**NCERT
Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1**

NCERT
Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1 are the part of NCERT Solutions for Class 6
Maths. Here you can find the NCERT Solutions for Class 6 Maths Chapter 11
Algebra Ex 11.1.

**NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1****NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.2****NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.3****NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.4****NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.5**

**Ex 11.1 Class 6 Maths Question 1.**

Find the rule which gives the
number of matchsticks required to make the following matchstick patterns. Use a
variable to write the rule.(a) A pattern of letter T as T

(b) A pattern of letter Z as Z

(c) A pattern of letter U as U

(d) A pattern of letter V as V

(e) A pattern of letter E as E

(f) A pattern of letter S as S

(g) A pattern of letter A as A

**Solution:**

Number
of matchsticks required to make two T is 4.

Number
of matchsticks required to make three T is 6.

∴ Rule is **2n** where n is number of Ts.

Because

For n = 1, 2n = 2 × n = 2 × 1 = 2

For n = 2, 2n = 2 × n = 2 × 2 = 4

For n = 3, 2n = 2 × n = 2 × 3 = 6

Number of matchsticks required to make one Z is 3.

Number of matchsticks required to make two Z is 6.

Number of matchsticks required to make three Z is 9.

∴ Rule is **3n** where n is number of Zs.

Because

For n = 1, 3n = 3 × n = 3 × 1 = 3

For n = 2, 3n = 3 × n = 3 × 2 = 6

For n = 3, 3n = 3 × n = 3 × 3 = 9

Number of matchsticks required to make two U is 6.

Number of matchsticks required to make three U is 9.

Number of matchsticks required to make four U is 12.

∴ Rule is **3n** where n is number of Us.

Because

For n = 1, 3n = 3 × n = 3 × 1 = 3

For n = 2, 3n = 3 × n = 3 × 2 = 6

For n = 3, 3n = 3 × n = 3 × 3 = 9

For n = 4, 3n = 3 × n = 3 × 4 = 12

Number of matchsticks
required to make two V is 4.

Number of matchsticks
required to make three V is 6.

Number of matchsticks
required to make four V is 8.

∴ Rule is **2n** where n is number of Vs.

Because

For n = 1, 2n = 2 × n = 2 × 1 = 2

For n = 2, 2n = 2 × n = 2 × 2 = 4

For n = 3, 2n = 2 × n = 2 × 3 = 6

For n = 4, 2n = 2 × n = 2 × 4 = 8

Number of matchsticks required to make one E is 5.

Number of matchsticks required to make two E is 10.

Number of matchsticks required to make three E is
15.

∴ Rule is **5n** where n is number of Es.

Because

For n = 1, 5n = 5 × n = 5 × 1 = 5

For n = 2, 5n = 5 × n = 5 × 2 = 10

For n = 3, 5n = 5 × n = 5 × 3 = 15

Number of matchsticks required to make two S is 10.

Number of matchsticks required to make three S is
15.

∴ Rule is **5n** where n is number of S.

Because

For n = 1, 5n = 5 × n = 5 × 1 = 5

For n = 2, 5n = 5 × n = 5 × 2 = 10

For n = 3, 5n = 5 × n = 5 × 3 = 15

Number of matchsticks required to make two A is 12.

Number of matchsticks required to make three A is
18.

∴ Rule is **6n** where n is number of As.

Because

For n = 1, 6n = 6 × n = 6 × 1 = 6

For n = 2, 6n = 6 × n = 6 × 2 = 12

For n = 3, 6n = 6 × n = 6 × 3 = 18

**Ex 11.1 Class 6 Maths Question 2.**

We already know the rule for the pattern of letters
L, C and F. Some of the letters from Q.1 (given above) give us the same rule as
that given by L. Which are these? Why does this happen?**Solution:
**Rules for the following letters are as follows:

For L it is 2n.

For C it is 3n.

For V it is 2n.

For F it is 3n.

For T it is 2n.

For U it is 3n.

We observe that the rule is the same for L, V and T, i.e., 2n, as they required only 2 matchsticks.

Letters C, F and U have the same rule, i.e., 3n, as they require only 3 matchsticks.

**Ex 11.1 Class 6 Maths Question 3.**

Cadets are marching in a parade. There are 5 cadets
in a row. What is the rule which gives the number of cadets, given the number
of rows? (use n for the number of rows.)**Solution:
**Number of cadets in a row = 5

Number of rows = n

For n = 1 is 5 × n = 5 × 1 = 5

For n = 2 is 5 × n = 5 × 2 = 10

For n = 3 is 5 × n = 5 × 3 = 15

∴ Rule is

**5n**where n is the number of rows.

**Ex 11.1 Class 6 Maths Question 4.**

If there are 50 mangoes in a box, how will you write
the total number of mangoes in terms of the number of boxes? (Use b for the
number of boxes.)**Solution:
**Number of mangoes in a box = 50

Number of boxes = b

Number of mangoes,

For b = 1 is 50 × b = 50 × 1 = 50

For b = 2 is 50 × b = 50 × 2 = 100

For b = 3 is 50 × b = 50 × 3 = 150

∴ Rule is

**50b**where b represents the number of boxes.

**Ex 11.1 Class 6 Maths Question 5.**

The teacher distributes 5 pencils per student. Can
you tell how many pencils are needed, given the number of students? (Use s for
the number of students.)**Solution:
**Number of pencils distributed per student = 5

Number of students = s

Number of pencils required

For s = 1 is 5 × s = 5 × 1 = 5

For s = 2 is 5 × s = 5 × 2 = 10

For s = 3 is 5 × s = 5 × 3 = 15

∴ Rule is

**5s**where s represents the number of students.

**Ex 11.1 Class 6 Maths Question 6.**

A bird flies 1 kilometre in one minute. Can you
express the distance covered by the bird in terms of is flying time in minutes?
(Use t for flying time in minutes.)**Solution:
**Distance covered in 1 minute = 1 km

The flying time = t

Distance covered,

For t = 1 is 1 × t = 1 × 1 = 1 km

For t = 2 is 1 × t = 1 × 2 = 2 km

For t = 3 is 1 × t = 1 × 3 = 3 km

∴ Rule is

**1.t**km where t represents the flying time.

**Ex 11.1 Class 6 Maths Question 7.**

Radha is drawing a dot Rangoli (a beautiful pattern
of lines joining dots with chalk powder. She has 9 dots in a row. How many dots
will her rangoli have for r rows? How many dots are there if there are 8 rows?
If there are 10 rows?**Solution:
**Number of rows = r

Number of dots in a row drawn by Radha = 9

∴ The number of dots required

For r = 1 is 9 × r = 9 × 1 = 9

For r = 2 is 9 × r = 9 × 2 = 18

For r = 3 is 9 × r = 9 × 3 = 27

∴ Rule is 9r where r represents the number of rows.

For r = 8, the number of dots = 9 × 8 = 72

For r = 10, the number of dots = 9 × 10 = 90

**Ex 11.1 Class 6 Maths Question 8.**

Leela is Radha’s younger sister. Leela is 4 years
younger than Radha. Can you write Leela’s age in terms of Radha’s age? Take
Radha’s age to be x years.

**Solution:
**Given: Radha’s age = x years

Given that Leela’s age = Radha’s age – 4 years

= x years – 4 years

= (x – 4) years

**Ex 11.1 Class 6 Maths Question 9.**

Mother has made laddus. She gives some laddus to
guests and family members, still 5 laddus remain. If the number of laddus
mother gave away is *l*, how many laddus did she make?

**Solution:
**Given: The number of laddus given away =

*l*

Number of laddus left = 5

∴ Number of laddus made by mother =

*l*+ 5

**Ex 11.1 Class 6 Maths Question 10.**

Oranges are to be transferred from larger boxes into
smaller boxes. When a large box is emptied, the oranges from it fill two
smaller boxes and still 10 oranges remain outside. If the number of oranges in
a small box are taken to be x, what is the number of oranges in the larger box?**Solution:
**Given: The number of oranges in smaller box = x

∴ Number of oranges in larger box = 2(number of oranges in small box) + (Number of oranges remain outside)

So, the number of oranges in larger box = 2x + 10

**Ex 11.1 Class 6 Maths Question 11.**

(a) Look at the following matchstick pattern of
square. The squares are not separate. Two neighbouring squares have a common
matchstick. Observe the patterns and find the rule that gives the number of
matchsticks in terms of the number of squares.(Hint: If you remove the vertical stick at the end, you will get a pattern of Cs.)

(b) Following figure gives a matchstick pattern of triangles. As in Exercise 11(a) above, find the general rule that gives the number of matchsticks in terms of the number of triangles.

**Solution:
**(a) Let n be the number of squares.

∴ Number of matchsticks required

For n = 1 is 3 × n + 1 = 3n + 1 = 4

For n = 2 is 3 × n + 1 = 3n + 1 = 7

For n = 3 is 3 × n + 1 = 3n + 1 = 10

For n = 4 is 3 × n + 1 = 3n + 1 = 13

∴ Rule is 3n + 1 where n represents the number of squares.

(b) Let n be the number of triangles.

∴ Number of matchsticks required

For n = 1 is 2n + 1 = 3

For n = 2 is 2n + 1 = 5

For n = 3 is 2n + 1 = 7

For n = 4 is 2n + 1 = 9

∴ Rule is 2n + 1 where n represents the number of triangles.

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