RBSE Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1

Rajasthan Board RBSE Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1 Textbook Exercise Questions and Answers.

RBSE Class 6 Maths Solutions Chapter 11 Algebra Ex 11.1

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.

Answer:
(a) A patern of letter T = 2n (as two matchsticks used to make letter)
(b) A pattern of letter Z = 3n (as three matchsticks used to make letter)
(c) A pattern of letter U = 3n (as three matchsticks used to make letter)
(d) A pattern of letter V = 2n (as two matchsticks used to make letter)
(e) A pattern of letter E = 5n (as five matchsticks used to make letter)
(f) A pattern of letter S = 5n (as five matchsticks used to make letter)
(g) A pattern of letter A = 6n (as six matchsticks used to make letter)

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?
Answer:
L requires two matchsticks, therefore, pattern of L is 2n. The letter T and V has pattern 2n, since 2 matchsticks are used in all these letters.

Question 3.
Cadets are marching in a parade. There are 5 cadets in arow. What is the rule which gives the number of cadets, given the number of rows? (Use n for the number of rows)
Annswer:
Number of rows = n
Cadets in each row = 5
Therefore, total number of cadets = Number of cadets in a row × total number of rows = 5n

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.) Answer:
Number of boxes = 6
Number of mangoes in each box = 50
Therefore, total number of mangoes
= number of mangoes in a box × number of boxes
= 50 × b = 50b

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.)
Answer:
Number of students = s
Number of pencils to each student = 5
Therefore, total number of pencils needed
= Number of pencils given to each student × number of pencils
= 5s

Question 6.
A bird flies 1 km in one minute. Can you express the distance covered by the bird in terms of its flying times in minutes? (Use t for flying time in minutes.)
Answer:
Time taken by bird = t minutes
Speed of bird = 1 km per minute Therefore, distance covered by bird
= Speed of bird × time taken by bird
= 1 × t km = t km.

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?
Answer:
Number of rows = r
Number of dots in each row = 9
Total number of dots = Number of rows
x number of dots in each row = 9 × r = 9r
When there are 8 rows, then number of dots
= 9 × 8 = 72 dots When there are 10 rows, then number of dots
= 9 × 10 = 90 dots.

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.
Answer:
Yes!. We can write Leela’s age in terms of Radha’s age.
Radha’s age = x years
Therefore, Leela's age = (x - 4) 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 l, how many laddus did she make?
Answer:
Number of laddus given away = l
Number of laddus remaining = 5
Total number of laddus = l + 5.

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?
Answer:
Number of oranges in one small box = x
Number of boxes = 2
Therefore, total number of oranges in two small boxes = 2x
Remaining oranges = 10
Thus, number of oranges
= Number of oranges in two small boxes + number of oranges left
= 2x + 10

Question 11.
(a) Look at the following matchstick pattern of squares in fig. 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 square at the end, you will get a pattern of Cs.)

Answer:
If we remove 1 from each then they makes table of 3, i.e. 3, 6, 9,12,...
So, the required equation = 3n + 1, where n is number of squares.

(b) Fig. 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:
If we remove 1 from each then they makes table of 2 i.e., 2, 4, 6, 81 ............
So, the required equation = 2n + 1, where n is number of triangles.