Regular revision with Class 6 Maths MCQ with Answers and Ganita Prakash Class 6 Maths Chapter 1 Patterns in Mathematics MCQ improves accuracy in objective exams.
MCQ on Patterns in Mathematics Class 6
Patterns in Mathematics MCQ Class 6
Class 6 Maths Patterns in Mathematics MCQ
Question 1.
Which of the following is a triangular number?
(a) 8
(b) 11
(c) 18
(d) 21
Solution:
(d) 21
We know, the number sequence of triangular numbers is 1, 3, 6, 10, 15, 21, 28 … .
From the given numbers, 21 is present in the number sequence of triangular numbers.
Hence, 21 is a triangular number.
Question 2.
Which of the following is not a cube number?
(a) 8
(b) 27
(c) 125
(d) 169
Solution:
(d) 169
We know, the number sequence of cubes is 1, 8, 27, 64, 125, 216, … .
From the given numbers, 169 is not present in the number sequence of cubes.
Hence, 169 is not a cube.
Question 3.
Which of the following is not a power of 3?
(a) 9
(b) 63
(c) 81
(d) 243
Solution:
(b) 243
We know, the number sequence of powers of 3 is 1, 3, 9, 27, 81, 243, 729 … .
From the given numbers, 63 is not present in the number sequence of powers of 3.
Hence, 63 is not a power of 3.
Question 4.
The pattern in the sequence 1, 4, 9, 16, 25, … is:
(a) nth term = 2n, where n = 1, 2, 3, 4, …
(b) nth term = n3, where n = 1, 2, 3, 4, …
(c) nth term = \(\frac{n}{2}\), where n = 1, 2, 3, 4, …
(d) nth term = n2, where n = 1, 2, 3, 4, …
Solution:
(d) nth term = n2, where n = 1, 2, 3, 4, …
Given sequence is 1, 4, 9, 16, 25, ….
First term = 1 = 1 × 1 = 12
Second term = 4 = 2 × 2 = 22
Third term = 9 = 3 × 3 = 32
Fourth term = 16 = 4 × 4 = 42
Fifth term = 25 = 5 × 5 = 52
Therefore, the sequence follows the pattern:
nth term = n~, where n = 1,2, 3, 4, …
Question 5.
The pattern in the sequence 1, 3, 6, 10, 15, 21, 28, … is:
(a) nth term = Sum of first n counting numbers + 1, where n = 1, 2, 3, 4, …
(b) nth term = Sum of first n counting numbers, where n = 1, 2, 3, 4, …
(c) nth term = Sum of first n counting numbers × 2, where n = 1, 2, 3, 4, …
(d) nth term = Sum of first n counting numbers ÷ 2, where n = 1, 2, 3, 4, …
Solution:
(b) nth term = Sum of first n counting numbers, where n = 1, 2, 3, 4, …
Given sequence is 1, 3, 6, 10, 15, 21, 28, … .
First term = 1 (First counting number)
Second term = 3 = 1 + 2 (Sum of first 2 . counting numbers)
Third term = 6 = 1 + 2 + 3 (Sum of first 3 counting numbers)
Fourth term = 10 = 1 + 2 + 3 + 4 (Sum of first 4 counting numbers)
Fifth term = 15 = 1 + 2 + 3 + 4 + 5 (Sum of first 5 counting numbers)
Therefore, the sequence follows the pattern:
nth term = Sum of first n counting numbers, where n = 1, 2, 3, 4, …
Question 6.
Which of the following sequence is represented by dots forming a square?
(a) 1, 4, 9, 16, 25, …
(b) 1, 3, 5, 7, 9, …
(c) 1, 2, 4, 8, 16, …
(d) 1, 3, 6, 10, 15, …
Solution:
(a) 1, 4, 9, 16, 25, …
We know, the square numbers 1, 4, 9, 16, 25,… are represented by dots forming the squares.
Question 7.
The sequence 1, 8, 27, 64, 125, … is visualised using:
(a) Squares
(b) Circles
(c) Triangles
(d) Cubes
Solution:
(d) Cubes
The given sequence 1, 8, 27, 64, 125, … is asequence of cubes.
We know, the sequence of cubes can be visualised using cubes.
Question 8.
What is the next number in the sequence: 1, 7, 19, 37,…?
(a) 50
(b) 61
(c) 63
(d) 65
Solution:
(b) 61
The given sequence is 1, 7, 19, 37, …, which is the sequence of hexagonal numbers.
The rule followed in the sequence of hexagonal numbers is
1st term = 1, nth number (term) = Preceding term + 6 × (n – 1); n = 2, 3, 4, …
∴ Next term, i.e. fifth term = 37 + 6 v (5 – 1) = 37 + 6 × 4 = 61
Question 9.
Triangular numbers can be visualised by arranging dots in the form of:
(a) Rectangles
(b) Squares
(c) Triangles
(d) Hexagons
Solution:
(c) Triangles
We know, the triangular numbers 1, 3, 6, 10, 15, … can be visualised by arranging dots in the form of triangles.
Question 10.
How many dots are there in the 4th triangular number?
(a) 6
(b) 10
(c) 15
(d) 21
Solution:
(b) 10
We know, the sequence of triangular numbers is 1, 3, 6, 10, 15, 21, 28, 36, 45, … .
So, the 4th triangular number is 10.
Thus, there are 10 dots in the triangle which represent the 4th triangular number.
Question 11.
How many dots are there in the 4th hexagonal number?
(a) 19
(b) 37
(c) 61
(d) 91
Solution:
(b) 37
We know, the sequence of hexagonal numbers is 1, 7, 19, 37, 61, 91, ……..
So, the 4th hexagonal number is 37.
Thus, there are 37 dots in the hexagon which represent the 4th hexagonal number.
Question 12.
The sum 1 + 7 + 19 + 37 gives which type of number?
(a) Triangular
(b) Virahanka
(c) Square
(d) Hexagonal
Solution:
(c) Square
1 + 7 + 19 + 37 = 64, which is a square number.
Question 13.
A polygon having 6 sides is known as:
(a) Quadrilateral
(b) Pentagon
(c) Hexagon
(d) Heptagon
Solution:
(c) Hexagon
Hexagon has 6 sides.
Question 14.
The geometric pattern 3, 12, 48, 192, 768, …, represents:
(a) The number of sides in the sequence of Koch Snowflakes
(b) The number of line segments in the sequence of Complete Graphs
(c) The number of vertices in the sequence of Regular Polygons
(d) The number of stacked triangles in the sequence of Stacked Triangles
Solution:
(a) The number of sides in the sequence of Koch Snowflakes
The geometric pattern 3, 12, 48, 192, 768, … represents the number of sides in the Koch snowflakes sequence.
Question 15.
The number of line segments in the sequence of complete graphs form a sequence of:
(a) even numbers
(b) virahanka numbers
(c) powers of 2
(d) triangular numbers
Solution:
(d) triangular numbers
The number of line segments in a complete graph follows the sequence: 0, 1, 3, 6, 10, 15…
Therefore, complete graphs sequence is related to triangular number sequence, i.e. i, 3, 6, 10,15 … .
Question 16.
The number of stacked triangles in the stacked triangles sequence form a sequence of:
(a) triangular numbers
(b) square numbers
(c) powers of 2
(d) hexagonal numbers
Solution:
(b) square numbers
We know,
Number of stacked triangles:
1 = 12 4 = 22 9 = 32
16 = 42 25 = 52
Thus, the number of stacked triangles in the stacked triangles sequence form a sequence of square numbers.
Question 17.
Which of the following statements is/are true regarding square numbers?
(i) The sum of the first n odd numbers gives a square number.
(ii) Adding counting numbers up from 1 to a number, and then back down again to 1, also gives a square number.
(iii) Adding up consecutive powers of 2, yields square number.
(iv) Multiplying triangular numbers by 6 and adding 1 to each term gives square numbers.
Choose the correct option from the following:
(a) (i) and (iii) only
(b) (i) and (ii) only
(c) (iii) and (iv) only
(d) (i), (iii) and (iv)
Solution:
(b) (i) and (ii) only
We have, the sum of the first two odd numbers = 1 + 3 = 4 = 22
The sum of the first three odd numbers = 1 + 3 + 5 = 9 = 32
The sum of the first four odd numbers =1 + 3 + 5 + 7 = 16 = 42 and so on.
Hence, the sum of the first n odd numbers gives a square number.
So, statement (i) is correct.
Also, adding counting numbers up and then down gives a square number.
For example, 1 + 2 + 1 = 4 = 22 and 1 + 2 + 3 + 2 + 1 = 9 = 32 and so on.
So, statement (ii) is also correct.
Now, adding consecutive powers of 2 does not give square numbers. The sequence powers of 2 is given as 1,2, 4, 8, 16, 32, …
Adding two consecutive numbers at a time, we get 3 (1 + 2 ), 6 (2 + 4), etc., which are not square numbers.
So, statement (iii) is incorrect.
We know that if we multiply triangular numbers by 6 and then add 1, we get a new number sequence: 7, 19, 37, 61 and so on. The new sequence is the sequence of hexagonal numbers starting with 7.
So, statement (iv) is also incorrect.
Question 18.
Which of the following statements is/are true?
(i) The regular polygons sequence is related to counting numbers sequence starting with 3.
(ii) The complete graphs sequence is related to triangular numbers sequence, where numbers are given by \(\frac{n(n-1)}{2}\), n = 1, 2, 3, …, i.e. 0, 1, 3, 6, 10, 15 and so on.
(iii) The stacked squares sequence is related to square numbers sequence, i.e. 1, 4, 9, 16, 25 and so on.
(iv) The stacked triangles sequence is related to the square numbers sequence, i.e. 1, 4, 9, 16, 25 and so on.
Choose the correct option from the following:
(a) (i) and (ii) only
(b) (ii) and (iv) only
(c) (i) (ii) and (iii) only
(d) (i), (ii), (iii) and (iv)
Solution:
(d) (i), (ii), (iii) and (iv)
All the statements are correct.
Patterns in Mathematics Class 6 Assertion and Reason Questions
The following questions are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Question 1.
(A): All is sequence (1, 1, 1, 1, …) gives counting numbers when added up successively.
(R): Adding 1 repeatedly increases the total by 1 each time.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know, all is sequence is 1, 1, 1, 1, …..
Here, 1 = 1 = 1
1 + 1 = 2 = 1 + 1
1 + 1 + 1 = 3 = 2 + 1
1 + 1 + 1 + 1 = 4 = 3 + 1
So, all is sequence (1, 1, 1, 1, ….) gives the counting numbers when added up successively and adding 1 repeatedly increases the total by 1 each time.
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 2.
(A): The pattern 1, 2, 4, 8, 16, … represents the powers of 2.
(R): Each number in this sequence is obtained by adding 2 to the previous term.
Solution:
(c) A is true but R is false.
We know, the number sequence of powers of 2 is 1, 2, 4, 8, 16, 32, 64, … .
First term = 1
Second term = 2 = 1 × 2 (First term × 2)
Third term = 4 = 2 × 2 (Second term × 2)
Fourth term = 8 = 4 × 2 (Third term × 2)
Fifth term = 16 = 8 × 2 (Fourth term × 2)
So, we can say that each term of the number sequence of powers of 2 is obtained by multiplying 2 to the previous term.
Thus, Assertion (A) is true, but Reason (R) is false.
Question 3.
(A): Square numbers can be obtained by adding up the odd numbers.
(R): The sum 1 + 3 + 5 + 7 + 9 = 25, which is a perfect square.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know, the sequence of odd numbers is 1, 3, 5, 7, 9, … .
And, the sequence of squares is 1, 4, 9, 16, 25, ….
Now, 1 = 1
1 + 3 = 4
1 + 3 + 5 = 9
1 + 3 + 5 + 7 = 16
1 + 3 + 5 + 7 + 9 = 25
So, the square numbers can be obtained by adding up the odd numbers.
Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Question 4.
(A): The hexagonal number sequence starts with 1 and continues with 7, 19, 37, 61, and so on.
(R): Each number in the sequence adds a growing number of layers of dots in a hexagonal form.
Solution:
(a) Both A and R are true and R is the correct explanation of A.
We know, the sequence of hexagonal numbers is 1, 7, 19, 37, 61, 91, … .
Pictorial representation of hexagonal numbers is given below:
Here, we observe that each number in the sequence adds a growing number of layers of dots in a hexagonal form.Thus, both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A).
Patterns in Mathematics Class 6 Fill in the Blanks
Question 1.
The next term of the sequence 1, 16, 49, 100, 169,… is _______.
Solution: 256
Given sequence is 1, 16, 49, 100, 169, ….
First term = 1 = (3 × 0 + 1)2
Second term = 16 = (3 × 1 + 1)2
Third term = 49 = (3 × 2 + 1)2
Fourth term = 100 = (3 × 3 + 1)2
Fifth term = 169 = (3 × 4 + 1)2
∴ Next term, i.e. sixth term = (3 × 5 + 1)2
= (16)2 = 256
Hence, the next term of the sequence 1, 16, 49, 100, 169, … is 256.
Question 2.
A square number sequence can be visualised as dots arranged in shape of a _______ .
Solution: square
We know, a square number sequence can be visualised as dots arranged in the shape of a square.
Question 3.
In the triangular number sequence, the 5th number is ________ .
Solution: 15
We know, the triangular number sequence is 1,3, 6, 10, 15, 21, 28,… .
So, in the triangular number sequence, the 5th number is 15.
Question 4.
The difference between consecutive square numbers forms an _______ sequence.
Solution: odd number
The difference between consecutive square numbers forms an odd number sequence: 3, 5, 7, 9, 11, … i.e. 4 – 1 = 3, 9 – 4 = 5, 16 – 9 = 7, and so on.
Question 5.
The pictorial representation of the sequence 1, 8, 27, 64, … is based on _______ .
Solution: cubes
We know, the sequence 1, 8, 27, 64, … is the sequence of cubes.
Thus, the pictorial representation of the sequence 1,8, 27, 64, … is based on cubes.
Question 6.
A polygon having 8 sides is known as __________ .
Solution: Octagon
A polygon having 8 sides is known as Octagon.
Question 7.
The difference between the number of sides of a nonagon and a pentagon is _________ .
Solution: 4
A pentagon has 5 sides whereas a nonagon has 9 sides.
∴ The difference between the number of sides of a nonagon and a pentagon is 9 – 5 = 4.