere of any place in regard to temperature, pressure, wind, humidity and rainfall.
• It is calculated for a day or a short period of time.

Climate:

• Climate is the average state of weather for a longer period of time at any place.
• To get reliable average of climate, a minimum of 35 years records of weather are necessary.

(b) Give reason: The river Godavari is often referred as Vridha Ganga.

• The Godavari is India’s second longest river after Ganga.
• It rises from the slopes of the Western Ghats in the Nasik district of Maharashtra.
• It covers a large number of states as the Ganga does. Because of its large size and extend among the peninsular rivers, the river Godavari is often referred to as Vridha Ganga.

Question 33.
Narrate the history of transformation of Council of Europe into an European Union.
(i) After World War II, it was decided to integrate the states of western Europe. One of the chief objectives was to prevent further European wars by ending the rivalry between France and Germany. In May 1949, ten countries met in London and signed a form called Council of Europe.

(ii) Since the Council of Europe had no real power, a proposal to set up two European organisations were made. Accordingly, the European Defence Community (EDC) and the European Coal and Steel Community (ECSC) were established. Six countries belonging to ECSC signed the treaty of Rome which established the European Economic Community (EEC) or the European Common Market, with headquarters at Brussels.

(iii) The EEC facilitated the elimination of barriers to the movement of goods and services, capital, and labour. It also prohibited public policies or private agreements that restricted market comptetion. Throughout the 1970s and 80s the EEC kept expanding its membership.

(iv) The single European Act came into force on July 1, 1987. It significantly expanded the EEC’s scope giving the meetings of the EPC a legal basis. It also called for more intensive coordination of foreign policy among member countries. According to the SEA each member was given multiple votes, depending on the countries population.

(v) The Maastricht (Netherlands) Treaty signed on February 7, 1992, created the European Union (EU). Today the European Union has 28 member states, and is functioning from its headquarters at Brussels, Belgium.

Question 34.
Eumerate the cause for the failure of the great Revolt of 1857.

• Disunity among the Indians was the first and the foremost cause.
• A large number of rulers of the Indian states and the big zamindars did not j oin the movement.
• The rulers of the Indian states, who did not support the movement, remained neutral.
• The educated Indians did not support the movement.
• The telegraph and postal communication proved very helpful to the British for proper military actions and sending their reinforcements at the earliest time.
• The rebellious soldiers were short of modem weapons and other materials of war.
• The rebellious soldiers had to fight with traditional weapons which were no match to modem weapons possessed by the British forces.
• The revolt was not extended beyond North.
• The Indian leaders like Nana Saheb, Tantia Tope, Rani Lakshmi Bai where no match to the British generals.
• The revolt broke out prematurely and the preparations for the revolt remained incomplete.
• The organization and the planning of the rebels was very poor.
• The Indian leaders were brave and selfless but they lacked unity of command and discipline.
• The revolutionaries had no common idea.
• The Muslims wanted to revive Mughal rule and the Hindus wanted to receive the Peshwa Raj.
• The British diplomacy of Divide and Rule prevented most of the Indian rulers to j oin together for a common cause.

Question 35.
Write about any two multipurpose projects of India.
A comprehensive river valley project which serves a number of purposes simultaneously is called a “Multi purposes project”.
1. The Bhakra Nangal Project: India’s biggest multipurpose river valley project is ‘Bhakra Nangal Project’. It has been built at a strategic point where two hills on either side of the Sutlej are very close to each other. It is the highest gravity dam in the world. Its length is 226 metres from the riverbed. The canals taken out are 1100 kilometres long. The ‘Nangal Power Plant’ on the Sutlej produces electricity, and serves the states of Himachal Pradesh, Punjab, Haryana, Rajasthan and New Delhi. The distributaries are 8400 km in length. It irrigates an area of 1.4 million hectares.

2. Indira Gandhi Project: This project is an ambitious scheme to bring new areas under irrigation so that more areas could be cultivated. The waters of the River Beas and the Ravi are diverted to the River Sutlej. The ‘Pong’ Dam on the River Beas has been constructed to divert the Beas water into the Sutlej in a regulated manner. So that ‘Rajasthan canal’, the longest irrigation canal in the world can irrigate Gandhi Nagar, Bikaner and Jaisalmer districts of North West Rajasthan, (i.e) a part of Thar desert. The main canal now called ‘Indira Gandhi Canal’ is 468 km long runs entirely in Rajasthan, Western of Sutlej, Beas and Ravi are now being fully utilised for irrigating thirsty lands of South Western parts of our country.

Question 36.

• Tea, coffee, cashew, rubber and cinchona are the major plantation crops of the state.
• Tamil Nadu ranks second in area and production of tea in India next to Assam.
• Tea plantations are found in the hills of the Nilgiris and Coimbatore.
• Coffee plants are grown in the hills of Western Ghats as well as Eastern Ghats.
• The Nilgiris and Yercaud in Salem are the notable regions for tea plantations.
• It is also found in the hilly slopes of Dindigul, Madurai, Theni and Dharmapuri districts.
• Tamil Nadu stands second in area and in production of coffee next to Karnataka.
• Rubber plantations are significant in Kanyakumari.
• Pepper is confined to the warm and wet slopes of Eastern and Western Ghats of Tamil Nadu. .
• Cashew is extensively cultivated in Cuddalore district.
• Cinchona is planted at heights varying from 1060 to 1280 metres in Anaimalai hills.
• Cardamom estates are located at few places in the hills of Madurai region at an elevation of 915 to 1525 metres.

Question 37.
Explain the salient features of the constitution of India.
Here are the salient features of the Indian Constitution.

• It is the lengthiest of all the written Constitutions of the world.
• It is partly rigid and partly flexible.
• It establishes a federal system of Government.
• It establishes the Parliamentary systems not only at the Centre but also in the States.
• It provides an independent judiciary.
• It makes India as a secular state.
• It introduces Universal Adult Franchise and accords the right to vote to all citizens above 18 years of age without any discrimination.
• It provides single citizenship.
• It makes special provisions for minorities, SCs, STs, etc.

Question 38.
Write a short note on SAARC.
SAARC:
SAARC means, The South Asian Association for regional co-operation.

• India took the initiative to form SAARC to maintain peace in the regional level.
• SAARC’s first meeting was held at Dacca in Bangladesh in Dec 7, 1985.
• Ashan of Bangladesh was the first secretary general of SAARC.
• The member countries are Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Afghanistan and Sri Lanka.
• On April 3, 2007 the SAARC’s annual summit was held in New Delhi. Afghan president Hamid Karzai attended this meeting. Afghanistan became its 8th member.
• 18th SAARC summit took place on 26* and 27* of November 2014 at Kathmandu the capital of Nepal.
• The SAARC countries identified mutual co-operation in the following areas transportation postal service, tourism, shipping meteorology, health, agriculture rural reconstruction and telecommunication.

Question 39.
What are the methods of calculating Gross Domestic Product?
Methods of calculating Gross Domestic Product or GDP:

• Expenditure Approach – In this method, the GDP is measured by adding the expenditure on all the final goods and services produced in the country during a specified period.
• Income Approach – This method looks at GDP from the perspective of the earnings of the men and women who are involved in producing the goods and services.
• Value-added Approach – In the value – added approach the value added by each intermediate good is summed to estimate the value of the fiscal good. The sum of the value added by all the intermediate goods used in productions gives us the total value of the final goods produced in the economy.

Question 40.
Briefly explain the nutritional and health status of Tamil Nadu.
Status of Nutrition:

• We noted earlier that food security includes nutrition security too. Though our country has reached self-sufficiency in food production, the nutrition status of the population has not seen corresponding levels of improvement.
• In 2015-16, 27% of the rural women and 16% of the urban women (in the age group of 15-49 years) were counted as undernourished or chronically energy deficient by the National Family Health Survey.
• More than half of the women in the reproductive age group (15-49 years) in both rural and urban India were anaemic in 2015-16. As regards children, about 60% of the rural and 56% of the urban children (in the age group of 6-59 months) are counted to be anaemic, in 2015-16.
• About 41 % of the rural and 31 % of urban children are stunted, that is, they are not of the required height in correspondence to their age. Another indicator of nutrition deficiency . among children is “underweight”, which is weight in relation to age.
• In India, in 2015-16, about 20% of children (in the age group of 6-59 months) in rural and urban India are estimated to be underweight.

Question 41.
Draw a time line for the following:
Write any five important events between 1934-1961

Question 42.
Mark the following places on the world map.
(i) Great Britain
(ii) Germany
(iii) France
(iv) Italy
(v) Greece

Part – IV

Answer both questions. [2 × 8 = 16]

Question 43.
(a) German Emperor
(i) What was the nature of Emperor Kaiser Wilhelm II of Germany?
(ii) What was the violent form of Germany called?
(iii) Why did Kaiser Wilhelm intervene in the Morocco affair?
(iv) What happened to Germany’s colonies in Africa?
(a) German Emperor

(i) The Emperor Kaiser Wilhelm II of Germany was ruthlessly assertive and aggressive. He proclaimed that Germany would be the leader of the world.

(ii) It was called Germany’s Kultur.

(iii) The British agreement with France over the latter’s interest in Morocco was consented by Germany. So Kaiser Wilhelm II of Germany intentionally recognised the independence of the Sultan and demanded an international conference to decide on the future of Morocco.

(iv) The German colonies in western and eastern Africa were attacked by the Allies. As these
colonies were quite far off from Germany they could not receive any immediate help, and therefore had to surrender to the Allies.

(b) Korean War
(i) Who was the President of North Korea during the Korean War?
(ii) Name the southern rival to the President of North Korea.
(iii) How long did the Korean War last?
(iv) What was the human cost of the War?
(b) Korean War
(i) Kim II was the President of North Korea during the Korean War.
(ii) Syngman Rhee
(iii) The Korean War lasted three years
(iv) The human cost was enormous, there were 500,000 western casualties and three times that number on the other side. Approximately two million Korean civilian died.

[OR]

Question 43.
(c) The Revolt of 1857
(i) Who assaulted his officer, an incident that led to the outbreak of 1857 Revolt?
(ii) Who was proclaimed the Shahenshah-e-Hindustan in Delhi?
(iii) Who was the correspondent of London Times to report on the brutality of the 1857 revolt?
(iv) What did the Queen’s proclamation say on matters relating to religion?
(c) The Revolt of 1857
(i) Mangal Pandey assaulted his officer.
(ii) The Mughal Emperor Bahadur Shah II was proclaimed the Shahenshah-e-Hindustan in Delhi.
(iii) The correspondent’s name was William Howard Russell.
(iv) The Queen proclaimed to the Indian people that the British government would not interfere in traditional institutions and religious matters. ‘

(d) Constructive Programme of Gandhi
(i) What is constructive programme?
(ii) What did Gandhi exhort the Congressmen to do?
(iii) How did Gandhi try to bring about Hindu-Muslim unity?
(iv) What is the contribution of Gandhi towards abolition of untouchability?
(d) Constructive Programme of Gandhi
(i) Programmes that aimed at Khadi promotion, Hindu-Muslim unity and the abolition of untouchability are called constructive programmes.
(ii) He exhorted the Congressmen to go throughout their districts and spread the message of Khaddar, the message of Hindu-Muslim unity, the message of anti-untouchability and take up in hand the youth of the country and make them the real soldiers of Swaraj.
(iii) Gandhi tried to bring about Hindu-Muslim unity to strengthen the cause of Swaraj.
(iv) Gandhiji wanted to abolish untouchability from the country. He undertook an all-India tour called the Harijan Tour. He started the Harijan Sevak Sangh to work for the removal of discriminations. He worked to promote education, cleanliness and hygiene and giving up of liquor among the depressed class. He also launched the Temple Entry Movement.

Question 44.
Mark the following places on the given outline map of India.
(i) Western Ghats
(ii) Mumbai
(iii) Rice cultivation area
(iv) Panna biosphere reserve
(v) Air route from Chennai to Delhi
(vi) Mountain forests
(vii) Direction of South West monsoon
(viii) Cotton growing area

[OR]

Mark the following places on the given outline map of Tamil Nadu:
(i) Gulf of Mannar .
(ii) Manimutharu dam
(iii) Pamban
(iv) Chennai port
(v) Any one international airport
(vi) Graphite ore production centre
(vii) Rubber growing area
(viii) Magnesite ore production centre .

Map for Q 42
(i) Great Britain
(ii) Germany
(iii) France
(iv) Italy
(v) Greece

Map for Q. 44
(i) Western Ghats
(ii) Mumbai
(Hi) Rice cultivation area
(iv) Panna biosphere reserve
(v) Air route from Chennai to Delhi
(vi) Mountain forests
(vii) Direction of South West monsoon
(viii) Cotton growing area

Map for Q. 44
(i) Gulf of Mannar
(ii) Manimutharu dam
(iii) Pamban
(iv) Chennai port
(v) Any one international airport
(vi) Graphite ore production centre
(vii) Rubber growing area
(viii) Magnesite ore production centre

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