NCERT Solutions for Class 6 Maths Exercise 11.1

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NCERT Solutions for Class 6 Maths Exercise 11.1

NCERT Solutions for Class 6 Maths Algebra

Class –VI Mathematics
(Ex. 11.1)
Question 1.Find the rule, which gives the number of matchsticks required to make the following matchsticks patterns. Use a variable to write the rule.

(a)A pattern of letter T as

(b)A pattern of letter Z as

(c)A pattern of letter U as

(d)A pattern of letter V as

(e)A pattern of letter E as

(f)A pattern of letter S as

(g)A pattern of letter A as

Answer:

(a)Pattern of letter

= {tex}2n{/tex} (as two matchstick used in each letter)

(b) Pattern of letter

= {tex}3n{/tex} (as three matchstick used in each letter)

(c) Pattern of letter

= {tex}3n{/tex} (as three matchstick used in each letter)

(d) Pattern of letter

= {tex}2n{/tex} (as two matchstick used in each letter)

(e) Pattern of letter

= {tex}5n{/tex} (as five matchstick used in each letter)

(f) Pattern of letter

= {tex}5n{/tex} (as five matchstick used in each letter)

(g) Pattern of letter

= {tex}6n{/tex} (as six matchstick used in each letter)


NCERT Solutions for Class 6 Maths Exercise 11.1

Question 2.We already know the rule for the pattern of letter 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?

Answer: The letter ‘T’ and ‘V’ that has pattern {tex}2n,{/tex} since 2 matchsticks are used in all these letters.


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 {tex}n{/tex} for the number of rows)

Answer: Number of rows = {tex}n{/tex}

Cadets in each row = 5

Therefore, total number of cadets = {tex}5n{/tex}


NCERT Solutions for Class 6 Maths Exercise 11.1

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 {tex}b{/tex} for the number of boxes)

Answer: Number of boxes = {tex}b{/tex}

Number of mangoes in each box = 50

Therefore, total number of mangoes = {tex}50b{/tex}


Question 5.The teacher distributes 5 pencils per student. Can you tell how many pencils are needed, given the number of students? (Use {tex}s{/tex} for the number of students)

Answer:

Number of students = {tex}s{/tex}

Number of pencils to each student = 5

Therefore, total number of pencils needed are = {tex}5s{/tex}


NCERT Solutions for Class 6 Maths Exercise 11.1

Question 6.A bird flies 1 kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time in minutes? (Use {tex}t{/tex} for flying time in minutes)

Answer: Time taken by bird = {tex}t{/tex} minutes

Speed of bird = 1 km per minute

Therefore, Distance covered by bird = speed x time = {tex}1 \times t = t{/tex} km


Question 7.Radha is drawing a dot Rangoli (a beautiful pattern of lines joining dots with chalk powder as in figure). She has 8 dots in a row. How many dots will her Rangoli have for {tex}r{/tex} rows? How many dots are there if there are 8 rows? If there are 10 rows?

Answer: Number of dots in each row = 8 dots

Number of rows = {tex}r{/tex}

Therefore, number of dots = {tex}8r{/tex}

When there are 8 rows, then number of dots = 8 x 8 = 64 dots

When there are 10 rows, then number of dots = 8 x 10 = 80 dots


NCERT Solutions for Class 6 Maths Exercise 11.1

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 {tex}x{/tex} years.

Answer: Radha’s age = {tex}x{/tex} years

Therefore, Leela’s age = {tex}\left( {x – 4} \right){/tex} years


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 {tex}l,{/tex} how many laddus did she make?

Answer: Number of laddus gave away = {tex}l{/tex}

Number of laddus remaining = 5

Total number of laddus = {tex}\left( {l + 5} \right){/tex}


NCERT Solutions for Class 6 Maths Exercise 11.1

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 {tex}x,{/tex} what is the number of oranges in the larger box?

Answer:

Number of oranges in one box = {tex}x{/tex}

Number of boxes = 2

Therefore, total number of oranges in boxes = {tex}2x{/tex}

Remaining oranges = 10

Thus, number of oranges = {tex}2x + 10{/tex}


NCERT Solutions for Class 6 Maths Exercise 11.1

Question 11.

(a) Look at the following matchstick pattern of squares. 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) Figs. Below 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.

Answer:

4 matchsticks

7 matchsticks

10 matchsticks

13 matchsticks

If we remove 1 from each then they makes table of 3, i.e., 3, 6, 9, 12, ……….

So the required equation = {tex}3x + 1{/tex} , where {tex}x{/tex} is number of squares.

3 matchsticks

7 matchsticks

10 matchsticks

13 matchsticks

If we remove 1 from each then they makes table of 2, i.e., 2, 4, 6, 8, ……….

So the required equation = {tex}2x + 1{/tex} , where {tex}x{/tex} is number of triangles.

NCERT Solutions for Class 6 Maths Exercise 11.1

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