DEMO
Look around freely · sample student, nothing is saved
Get the app
11
x
2
+y
NCERT Solutions · Maths Ch 11
Finding Common Ground
23 questions · 4 exercises
Closed
Open all
Ex 11.1
Ex 11.2
Ex 11.3
Ex 11.4
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 11.1 · 2 QUESTIONS
Prime Factorisation and Factors
Q1
List all the factors of the following numbers: (a) 90 (b) 105 (c) 132 (d) 360 (this number has 24 factors) (e) 840 (this number has 32 factors)
(5 marks)
Q2
Anshu claims: 'The larger a number is, the longer its prime factorisation will be.' What do you think of Anshu's claim?
(2 marks)
2
EXERCISE 11.2 · 5 QUESTIONS
Common Factors and HCF
Q3
Find the common factors and the HCF of the following numbers: (a) 50, 60 (b) 140, 275 (c) 77, 725 (d) 370, 592 (e) 81, 243
(5 marks)
Q4
Find the HCF of the following numbers: (a) 24, 180 (b) 42, 75, 24 (c) 240, 378 (d) 400, 2500 (e) 300, 800
(5 marks)
Q5
Consider the numbers 72 and 144. Suppose they are factorised into composite numbers as 72 = 6 × 12 and 144 = 8 × 18. Seeing this, can one say that these two numbers have no common factor other than 1? Why not?
(3 marks)
Q6
Make a general statement about the HCF for the following pairs of numbers: (a) Two consecutive even numbers (b) Two consecutive odd numbers (c) Two even numbers (d) Two consecutive numbers (e) Two co-prime numbers
(5 marks)
Q7
(a) If m is a number, what could the other number be so that the HCF of the two numbers is m? (b) If 7k is one of two numbers, what could the other number be so that their HCF is 7?
(3 marks)
3
EXERCISE 11.3 · 3 QUESTIONS
LCM and Patterns
Q8
Find the LCM of the following numbers: (a) 30, 72 (b) 36, 54 (c) 105, 195, 65 (d) 222, 370
(5 marks)
Q9
Make a general statement about the LCM: (a) The LCM of 3 and 24 is 24 (one of the two given numbers). Find more such number pairs where the LCM is one of the two numbers. (b) Describe such number pairs using algebra.
(3 marks)
Q10
Make a general statement about the LCM for the following pairs of numbers: (a) Two multiples of 3 (b) Two consecutive even numbers (c) Two consecutive numbers (d) Two co-prime numbers
(5 marks)
4
EXERCISE 11.4 · 13 QUESTIONS
End of Chapter
Q11
In the two rows of stars, colours repeat as shown. When will the blue stars meet next? (Figure: Row 1 repeats the six colours yellow, green, orange, blue, magenta, grey. Row 2 repeats the four colours green, orange, yellow, blue.)
(3 marks)
Q12
(a) Is 5 × 7 × 11 × 11 a multiple of 5 × 7 × 7 × 11 × 2? (b) Is 5 × 7 × 11 × 11 a factor of 5 × 7 × 7 × 11 × 2?
(3 marks)
Q13
Find the HCF and LCM of the following (state your answers in the form of prime factorisations): (a) 3 × 3 × 5 × 7 × 7 and 12 × 7 × 11 (b) 45 and 36
(3 marks)
Q14
Find two numbers whose HCF is 1 and LCM is 66.
(3 marks)
Q15
A cowherd took all his cows to graze. The cows came to a crossing with 3 gates, and an equal number of cows passed through each gate. At another crossing with 5 gates, again an equal number passed through each gate. At the third crossing with 7 gates the same happened. If the cowherd had less than 200 cows, how many cows did he have?
(2 marks)
Q16
The length, width and height of a box are 12 cm, 18 cm and 36 cm. Which of the following sized cubes can be packed in this box without leaving gaps? (a) 9 cm (b) 6 cm (c) 4 cm (d) 3 cm (e) 2 cm
(3 marks)
Q17
Among the numbers below, which is the largest number that perfectly divides both 306 and 36? (a) 36 (b) 612 (c) 18 (d) 3 (e) 2 (f) 360
(2 marks)
Q18
Find the smallest number that is divisible by 3, 4, 5 and 7, but leaves a remainder of 10 when divided by 11.
(3 marks)
Q19
Children are playing 'Fire in the Mountain'. When the number 6 was called out, no one got out. When the number 9 was called out, no one got out. But when the number 10 was called out, some people got out. How many children could have been playing initially? (a) 72 (b) 90 (c) 45 (d) 3 (e) 36 (f) None of these
(3 marks)
Q20
Tick the correct statement(s). The LCM of two different prime numbers (m, n) can be: (a) Less than both numbers (b) In between the two numbers (c) Greater than both numbers (d) Less than m × n (e) Greater than m × n
(3 marks)
Q21
A dog is chasing a rabbit that has a head start of 150 feet. The dog jumps 9 feet every time the rabbit jumps 7 feet. In how many leaps does the dog catch up with the rabbit?
(3 marks)
Q22
What is the smallest number that is a multiple of 1, 2, 3, 4, 5, 6, 8, 9, 10?
(3 marks)
Q23
Mahaviracharya (850 C.E.) posed: Add together 8/15, 1/20, 7/36, 11/63 and 1/21. What do you get? How can we find this sum efficiently?
(5 marks)