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## REAL NUMBERS

EUCLID'S DIVISION LEMMA

Given positive integers a and b. there exist unique integers q and r satisfying a = bq + r where
0<  r <b,
Here we call 'a' as a dividend, 'b' as divisor 'q' as quotient and 'r' as the remainder,

Dividend = (Divisor x Quotient) + Remainder

If in Euclid's lemma r= 0 then b would be HCF of 'a' and 'b'.

### IMPORTANT QUESTIONS

Show that any positive even integer is of the form 6q, or 6q+ 2, or 6q + 4. where q is some integer.

Solution: Let x be any positive integer such that x >6, Then, by Euclid's algorithm, x = 6q +r for some integer q > 0 and 0 <  r < 6.
Therefore, x= 6q or 6q+1 or 6q + 2 or 6q + 3 or 6q + 4 or 6q + 5 .
Now, 6q is an even integer being a multiple of 2.
We know that the sum of  two even integers are always even integers.
Therefore, 6q+2 and 6q + 4 are even integers .
Hence any positive even integer is of the form 6q. or 6q + 2, or 6q + 4. where q is some integer,

#### Questions for practice

1. Show that any positive even integer is of the form 4q or 4q + 2, where q is some integer.

2. Show that any positive odd integer is of the form 4q + 1, or 4q+3, where is some integer.

3. Show that any positive odd integer is of the form 6q + 1. or 6q + 3, or 6q + 5, where is some integer.

4. Use Euclid's division lemma to show that the square of any positive integer is either of the form 3m or 3m + 1 for some integer m.

5. Use Euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m + 1 or 9m +8.

EUCLID'S DIVISION ALGORITHM

Euclid's division algorithm is a technique to compute the Highest Common Factor (HCF) of two given positive integers. Recall that the HCF of two positive integers a and b is the largest positive integer d that divides both a and b.

To obtain the HCF of two positive integers, say c and d, with c > d, follow the steps below:

Step 1: Apply Euclid's division lemma, to c and d. So, we find whole numbers, q and r such that c =dq+r. 0 < r < d

Step 2: If r=0. d is HCF of c and d. If r is not equal 0 apply the division lemma to d and r .

Step 3: Continue the process till the remainder is zero. The divisor at this stage will be the required HCF.

This algorithm works because of HCF (c,d) = HCF (d,r) where the symbol HCF (c,d) denotes the HCF of c and d, etc.

IMPORTANT QUESTIONS

Use Euclid's division algorithm to find the HCF of 867 and 255

Solution: Since 867 > 255, we apply the division lemma to 867 and 255 to obtain 867 = 255  X  3 + 102.
Since remainder    $102&space;\neq&space;0$ , we apply the division lemma to 255 and 102 to obtain.
255 = 102 X 2 + 51
We consider the new divisor 102 and new remainder 51, and apply the division lemma to obtain 102 = 51 X 2 + 0
Since the remainder is zero, the process stops.
Since the divisor at this stage is 51
Therefore, HCF of 867 and 255 is 51.

Questions for practice

1. Use Euclid's algorithm to find the HCF of 4052 and 12576.

2.Use Euclid's division algorithm to find the HCF of 135 and 225.

3. Use Euclid's division algorithm to find the HCF of 196 and 38220.

4. Use Euclid's division algorithm to find the HCF of 455 and 42.

5. Using Euclid's algorithm, find the HCF of (i) 405 and 2520 (ii) 504 and 1188  (iii) 960 and 1575

## CLASS: X

### General Instruction:

(i) All the questions are compulsory.
(ii)The question paper costs of 40 questions divided into 4 sections ABC, and D
(iii) Section A comprises of 20 questions of 1 marks each. Section B comprises of 6 questions of 2 marks Section B comprises of 8 questions of 3 marks each. Section D comprises of 6  questions of 4 marks each.

#### SECTION -A

Questions 1 to 20 carry 1 mark each.

1. LCM of two co-prime numbers is always

(a) product of number
(b) sum of numbers
(c) difference of numbers.
(d)none

2 .For some integer q. every odd integer is of the form
(a)q
(b)q+1
(c)2q
(d)2q+1

3.$\sqrt{3}$ is

(a) a natural number
(b) a rational number
(c) not o a real number
(d) an irrational number

4. The product and sum of zeroes of the quadratic polynomial x2 + bx + c respectively are:

(a) b  ,   c
a      a

(a) c  ,   b
a      a

(a) c  ,   1
b

(a) c ,   -b
a      a

5. The ratio in which x-axis divides the line segment joining the points (5, 4) and (2-3) is
(a) 5:2
(b) 3:4
(C) 2:5
(d) 4: 3

6. Point on y-axis has coordinates

(a)(a,b)
(b)(a,0)
(c) (0,6)
(d) (-2, -b)

7 .From a point P,10 cm away from the centre of a circle, a tangent PT of length 8 cm is drawn Find the radius of the circle

(a)4 cm
(b) 5 cm
(c) 7 cm
(d)6 cm

8.

9. A box contains 3 blue, 2 white, and 5 red marbles. If a marble is drawn at random from the box then what is the probability that the marble will be blue ?

(a)  3,
10

(b) 1
2

(c) 1

(a)  0

11. The end points of diameter of circle are (2,4) and (-3,1). The radius of circle is _____

12. Value of tan 30 - cos 45 is ______

13. The value of san60° cos 30° - cos 60°sin30° is_____

14. 1f ∆ABC and ∆DEF are two triangles such that AB. = BC  = CA  =2 , Then ar(∆ABC) =
DE.     EF.     FD.   5            ar(∆DEF)

15. If (6, k) sa solution of the equation 3x + y-22=0, then the value of k is

16. Find the area of a sector of a circle with radii 6 cm if angle of the sectors is 90°.

17. IF P(E) = 0 47, what is the probability of 'not E'?

18. Find the 9th term from the end (towards the first term) of the AP 5,9.,13,..... ,185.

19. 1f  cot2© =tan1© , where 2θ nd 4θ are acute angles, find the value of sin 3θ.

20.ABC and BDE are two equilateral triangles such that D is the  midpoint of BC .Find the ratio of the areas of triangles ABC and BDE

### SECTION B Questions 21 to 26 carry 2 marks each

21. Three cards of spades are lost from a pack of 52 playing cards The remaining cards were well stuffed and then a card was drawn al random from them .Find the probability that the drawn cards of black colour

OR

Find the probability that a leap year should have exactly 52 Tuesday.

22. Two different dice are tossed together. Find the probability (i) that the Number on each dice is  Even (ii) that the sum of numbers appear on two dice is 5.

23. A wie s loped in the form of a circle of radan 28 cm .It reverted into a square form.Determine the side of the square.

24. Show that tan48° tan 23° tan 42°tan 67° =1

25. Find a quadratic polynomial whose zeroes are -5 and 7.

26. A quadrilateral ABCD is drawn to circumscribe circle Prove that AB + CD = AD + BC.

### SECTION -C Questions 27 to 34 carry marks each.

27.Find the HCF and LCM of 180 and 288 by prime factorisation method.

28 To conduct Sports Day activities, in your rectangular aided school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each 100 flower pots have been placed at a distance of 1m from each other along AD, as shown in the  figure Aditi name 1/5th the distance AD on the 2nd lne and posts a green fag Priyanka runs 1/4th the distance AD on the eighth line and posts a red flag
(i) What is the distance between both the flags?

(ii) If Manta has to post a blue flag exactly halfway between the line segment joining the two Nags, where should the post her flag?

29. Find the zeroes of the quadratic polynomial 9t - 6t + 1, and verify the relationship between the zeroes and the coefficients.

30. Solve the following system of equations graphically for x and y 3x + 2y= 12, 5x-2y=4

31. Prove that The lengths of the two tangents from an external point to a circle are equal.

32. Draw a line segment of length 9 cm and divide in the rate 3:4. Measure the two parts.

33. Prove that. A conec Ayrcos A CAY - 7+ A+ cor A

OR

Prove that

setan

14 sin A 1-m 4

34. In the below for sure OABC is inscribed quadrant OPBQ. If OA =20 cm, find the area of the shaded region.(Use Π= 3.14)

### SECTION -D Questions 35 to 40 carry marks rach

35. A 1.5 m tall boy is standing at some distance from a 30 m tall building. The angle of elevation from his eyes to the top of the building increases from 30° to 60° as he walks towards the building. Find the distance he walked towards the building.

36. The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

37. Find the sum of first 24 terms of the list of numbers whose nth term is given by An= 3 + 2n

38.Prove that If Image is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then the other two sides are divided in the same ratio

OR

State and prove converse of Pythagoras theorem

39. A cubical block of side 7 cm is surmounted by a hemisphere. What is the greatest diameter the hemisphere can have? Find the surface area of the solid.

40.

### Sample Paper 1 | Based on full NCERT | MATHS | Class 10

SUBJECT: MATHEMATICS
SAMPLE PAPER 1
CLASS : X
MAX. MARKS: 80
DURATION : 3 HRS

General Instruction:

(i) All the questions are compulsory.

(ii) The question paper consists of 40 questions divided into 4 sections A, B, C, and D.

(iii) Section A comprises of 20 questions of 1 mark each. Section B comprises of 6 questions of 2 marks each. Section C comprises of 8 questions of 3 marks each. Section D comprises of 6 questions of 4 marks each.

(iv) Use of calculators is not permitted.

SECTION - A

1.The decimal expansion of pie
(a) is terminating
(b) is non terminating and recurring
(c) is non-terminating and non-recurring
(d) does not exist.

2.The product of L.C.M and H.C.F. of two numbers is equal to
(a) Sum of numbers
(b) Difference of numbers
(c) Product of numbers
(d) Quotients of numbers

3. What is the H.C.F. of two consecutive even numbers
(a) 1
(b)2
(c) 4
(d) 8

4. A quadratic polynomial can have at most... zeros
(a) 0
(b) 1
(c)2
(d) 3

5. Which are the zeroes of p(x) = (x - 1)(x-2):

(a) 1,-2
(b) - 1,2
(c) 1,2
(d)-1,-2

6. X-axis divides the join of A(2.-3) and B(5,6) in the ratio
(a) 3:5
(b) 2:3
(c) 2:1
(d) 1:2

7. If the distance between the points (8. p) and (4.3) is 5 then value of p is
(a) 6
(b) 0
(c) both (a) and (b)
(d) none of these

8. TP and TQ are the two tangents to a circle with center O so that angle POQ = 130°. Find angle PTQ.

(a) 50°
(b) 70
(c) 80"
(d) none of these

9. Cards are marked with numbers 1 to 25 are placed in the box and mixed thoroughly. What is the probability of getting a number 5?

(a) 1
(b) 0
(c) 1
25

(d) 1
5

10. The value of y for which the points A(1.4), B(3. y) and C-3, 16) collinear is

11. If  ∆ABC is right-angled at B, then the value of cos(A + C) is

12. If tanA =  , then the value of cosA is
3
13. In ABC, DE || BC and AD = 4 cm, AB =9 cm. AC = 13.5 cm then the value of EC is

14. The value of k for which the quadratic equation 4x 3kx +1=0 has real and equal roots

15. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. Find the area of the sector formed by the arc

16. A bag contains lemon flavoured candies only. Malini takes out one candy without looking into the bag. What is the probability that she takes out a lemon flavoured candy?

17. In ∆ ABC, right-angled at B, AB = 5 cm and ㄥACB = 30° then find the length of the side BC

18. If sin 30 = cos(0-6) here, 30 and (0-6°) are acute angles, find the value of 0.

19. For what value of p, are 2p+1, 13,5p - 3 three consecutive terms of an AP?

20. The areas of two similar triangles ABC and ADEF are 144 cm and 81 cm, respectively. If the longest side of larger ABC be 36 cm, then find the longest side of the similar triangle ADEF.

SECTION B

21.15 cards, numbered 1,,. 3,. . ,15 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card is drawn bears (i) an even number (ii) a number divisible by 3.

22. A card is drawn at random from a pack of 52 playing cards. Find the probability that the card is drawn is neither an ace nor a king.

23. The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in three minutes. [Use pie = 22/7]

24.If tan A = cot B, prove that A+B= 90°

25. If the product of the zeroes of the polynomial  $ax^2&space;-&space;6x&space;-&space;6$  is 4, then find the value of a. Also, find the sum of zeroes of the polynomial.

26. The two tangents from an external point P to a circle with centre O are PA and PB. If APB = 70°, what is the value of AOB?

SECTION C

27. Prove that   $2+5\sqrt{3}$  is an irrational number.

28. Find the zeroes of the quadratic polynomial   $6x^{2}&space;-&space;7x-&space;3$   and verify the relationship between the zeroes and the coefficients of the polynomial.

29. Given   linear equation 3x - 5y = 1 form another linear equation in these variables such that the geometric representation of pair so formed is: (i) intersecting lines (ii) coincident lines (iii) parallel lines.

30. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the below figure. Niharika runs 1/4th the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 th the distance AD on the eighth line and posts a red flag.

(i) What is the distance between both the flags?

(ii) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

31. Prove that:

32. Construct a triangle ABC with BC = 7 cm. ㄥB = 60° and AB = 6 cm. Construct another triangle whose sides are times the corresponding sides of AABC.

OR

Draw a line segment of length 10 cm and divide it in the ratio 3:5. Measure the two parts.

33. In the below figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If OA = 7 cm, find the area of the shaded region.

34. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

SECTION D

35. A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is 60°. After some time, the angle of elevation reduces to 30° (see the below figure). Find the distance travelled by the balloon during the interval.

36. In a class test, the sum of Shefali's marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

37. Show that a1 ......... form an AP where an is defined as the first 15 terms in each case.
=9-5n. Also find the sum of

38. Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
OR
State and prove Basic proportionality theorem,

39. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. Determine the volume of the toy. (Take pie =3.14)

40.

### CLASS 10 MCQ QUESTIONS | MATHS

1. If a and b are positive integers, then HCF (a, b) x LCM (a, b) =

(a)   a x b
(b) a + b
(c) a b
(d) a/b

2.If the HCF of two numbers is 1, then the two numbers are called

(a) composite
(b) relatively prime or co-prime
(c) perfect
(d) irrational numbers

The decimal expansion of      93      will be

1500
(a) terminating
(b) non-terminating
(c) non-terminating repeating
(d) non-terminating non-repeating.

4.  A quadratic polynomial whose sum and product of zeroes are –3 and 2 is
(a) x2 3x +2
(b) x2 + 3x + 2
(c) x2 + 2x 3.
(d) x2 + 2x + 3.

5.A point P divides the join of A(5, –2) and B(9, 6) are in the ratio 3 : 1. The coordinates of P are

(a) (4, 7)
(b) (8, 4)

(c) ( 11 , 5)
2
(d) (12, 8)

6. The distance of the point P(4, –3) from the origin is

(a)  1 unit
(b) 7 units
(c) 5 units
(d) 3 units

7. A point P is 26 cm away from the centre of a circle and the length of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
(a) 11 cm         (b) 10 cm         (c) 16 cm         (d) 15 cm

8.Which measure of central tendency is given by the x – coordinate of the point of intersection of the more than ogive and less than ogive?

(a) mode
(b) median
(c) mean
(d) all the above three measures

9.   If the points (1, x), (5, 2) and (9, 5) are collinear then the value of x is

10.   Product tan10.tan20.tan30……tan890 is

11.   If ABC and DEF are similar triangles such that ÐA = 470 and ÐE = 830, then ÐC =

12.   The values of k for which the quadratic equation 2x2 + kx + 3 = 0 has real equal roots is

13.The value of k for which the system of equations x + 2y = 3 and 5x + ky + 7 = 0 has no solution is

14.How many three-digit numbers are divisible by 7?

15.The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the areas of the two circles.

16.It is given that in a group of 3 students, the probability of 2 students not having the same birthday is 0.992. What is the probability that the 2 students have the same birthday?

 17.LCM of 6 and 20 is (a) 30                           (b) 60                 (c)120                        (d)none of these 18.  Given 15 cot A = 8, then sin A =

### Chapter 13: Magnetic Effects of Electric Current

1(a) State Fleming’s left hand rule. or  Why does a current carrying conductor kept in a magnetic field experience force? On what factors does the direction of this force depend? Name and state the rule used for determination of direction of this force. Or  What does the direction of thumb indicate in the right hand thumb rule? In what way this rule is different from Fleming’s left hand rule?
(b)Write the principle of working of an electric motor.
(c)Explain the function of the following parts of an electric motor.
(i)Armature (ii) Brushes (iii) Split ring

2.(a) Explain any three properties of magnetic field lines.
(b) Give two uses of magnetic compass.

Ans (a)Properties of magnetic field lines:
1.Magnetic field lines emerge from N  pole  and merge at S pole outside a bar magnet and travel from S pole to N pole inside the magnet.
2.These are continuous and closed curves.
3.Two field lines never intersect each other.
(b)Uses of magnetic compass :
1.In navigation it is used to find direction.
2.It is used to detect the magnetic field.
3.It can be used to test whether a substance is magnetic or not.
3.State one main difference between ac and dc. Why   ac is preferred over dc for long range transmission of electric power? Name one source each of dc and ac.
Ans : The magnitude and direction of ac remains same whereas a.c. changes its magnitude and direction periodically. Low AC voltage can be increase to high voltage to prevent loss in electric energy during its long distance transmission.
AC generator and DC generator/or cell.
4.Under what condition does a current carrying conductor kept in a magnetic field experience maximum force? On what other factors does the magnitude of this force depend? Name and state the rule used for determination of direction of this force.
Ans :Force on a current carrying conductor in a magnetic field depends upon
a.length of the conductor
b.strength of the magnetic field
strength of the current
c.angle between direction of magnetic field and current.

## Fleming’s Left Hand Rule:

Fleming’s left hand rule gives the direction of force experienced by a current carrying straight conductor placed in a magnetic field which is perpendicular to it. According to Fleming’s left hand rule if we stretch our left hand thumb, forefinger  and  middle  finger in such a way that forefinger points the direction of magnetic field, middle finger points the direction of current then thumb will give the direction of force on the conductor.

5.What is meant by overloading of an electrical circuit? Explain two possible causes due to which overloading may occur in household circuit. Explain one precaution that should be taken to avoid the overloading of domestic electric circuit.
Ans :Connecting large number of electric appliances in  one socket whose load is more than the maximum permitted limit. The two possible cause are
1.all of a sudden supply of high voltage and
2.too many devices connected in a single socket.

## Precautions:1.use of voltage regulator,

2.load of a socket must be greater than its permitted rating.

4.Explain the meanings of the words “electromagnetic” and “induction” in the term electromagnetic induction. List three factors on which the value of induced current produced in a circuit depends. Name and state the rule used to determine the direction of induced current. State one practical application of this phenomenon in everyday life.
Ans The word electromagnetic means that an electric potential dipole is being produced in a coil due to change in magnetic field. The word induction means that the current has been induced. The value of induced current produced in a circuit depends on the following factors:
number of turns in given coil
area of each turn in coil
rate of change of magnetic field.
The rule is Fleming’s right hand rule.  Stretch  the thumb, forefinger and middle finger of right- hand perpendicular to each other that forefinger indicates the direction of magnetic field, thumb gives the direction of motion (or force) of the conductor, then middle finger will point the direction of induced current.
Application: AC generator or DC generator.

6.Name two safety measures commonly used in electric circuits and appliances, what precautions should be taken to avoid the over loading of domestic electric circuits?
Ans :  Proper earthing and using a fuse load in the electric circuit must be as per rating of the fuse and do not connect to many plugs in a single socket.
7. What is a solenoid? Sketch magnetic field lines produced around a current carrying solenoid. Mark the region where field is uniform. Compare its field with that of a bar magnet.
AnsA solenoid is a large number of insulated turns of the copper wire in the shape of helix (or cylinder).
The patterns of the magnetic field lines around a current carrying solenoid is as given in figure. At the centre of the solenoid the magnetic field is uniform and magnetic field lines are parallel.
Similarities:In both the cases of a current carrying solenoid and bar magnet the magnetic lines of forces inside the body is strong and uniform. In both the cases there exists stronger magnetic field at the poles compared to the middle parts.
Dissimilarities:
(i)The poles in a bar magnet do not exist at the extreme ends of the magnet whereas in solenoid the poles can be considered to be lying at the edge.
(ii)In a bar magnet, magnetism is retained naturally, but in solenoid magnetism is there so long current flows through it.

8.(a) What is meant by a ‘magnetic field’ ?
(b)How is the direction of magnetic field at a point determined?
(c)Describe an activity to demonstrate the direction of the magnetic field generated around a current carrying conductor.
(d)What is the direction of magnetic field at the centre of a current carrying circular loop?
Ans :a.Magnetic field is the space around a magnet or a current carrying conductor in which its magnetic force can be experienced.
b.A magnetic compass is used to demonstrate the direction of the magnetic field generated around a current carrying conductor.
c.Fix a cardboard and insert a wire to pass through its centre normal to the plane of the card board. Sprinkle iron filings on card board uniformly. Pass the current in the wire. Tap the cardboard gently. You will find that iron  filings  align  themselves in the concentric circles around the wire. These circles represents magnetic field lines around the conductor.

d.At the centre of circular loop, the magnetic field lines are straight

9.Two coils C1 and C2 are wrapped around a non- conducting cylinder. Coil C1 is connected to a battery and key and C2 with galvanometer G. On pressing the key (K), current starts flowing in the coil C1  State your observation in the galvanometer.

a.What key K is pressed on.
b.When current in the coil C1 is switched off.
c.When the current is passed continuously through coil C1.
d.Name and state the phenomenon responsible for the above observation. Write the name of the rule that is used to determine the direction of current produced in the phenomena.
Ans:a.Induced current in coil C2 is produced so galvanometer shows a deflection.
b..Again galvanometer shows a deflection but in opposite direction to the previous one.
c.There will be no deflection in galvanometer.
d.This phenomenon is called electromagnetic induction. The phenomenon in which a changing magnetic field in a coil induces a current in another coil kept near it. Fleming’s right hand rule is used to find the direction of induced current.
10.What is the advantage of the third wire of earth connection in domestic appliances?
Ans :  In case of any electric fault in domestic appliances, current may comes in appliance body. The third wire called earth wire transfer this current to the earth and user remains safe from any such electric shock.
11.How can you show that the magnetic field produced by a given electric current in the wire decreases as the distance from the wire decreases?
Ans : If we bring a magnetic compass from a distance to near a current carrying conductor its deflection goes on increasing and when magnetic compass is brought away from the current carrying wire its deflection goes on decreasing which shows that magnetic field near current carrying wire is maximum and decreasing on increasing the separation.
12When is the force experienced by a current carrying conductor placed in a magnetic field the maximum?
Ans : A current carrying conductor experience maximum force in a magnetic field when the direction of current is perpendicular to the magnetic field.
13.How is the induced current in a secondary coil related to current in a primary coil?
Ans :  Induced current in a secondary coil may be more or lesser than the current in primary coil depending upon the number of turns in secondary.

14. What is the role of fuse, used in series with any electrical appliance? Why should a fuse with defined rating not be replaced by one with a larger rating?
Ans : Fuse wire is safety device to prevent electrical devices due to short circuiting or overloading. The fuse wire is rated for a maximum current which has high resistance and low melting point. When there is short circuiting large current is passed in the circuit. Due to large current in fuse wire heat is produced and     by melting fuse wire breaks the circuit to keep other appliances safe.
If a fuse wire is replaced by an ordinary copper wire which has low resistance and high melting point it will not melt and domestic appliance may get damaged due to excessive heat due to short circuiting or overloading.