These NCERT Solutions for Class 6 Maths Chapter 11 Algebra Ex 11.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 6 Maths Chapter 11 Algebra Exercise 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:
Question 2.
We already know the rule for the pattern of letters L, C and F. Some of the letters from Q.l (given above) give us the same rule as that given by L. Which are these? Why does this happen?
Answer:
The rules to find the number of matchsticks for:
The letter L is 2n The letter C is 3n
The letter V is 2n The letter U is 3n
The letter T is 2n The letter F is 4n
∴ It is same for L, V and T. The number of matchsticks required in each of them is 2.
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.)
Answer:
Number of rows = n
Cadets in each row = 5
Therefore, total number of cadets = 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 = b
Number of mangoes in each box = 50
Therefore, total number of mangoes = 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.)
Ans. Number of students = s
Number of pencils to each student = 5
Therefore, total number of pencils needed are = 5s.
Question 6.
A bird flies i kilometer in one minute. Can you express the distance covered by the bird in terms of its flying time 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 × time = 1 × t = 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 rowrs? How many dots are there if there are 8 rows? If there are 10 rows?
Answer:
1 row = 9 dots
r rows = (9*r) dots
= 9r dots
8rows = 9*8 = 72dots
10rows = 10*9 = 90dots
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 × years.
Answer:
Radhas 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 gave 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 box = x
Number of boxes = 2
Therefore, total number of oranges in boxes = 2x
Remaining oranges =10
Thus, number of oranges = 2x + 10
Question 11.
(a) Look at the following matchstick pattern of squares. The squares are not separate. Two neighbouring squares have a common match- stick. 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) The given figure gives a matchstick pattern of triangles. Find the general rule that gives the number of matchsticks in terms of the number of triangles.
Answer:
13 matchsticks
If we remove 1 from each then they makes table of 3, i.e., 3, 6, 9, 12…
So the required equation = 3x + 1, where x is number of squares.
If we remove 1 from each then they makes table of 2, i.e., 2, 4, 6, 8…
So the required equation = 2x +1, where x is number of triangles.