Test: Number Play - Class 7 MCQ

To find the number of distinct combinations of 4 beats using short (1 beat) and long (2 beats) syllables, we can represent the possible combinations mathematically.

• Let S represent a short syllable and L represent a long syllable.
• We can have combinations of short and long syllables that add up to 4 beats.
• Here are the possible combinations:
  • 4 short syllables: SSSS
  • 2 short syllables and 1 long syllable: SSL, SLS, LSS
  • 2 long syllables: LL

Therefore, the combinations are:

• SSSS
• SSL
• SLS
• LSS
• LL

This gives us a total of 5 distinct combinations.

The magic sum of a 3x3 magic square filled with the numbers 1 to 9 is 15. This can be calculated as follows:

• The total sum of the numbers from 1 to 9 is 45.
• To find the magic sum, divide this total by the number of rows, which is 3.
• So, 45 ÷ 3 = 15.

Magic squares illustrate important concepts in mathematics, including patterns and symmetry.

The Fibonacci sequence is important in nature because it appears in many biological forms. Here are some examples of its significance:

• Flower petals: Many flowers have a number of petals that is a Fibonacci number, such as 3, 5, or 8.
• Leaf arrangements: The arrangement of leaves around a stem often follows Fibonacci numbers, maximising sunlight exposure.

This connection highlights how mathematics not only explains ideas but also reveals patterns in the natural world.

The nth odd number in a sequence is represented by:

• The formula for the nth odd number is 2n - 1.
• In this formula:
  • n is the position in the sequence.
  • Multiplying n by 2 gives you the first even number, and subtracting 1 converts it to the corresponding odd number.
• For example:
  • If n = 1: 2(1) - 1 = 1
  • If n = 2: 2(2) - 1 = 3
  • If n = 3: 2(3) - 1 = 5

This shows how the formula generates the sequence of odd numbers: 1, 3, 5, 7, and so on.

In a magic square, both diagonals must sum to the same total as the rows and columns. This requirement ensures the balance and symmetry that characterise magic squares in mathematics.

The sum of two odd numbers is always an even number. This occurs because:

• Odd numbers can be expressed as 2n + 1, where n is an integer.
• When you add two odd numbers (e.g., (2n + 1) + (2m + 1)), the result is:
• 2n + 2m + 2, which simplifies to 2(n + m + 1).
• This final expression is divisible by 2, confirming it is even.

This property is fundamental in understanding basic arithmetic and number characteristics.

The total number of squares in a grid is odd only if both dimensions are odd.

This condition arises from how multiplication works:

• When both dimensions are odd, the product (total squares) is also odd.
• If either dimension is even, the product becomes even.
• This relationship highlights the connection between geometry and arithmetic.

Parity indicates whether a number is odd or even. Here are the details:

• The number 123 ends in 3.
• Since it ends with an odd digit, it is classified as odd.

The product of an even number and an odd number is always even. This is a key principle in understanding multiplication between different types of numbers. Here are some important points to remember:

• The result of multiplying any even number by an odd number is even.
• This property helps illustrate the basic rules governing odd and even integers.
• It reinforces the concept that even numbers contribute a factor of 2 to the product.

The numbers to consider are:

• 20 - This is even and a multiple of 5.
• 25 - This is odd; therefore, it does not qualify.
• 30 - This is even and a multiple of 5.

Thus, the correct answer is:

• Both A and C

To determine the type of the number 121, we can analyse its properties:

• Even: 121 is not even because it cannot be divided by 2.
• Prime: 121 is not a prime number as it has divisors other than 1 and itself.
• Square: 121 is a square number, as it equals 11 multiplied by 11.
• Magic: There is no standard definition of a magic number in mathematics.

Therefore, the correct classification for 121 is that it is a square number.

The number 10 is not part of the Fibonacci sequence. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, and continues with each number being the sum of the two preceding ones.

The difference between two consecutive odd numbers is always 2. This is because odd numbers follow a sequence where each number is two units apart. For example:

• 1 and 3 have a difference of 2.
• 5 and 7 have a difference of 2.
• 9 and 11 also have a difference of 2.

Thus, the correct answer is 2.

The sequence consists of the squares of natural numbers:

• 1 is 1²
• 4 is 2²
• 9 is 3²
• 16 is 4²

The next number is the square of 5:

• 5 is 5², which equals 25.

Therefore, the next number in the sequence is 25.

The given sequence is formed by adding consecutive natural numbers:

• 1 (1)
• 1 + 2 = 3 (2)
• 3 + 3 = 6 (3)
• 6 + 4 = 10 (4)
• 10 + 5 = 15 (5)

To find the next number, we continue the pattern:

• 15 + 6 = 21

The next number in the sequence is 21.