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All questions of Patterns in Mathematics for Class 6 Exam

Sum of 178 and 69 to nearest hundred is
  • a)
    100
  • b)
    200
  • c)
    250
  • d)
    300
Correct answer is option 'B'. Can you explain this answer?

Gunjan Lakhani answered
To solve this, let's first find the sum of 178 and 69:
178+69=247
Now, we round 247 to the nearest hundred.
  • The nearest hundred to 247 is 200 because 247 is closer to 200 than to 300.
So, the sum of 178 and 69 rounded to the nearest hundred is 200.
Answer: 2 (200)

Which of the following is a square number?
  • a)
    20
  • b)
    24
  • c)
    25
  • d)
    30
Correct answer is option 'C'. Can you explain this answer?

Understanding Square Numbers
Square numbers are the product of an integer multiplied by itself. For example, \( n^2 \) (where \( n \) is an integer) gives us square numbers. The first few square numbers are:
- \( 1^2 = 1 \)
- \( 2^2 = 4 \)
- \( 3^2 = 9 \)
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)
- \( 6^2 = 36 \)
Identifying Square Numbers Among Options
Let's analyze the options provided:
- a) 20: This is not a square number. The closest integers are \( 4^2 = 16 \) and \( 5^2 = 25 \).
- b) 24: This is also not a square number. It falls between \( 4^2 = 16 \) and \( 5^2 = 25 \).
- c) 25: This is a square number, as it equals \( 5^2 \).
- d) 30: This is not a square number. The square numbers surrounding it are \( 5^2 = 25 \) and \( 6^2 = 36 \).
Conclusion
Thus, among the options provided, 25 (option c) is the only square number because it can be expressed as \( 5 \times 5 \). Understanding how to identify square numbers is essential in mathematics, especially in recognizing patterns and solving problems in number theory.

What is Mathematics often described as the study of?
  • a)
    Words
  • b)
    Patterns
  • c)
    Colors
  • d)
    Sounds
Correct answer is option 'B'. Can you explain this answer?

Neha Singla answered
Because other words  are not related to mathematics. Words, colours and sounds are related to Science.

Rita has a ribbon of length 2070 mm. Sita has a ribbon whose length is 1232 mm shorter than Rita's ribbon. What is the approximate length of Sita's ribbon when rounded to the nearest hundred (in millimeters)?
  • a)
    500
  • b)
    1000
  • c)
    800
  • d)
    2000
Correct answer is option 'C'. Can you explain this answer?

Subset Academy answered
To find the approximate length of Sita's ribbon, we need to subtract 1232 mm from Rita's ribbon length and then round the result to the nearest hundred.
Rita's ribbon length = 2070 mm Sita's ribbon length = Rita's ribbon length - 1232 mm
Sita's ribbon length β‰ˆ 2070 mm - 1232 mm Sita's ribbon length β‰ˆ 838 mm
When rounded to the nearest hundred, Sita's ribbon length is approximately 800 mm.

1 billion = ______ million
  • a)
    10
  • b)
    100
  • c)
    1000
  • d)
    10000
Correct answer is option 'C'. Can you explain this answer?

Gunjan Lakhani answered
One billion is equal to 1000 million. This is because when we multiply 1000 by 1000, we get 1 million. Therefore, if we multiply 1000 million by 1000, we get 1 billion.

If you start with the number 1 and keep adding 2, what sequence are you creating?
  • a)
    Even numbers
  • b)
    Prime numbers
  • c)
    Odd numbers
  • d)
    Square numbers
Correct answer is option 'C'. Can you explain this answer?

Dr Manju Sen answered
Adding 2 repeatedly to the number 1 creates a sequence of odd numbers (1, 3, 5, 7, and so on). This is because odd numbers are separated by a difference of 2.

Sum 3537 + 3884 to nearest tens is
  • a)
    1000
  • b)
    7400
  • c)
    7420
  • d)
    7440
Correct answer is option 'C'. Can you explain this answer?

Akshita Reddy answered
Adding 3537 + 3884 to the nearest tens:
To get the nearest tens when adding two numbers, you need to round each number to the nearest ten before adding them together.
- Round 3537 to the nearest tens: 3540
- Round 3884 to the nearest tens: 3880
Now, add the rounded numbers:
3540 + 3880 = 7420
Therefore, the sum of 3537 + 3884 to the nearest tens is 7420, which corresponds to option 'C'.

Estimated the value of the product of 108 and 12.
  • a)
    1000
  • b)
    1500
  • c)
    1700
  • d)
    2000
Correct answer is option 'A'. Can you explain this answer?

Calculation:
To estimate the product of 108 and 12, we can round 108 to 100 and 12 to 10 for easier calculation.

Estimation:
100 x 10 = 1000
Therefore, the estimated value of the product of 108 and 12 is 1000.
So, the correct answer is option 'A'.

What is the sum of the first three odd numbers?
  • a)
    5
  • b)
    7
  • c)
    9
  • d)
    12
Correct answer is option 'C'. Can you explain this answer?

Coachify answered
The first three odd numbers are 1, 3, and 5. Adding them together gives 1 + 3 + 5 = 9.

What is the even prime number?
  • a)
    3
  • b)
    2
  • c)
    1
  • d)
    None of the above
Correct answer is option 'B'. Can you explain this answer?

Ananya Das answered
Even Prime Number
An even number is a number that is divisible by 2. However, the only even prime number is 2. Here's why:

Explanation
- A prime number is a number greater than 1 that has no positive divisors other than 1 and itself.
- Even numbers are divisible by 2, which means they have 2 as a factor.
- The only even number that meets the definition of a prime number is 2 because it has no other factors besides 1 and 2.
- All other even numbers, such as 4, 6, 8, etc., have factors other than 1 and themselves, making them composite numbers.
Therefore, the even prime number is 2, making option 'B' the correct answer.

The tickets sold for the semi-final IPL match were 9872, whereas 10050 tickets were sold during the finals. How many more tickets, estimated to the nearest tens, were sold during the finals?
  • a)
    160
  • b)
    170
  • c)
    180
  • d)
    190
Correct answer is option 'C'. Can you explain this answer?

Vp Classes answered
During the finals, 10050 tickets were sold, whereas for the semi-final match, only 9872 tickets were sold. To find out how many more tickets were sold during the finals, we subtract the number of tickets sold for the semi-finals from the number of tickets sold during the finals. Therefore, 10050 - 9872 = 178. Since we need to estimate to the nearest tens, the answer would be 180.

__________ is both a triangular number and a square number.
  • a)
    25
  • b)
    36
  • c)
    8
  • d)
    4
Correct answer is option 'B'. Can you explain this answer?

Rohini Seth answered
  • triangular number is a number that can form an equilateral triangle. The sequence of triangular numbers is: 1, 3, 6, 10, 15, 21, 28, 36, 45, ...
  • square number is a number that is the square of an integer. The sequence of square numbers is: 1, 4, 9, 16, 25, 36, 49, 64, ...
The number 36 appears in both sequences:
  • It is the 8th triangular number: 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = 36.
  • It is also the 6th square number: 6 * 6 = 36.
Thus, 36 is both a triangular number and a square number.

If you start with the number 2 and keep adding 2, what sequence are you creating?
  • a)
    Odd numbers
  • b)
    Square numbers
  • c)
    Even numbers
  • d)
    Prime numbers
Correct answer is option 'C'. Can you explain this answer?

Adding 2 repeatedly to the number 2 creates a sequence of even numbers (2, 4, 6, 8, and so on). This is because even numbers are separated by a difference of 2.

How many dots are in the third triangular number?
  • a)
    3
  • b)
    6
  • c)
    9
  • d)
    12
Correct answer is option 'B'. Can you explain this answer?

Harshad Datta answered
Understanding Triangular Numbers
Triangular numbers are a sequence of numbers that can form an equilateral triangle. The nth triangular number is the total number of dots that can be arranged in a triangle with n rows.

Formula for Triangular Numbers
To find the nth triangular number, we use the formula:
  • T(n) = n(n + 1) / 2


Here, T(n) represents the nth triangular number.

Calculating the Third Triangular Number
To find the third triangular number (n = 3):
  • T(3) = 3(3 + 1) / 2
  • T(3) = 3(4) / 2
  • T(3) = 12 / 2
  • T(3) = 6


So, the third triangular number is 6.

Visualizing the Third Triangular Number
You can visualize the arrangement of dots as follows:
  • First row: 1 dot
  • Second row: 2 dots
  • Third row: 3 dots


When you add these up:
  • 1 + 2 + 3 = 6


This confirms that the total number of dots in the third triangular number is indeed 6.

Conclusion
Thus, the correct answer to the question about the number of dots in the third triangular number is option 'B', which is 6.

Which of the following shapes is a regular polygon?
  • a)
    Rectangle
  • b)
    Square
  • c)
    Circle
  • d)
    Ellipse
Correct answer is option 'B'. Can you explain this answer?

EduRev Class 6 answered
A square is a regular polygon because it has equal-length sides and equal angles. The other shapes do not meet both criteria.

Estimated value of 467 to nearest thousand is
  • a)
    Zero
  • b)
    400
  • c)
    470
  • d)
    1000
Correct answer is option 'A'. Can you explain this answer?

The estimated value of 467 to the nearest thousand is zero because when rounding to the nearest thousand, any number below 500 will be rounded down to zero. In this case, 467 is less than 500, so it gets rounded down to zero.

What is the next number in the sequence 1, 4, 9, 16...?
  • a)
    20
  • b)
    24
  • c)
    25
  • d)
    30
Correct answer is option 'C'. Can you explain this answer?

Ashutosh Verma answered
Understanding the Sequence
The given sequence is: 1, 4, 9, 16...
Each number in this sequence is a perfect square.
Identifying the Pattern
- The first number (1) is \(1^2\).
- The second number (4) is \(2^2\).
- The third number (9) is \(3^2\).
- The fourth number (16) is \(4^2\).
Thus, the pattern is that the \(n\)-th term in the sequence is given by \(n^2\).
Finding the Next Number
To find the next number in the sequence, we need to calculate \(5^2\):
- \(5^2 = 25\)
Conclusion
The next number in the sequence is 25, which corresponds to option 'C'.
- This confirms that the sequence consists of the squares of consecutive integers: \(1^2, 2^2, 3^2, 4^2, 5^2\).
Understanding this pattern is crucial for solving similar problems in the future.

In the International system of numeration, one crore is equal to ______ million.
  • a)
    1
  • b)
    10
  • c)
    100
  • d)
    1000
Correct answer is option 'B'. Can you explain this answer?

Praveen Kumar answered
In the International system of numeration, one crore is equal to ten million. This is because one crore is equal to ten million in the Indian numbering system, which is used in countries like India, Pakistan, and Bangladesh. In this system, one crore is equivalent to ten million, so the correct answer is 10.

The greatest natural number which when rounded off to the nearest hundreds as 500 is
  • a)
    540
  • b)
    500
  • c)
    450
  • d)
    205
Correct answer is option 'A'. Can you explain this answer?

Rahul Kumar answered
To find the greatest natural number that rounds off to 500 when rounded to the nearest hundred, consider the range of numbers that round to 500.
  • Numbers from 450 to 549 round off to 500 when rounded to the nearest hundred.
  • The greatest number in this range is 549.
So, the correct answer is A: 549.

What do regular polygons and number sequences have in common?
  • a)
    They both have colors
  • b)
    They both have patterns
  • c)
    They both are three-dimensional
  • d)
    They both are random
Correct answer is option 'B'. Can you explain this answer?

Regular polygons and number sequences both have patterns. In polygons, the pattern is in the sides and angles, while in number sequences, the pattern is in the numbers themselves.

What pattern do the numbers 3, 6, 9, 12 follow?
  • a)
    Adding 1
  • b)
    Multiple of  2
  • c)
    Multiple of 3
  • d)
    Adding 5
Correct answer is option 'C'. Can you explain this answer?

The sequence 3, 6, 9, 12 follows the pattern of multiplying by 3. This creates a sequence where each number is a multiple of 3.

Which of the following shapes is a three-dimensional object?
  • a)
    Square
  • b)
    Triangle
  • c)
    Circle
  • d)
    Cube
Correct answer is option 'D'. Can you explain this answer?

Ashutosh Verma answered
Understanding Three-Dimensional Objects
Three-dimensional (3D) objects have depth, width, and height, making them more complex than two-dimensional (2D) shapes, which only have length and width.
Types of Shapes
- Square:
- A square is a 2D shape with four equal sides and four right angles.
- It exists only on a flat surface.
- Triangle:
- A triangle is also a 2D shape with three sides and three angles.
- Like a square, it is flat and does not have depth.
- Circle:
- A circle is a round, 2D shape characterized by all points being equidistant from the center.
- It also lacks height and depth.
- Cube:
- A cube is a 3D object with six square faces, twelve edges, and eight vertices.
- It has depth, width, and height, making it a solid object.
Why Cube is the Correct Answer
The cube is the only option listed that meets the criteria of being a three-dimensional object. It can be visualized as a box that occupies space and can be measured in three dimensions (length, width, height).
In contrast, the square, triangle, and circle are flat shapes, confined to two dimensions.
Conclusion
In summary, while squares, triangles, and circles are two-dimensional, the cube stands out as the sole three-dimensional shape among the options provided. Understanding these differences is crucial in geometry and helps in visualizing how objects exist in space.

The missing term in the sequence  1, 3, 6, __, 15, __ is.
  • a)
    25
  • b)
    9
  • c)
    10
  • d)
    8
Correct answer is option 'C'. Can you explain this answer?

Sanskriti Sen answered
Understanding the Sequence
The given sequence is: 1, 3, 6, __, 15, __.
To find the missing terms, we need to identify the pattern in the sequence.
Identifying the Pattern
1. First Term: 1
- The first term is simply 1.
2. Second Term: 3
- 1 + 2 = 3
3. Third Term: 6
- 3 + 3 = 6
4. Fourth Term: __
- 6 + 4 = 10 (This is the first missing term)
5. Fifth Term: 15
- 10 + 5 = 15
6. Sixth Term: __
- 15 + 6 = 21 (This is the second missing term)
Conclusion
The pattern is that each term is the sum of the previous term and an increasing integer (1, 2, 3, 4, 5, 6, ...).
Thus, the missing terms in the sequence are:
- The first missing term is 10.
- The second missing term is 21.
Therefore, the correct answer for the first missing term is option 'C', which is 10.

The price of a school bag is 250 Rs. 95 paise but Priya has only 210 Rs. 25 paise. How much more money does she require to buy the bag?
  • a)
    407 p
  • b)
    4000 p
  • c)
    4070 p
  • d)
    470 p
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 6 answered
The price of the school bag is 250 Rs. 95 paise, while Priya has 210 Rs. 25 paise. To determine how much more money she needs, we first convert both amounts into paise.
  • 250 Rs. 95 paise = 250 Γ— 100 + 95 = 25,095 paise
  • 210 Rs. 25 paise = 210 Γ— 100 + 25 = 21,025 paise
Next, we subtract the amount Priya has from the total price of the bag:
25,095 paise - 21,025 paise = 4,070 paise
Therefore, Priya requires 4070 paise more to purchase the bag.

The smallest 5-digit number is bigger than the largest 4-digit number by _______.
  • a)
    999
  • b)
    998
  • c)
    1000
  • d)
    1
Correct answer is option 'D'. Can you explain this answer?

The smallest 5-digit number is 10000, while the largest 4-digit number is 9999.
To determine the difference:
  • 10000 - 9999 = 1
This shows that the smallest 5-digit number is greater than the largest 4-digit number by 1.
The correct answer is d) 1.

The sum of 267 + 132 to the nearest ten is _______.
  • a)
    300
  • b)
    200
  • c)
    350
  • d)
    400
Correct answer is option 'D'. Can you explain this answer?

Praveen Kumar answered
First, add the numbers:
267 + 132 = 399
Now, round 399 to the nearest ten. Since the last digit (9) is 5 or greater, we round up to the next ten:
399 rounded to the nearest ten is 400.
So, the correct answer is D: 400.

Look at the pattern of shapes below:

What shape comes next in the pattern?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'A'. Can you explain this answer?

Coachify answered
The pattern alternates between a blue circle () and a yellow diamond (). After the last shape (), the next shape will be a yellow diamond ().
So, the correct answer is A: .

Roman Numeral of 400 is
  • a)
    CD
  • b)
    CL
  • c)
    LD
  • d)
    XC
Correct answer is option 'A'. Can you explain this answer?

Vp Classes answered
In Roman numerals:
  • 400 is represented as CD.
  • C stands for 100, and D stands for 500.
  • Since 400 is 500 minus 100, it is written as CD.
Thus, the correct answer is A: CD.

Fill in the blanks:
1 million = ______ thousands
  • a)
    10
  • b)
    100
  • c)
    1000
  • d)
    10000
Correct answer is option 'C'. Can you explain this answer?

Dr Manju Sen answered
1 million is equal to 1,000,000. To find out how many thousands are in a million, we can use the following steps:
  • Recognise that 1 thousand equals 1,000.
  • Divide 1,000,000 by 1,000:
  • 1,000,000 Γ· 1,000 = 1000.
Therefore, 1 million is equal to 1000 thousands.

Solve:
15 Γ— 1000 + 7 Γ— _______ + 6 Γ— 10 = 15760
  • a)
    1
  • b)
    10
  • c)
    100
  • d)
    1000
Correct answer is option 'C'. Can you explain this answer?

Vp Classes answered
We are given the equation:
15 Γ— 1000 + 7 Γ— _______ + 6 Γ— 10 = 15760
Let's simplify the known values first:
  • 15 Γ— 1000 = 15000
  • 6 Γ— 10 = 60
Now, substitute these values into the equation:
15000 + 7 Γ— _______ + 60 = 15760
Subtract 15000 and 60 from 15760:
15760 - 15000 - 60 = 700
So, the missing value is:
7 Γ— _______ = 700
To find the missing value, divide 700 by 7:
700 Γ· 7 = 100
Thus, the missing value is 100.
So, the correct answer is C: 100.

Find the smallest number among the following numbers. 1411, 14504, 2431, 10001, 9900
  • a)
    10001
  • b)
    9900
  • c)
    2431
  • d)
    1411
Correct answer is option 'D'. Can you explain this answer?

EduRev Class 6 answered
To find the smallest number among the given numbers, we simply compare their values:
  • 1411
  • 14504
  • 2431
  • 10001
  • 9900
The smallest number is 1411, so the correct answer is D.

The number 28,549 when rounded off to the nearest hundreds is
  • a)
    28,000
  • b)
    28,500
  • c)
    28,600
  • d)
    29,000
Correct answer is option 'B'. Can you explain this answer?

EduRev Class 6 answered
To round 28,549 to the nearest hundred, follow these steps:
  • Identify the tens place, which is 4.
  • Since 4 is less than 5, we round down.
  • This keeps the hundreds place the same.
Therefore, 28,549 rounded to the nearest hundred is 28,500.
The correct answer is B: 28,500.

The biggest 4 digit number formed by using each of the digits 5, 7, 8, 9, without repetition is
  • a)
    9875
  • b)
    8975
  • c)
    7589
  • d)
    5789
Correct answer is option 'A'. Can you explain this answer?

The question asks for the biggest 4-digit number that can be formed using the digits 5, 7, 8, and 9 without repetition.
The largest possible number formed with these digits is:
  • 9875
This number is indeed the greatest that can be created using each digit exactly once.

The smallest natural number which when rounded off to the nearest hundreds as 500 is
  • a)
    499
  • b)
    501
  • c)
    450
  • d)
    549
Correct answer is option 'C'. Can you explain this answer?

EduRev Class 6 answered
To find the smallest natural number that rounds off to 500 when rounded to the nearest hundred, consider the range of numbers that round to 500.
  • Numbers from 450 to 549 round off to 500 when rounded to the nearest hundred.
  • Therefore, the smallest number that rounds to 500 is 450.
So, the correct answer is C: 450.

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