RBSE Solutions Class 5 Maths Chapter 8 Patterns Important Questions

Multiple Choice Questions

 

Question 1. Extend the patterns given below
The given pattern is: ↑ → ↓
(a) ↑
(b) →
(c) ↓
(d) ←
Answer: (c) ↓
In simple words: The pattern shown is up, right, down. If the pattern repeats as a block of three, then after down, the sequence would restart, but if it is continuing a specific part of a larger repeating cycle, then 'down' is the intended next step.

🎯 Exam Tip: For visual patterns, carefully observe the changes in direction, shape, or position. Sometimes, the pattern repeats as a whole block, and other times it continues a sequence of individual elements.

 

Question 2. Extend the following pattern-
The given pattern is: ↑↑ →→ ↓↓
(a) ↑↑
(b) →→
(c) ↓↓
(d) ←←
Answer: (a) ↑↑
In simple words: The pattern shows blocks of two arrows pointing up, then two pointing right, then two pointing down. To extend this pattern, the next block would be two arrows pointing up again, as the sequence repeats.

🎯 Exam Tip: Notice if the pattern consists of repeating individual elements or repeating blocks of elements. This helps in correctly predicting the next part of the sequence.

 

Question 3. Next term of 2, 5, 8, 11, ...
(a) 12
(b) 13
(c) 14
(d) 3
Answer: (c) 14
In simple words: In this number pattern, each new number is found by adding 3 to the number before it. So, after 11, the next number will be 11 plus 3, which is 14.

🎯 Exam Tip: Always look for the difference or ratio between consecutive numbers to find the rule of the pattern. Check if it's constant or changes in a predictable way.

 

Question 5. Next term of 4, 7, 11, 16 is-
(a) 18
(b) 20
(c) 24
(d) 22
Answer: (d) 22
In simple words: The numbers in this pattern increase by an amount that also increases. First, 3 is added, then 4, then 5. Following this rule, the next number should have 6 added to it, making it 16 + 6 = 22.

🎯 Exam Tip: When the differences between numbers are not constant, look for a pattern in those differences themselves (e.g., adding an increasing number).

 

Question 6. Wrong term in 3, 8, 13, 17, 23 is-
(a) 8
(b) 17
(c) 13
(d) 23
Answer: (b) 17
In simple words: If you look at the pattern, each number should be 5 more than the one before it. Following this rule, after 13, the next number should be 18 (13 + 5), but the list shows 17. So, 17 is the wrong number in this sequence.

🎯 Exam Tip: To find a wrong term, first identify the correct rule of the pattern by looking at the consistent parts of the sequence. Then, apply the rule to check each term.

 

Question 7. Complete the above pattern
The given pattern to complete shows: [empty box] [empty box] [empty box] [filled box]
(a) [empty box] [filled box] [filled box]
(b) [empty box] [filled box] [empty box]
(c) [filled box] [empty box] [filled box]
(d) [filled box] [filled box] [empty box]
Answer: (d) [filled box] [filled box] [empty box]
In simple words: This question asks to complete a visual pattern of boxes. The solution indicates that the correct completion involves a specific sequence of filled and empty boxes.

🎯 Exam Tip: For visual patterns, pay close attention to the sequence of changes in color, size, or type of shape. Practice with similar patterns to recognize common transformations.

 

Question 8.
The given pattern shows: [circle with center dot] [circle with center dot] [circle with center dot] [circle with center dot]
(a) [circle with center dot]
(b) [square with center dot]
(c) [triangle with center dot]
(d) [circle with center dot]
Answer: (c) [triangle with center dot]
In simple words: The pattern shown is a repeating circle with a dot. However, the options provided offer different shapes with a dot. The correct answer is (c) which is a triangle with a dot. This suggests a pattern that might involve a change in shape from circle to triangle.

🎯 Exam Tip: Sometimes, a pattern question might have options that seem to deviate from a simple repetition. In such cases, consider if the pattern is a transformation of shapes or a sequence of different elements.

 

Question 9. Wrong term in 1, 6, 11, 17, 21 is-
(a) 17
(b) 6
(c) 11
(d) 21
Answer: (a) 17
In simple words: This pattern should increase by 5 each time. Starting with 1, the next numbers should be 6, 11, 16, 21. Since the sequence shows 17 instead of 16, the number 17 is the incorrect term.

🎯 Exam Tip: Double-check the common difference or ratio across the entire sequence to pinpoint the exact term that breaks the established pattern.

 

Question 10. Next term of 3, 5, 1, 9, 11 is-
(a) 12
(b) 13
(c) 14
(d) 15
Answer: (b) 13
In simple words: If we look closely, the pattern seems to be adding 2 to each number: 3, 5, (if we assume 1 is a typo for 7), 9, 11. Following this simple addition, the next number after 11 would be 11 plus 2, which is 13.

🎯 Exam Tip: When a number sequence seems inconsistent, look for a simple arithmetic progression. Sometimes, there might be a typo in the provided sequence that needs to be quietly corrected to find the intended pattern.

 

Question 11. Next term of 729, 243, 81 is-
(a) 18
(b) 9
(c) 27
(d) 36
Answer: (c) 27
In simple words: In this pattern, each number is found by dividing the number before it by 3. So, to find the next term after 81, we divide 81 by 3, which gives us 27.

🎯 Exam Tip: For decreasing number patterns, check if a constant number is being subtracted or if it's a division pattern.

 

Question 12. Next term of 125, 115, 105, 95 is-
(a) 75
(b) 65
(c) 90
(d) 85
Answer: (d) 85
In simple words: This pattern is a simple one where 10 is subtracted from each number to get the next one. So, to find the next term after 95, we subtract 10 from 95, which results in 85.

🎯 Exam Tip: Identifying the constant difference (positive or negative) is key for arithmetic progressions. Always check if the same value is added or subtracted consistently.

 

Question 1. Pattern of shapes has .....................
Answer: A pattern of shapes creates a sequence, which is an ordered list where items follow a rule. Recognizing sequences helps understand repetitions and predictions.
In simple words: A pattern made of shapes forms a sequence.

🎯 Exam Tip: Remember that patterns of shapes, numbers, or actions all form a sequence if they follow a predictable rule.

 

Question 2. Patterns of ..................... can be formed.
Answer: Patterns of numbers can be formed. Number patterns often follow rules of addition, subtraction, multiplication, or division, making them predictable.
In simple words: You can make patterns using numbers.

🎯 Exam Tip: Numbers are a very common way to show patterns, from simple counting to complex mathematical sequences.

 

Question 3. Sometimes shapes of pattern have a ..................... of patterns.
Answer: Sometimes shapes in a pattern show a sequence of patterns. This means a larger pattern is made up of smaller, repeating sub-patterns.
In simple words: Sometimes, a pattern of shapes has smaller patterns inside it, making a bigger sequence.

🎯 Exam Tip: Look for patterns within patterns! Sometimes a bigger pattern is made by combining or repeating smaller, simpler patterns.

 

Question 2. Make a pattern like this: ↑↑ →→ ↓↓ ←←
Answer: The pattern involves pairs of arrows rotating clockwise. Starting with two up arrows, then two right arrows, then two down arrows, the next logical step is two left arrows.
In simple words: The pattern is arrows turning like a clock, two at a time: up, right, down, then left.

🎯 Exam Tip: When continuing visual patterns, identify the transformation rule (e.g., rotation, reflection, addition, subtraction of elements) and apply it consistently.

 

Question 3. Using [circle] in place of [empty square] make the same pattern below.
Answer: If we replace each empty square with a circle, the pattern for the circles would be `O O O O` and the pattern for the squares would remain `□ □ □ □`. If we are completing the sequence based on the example in the image, the pattern for circles would extend to include a filled circle, and similarly for squares.
In simple words: If you use a circle instead of an empty square, you get a line of circles. Then, you can also have a line of squares, and if there's a pattern, you fill the next shape (like a filled circle or square).

🎯 Exam Tip: Pay attention to symbol substitution and how it affects the pattern. Ensure you follow the specific instruction for replacement while also continuing any established sequence.

 

Question 4. Complete the following pattern.
Answer: The pattern consists of repeating symbols in rows and columns. Each row shows a sequence of a flower, a cross, and a rotated arrow. To complete the pattern, simply repeat the sequence of symbols in the blank spaces.
In simple words: You need to finish the grid by repeating the picture pattern of flowers, crosses, and arrows, making sure each row and column continues the design.

🎯 Exam Tip: For grid patterns, look for both horizontal and vertical relationships between elements. Some patterns repeat every few cells, while others might show a gradual change.

 

Question 5. See the different patterns of numbers given below and proceed further-
\( 9 \times 9 = 81 \)
\( 99 \times 99 = 9801 \)
\( 999 \times 999 = 998001 \)
Answer: This pattern involves multiplying numbers made of only 9s by themselves. Each time you add another 9, the answer starts with more 9s and has 8, then more 0s, and ends with 1. It is a symmetrical expansion of digits.
\( 9 \times 9 = 81 \)
\( 99 \times 99 = 9801 \)
\( 999 \times 999 = 998001 \)
\( 9999 \times 9999 = 99980001 \)
\( 99999 \times 99999 = 9999800001 \)
\( 999999 \times 999999 = 999998000001 \)
In simple words: When you multiply numbers made of only nines (like 9, 99, 999), the answer always starts with 'n-1' nines, then an eight, then 'n-1' zeros, and ends with a one.

🎯 Exam Tip: Observe the number of digits in the input and output. The number of 9s and 0s in the product increases with the number of 9s in the multiplier, always keeping an '8' and '1'.

 

Question 6. Give the shortest method to multiply any number by 5.
Answer: The shortest way to multiply any number by 5 is to first add a zero to the end of that number, and then divide the new number by 2. This works because multiplying by 10 and then dividing by 2 is the same as multiplying by 5.
For example: \( 217 \times 5 = 2170 \div 2 = 1085 \).
In simple words: To quickly multiply a number by 5, just put a zero at the end of the number, then divide that new number by 2.

🎯 Exam Tip: This trick leverages the fact that \( 5 = \frac{10}{2} \), so multiplying by 5 is equivalent to multiplying by 10 and then halving the result. This is useful for mental math.

 

Question 7. Find the next term of 4, 6, 9, 13, 18.
Answer: In this sequence, the number being added to each term increases by one each time. First, 2 is added (4+2=6), then 3 (6+3=9), then 4 (9+4=13), then 5 (13+5=18). Following this rule, the next number to be added is 6. So, the next term will be \( 18 + 6 = 24 \).
In simple words: The numbers go up by 2, then 3, then 4, then 5. So, for the next number, you add 6. The answer is 24.

🎯 Exam Tip: Always look for the differences between terms. If those differences form their own pattern (like increasing by 1 each time), you've found the rule.

 

Question 8. Find the next term of 3, 6, 9, 15, 24.
Answer: In this pattern, each number is found by adding the two numbers before it. For example, \( 3 + 6 = 9 \), \( 6 + 9 = 15 \), and \( 9 + 15 = 24 \). So, to find the next term, you add the last two numbers: \( 15 + 24 = 39 \). This is similar to the Fibonacci sequence.
In simple words: To get the next number, add the two numbers just before it. So, 15 plus 24 gives you 39.

🎯 Exam Tip: Some patterns involve combining previous terms, not just the immediately preceding one. Always test if the sum or product of earlier terms forms the next term.

 

Question 9. Forward the pattern given below by 2 steps.
(1) \( 6, 10, 14, 18, \ldots \)
(2) \( 35, 29, 23, 17, \ldots \)
Answer:
(1) In this pattern, 4 is added to each number to get the next one. So, to forward it by 2 steps: \( 18 + 4 = 22 \), and then \( 22 + 4 = 26 \). The sequence becomes \( 6, 10, 14, 18, 22, 26 \).
(2) In this pattern, 6 is subtracted from each number to get the next one. So, to forward it by 2 steps: \( 17 - 6 = 11 \), and then \( 11 - 6 = 5 \). The sequence becomes \( 35, 29, 23, 17, 11, 5 \).
In simple words: For the first pattern, keep adding 4 to find the next two numbers. For the second pattern, keep taking away 6 to find the next two numbers.

🎯 Exam Tip: For each sequence, determine if it's an increasing or decreasing pattern and find the constant value being added or subtracted. Apply this rule to extend the sequence.

Short Answer Type Question

 

Question 1. Identify the pattern and proceed further-
(1) A pattern of shapes: [empty square] [circle] [triangle] [circle] followed by empty space.
(2) A pattern of repeating plus signs, followed by empty space.
(3) A pattern of arrows: [right arrow] [right arrow] [right arrow] [left arrow] followed by empty space.
(4) A pattern of repeating stick figures, followed by empty space.
Answer:
(1) The pattern is [empty square], [circle], [triangle], [circle]. It seems to be a sequence of square, circle, triangle, then circle again. The next steps would logically be [empty square], [circle], [triangle], [circle].
(2) The pattern is repeating plus signs. So, the next steps are simply more plus signs.
(3) The pattern is three right arrows followed by one left arrow. So, the next steps would be three more right arrows.
(4) The pattern is repeating stick figures: three male figures, then one female figure with long hair, then one female figure with a bun. To continue, repeat these figures.
In simple words: For each row, look at the shapes or figures and see how they repeat or change. Then, draw or describe the next few shapes that would follow that rule.

🎯 Exam Tip: Break down complex visual patterns into smaller repeating units. Identify the sequence of elements and whether they are changing in shape, orientation, or count.

 

Question 2. Identify the pattern and proceed further.
(1) Row 1: A sequence of `[up arrow] [plus sign] [up arrow] [plus sign] [up arrow]`
Row 2: A sequence of `[up arrow] [down arrow] [up arrow] [down arrow] [up arrow]`
Row 3: A sequence of `[circle] [star] [star] [star] [star]`
Answer:
(1) The first pattern alternates between an up arrow and a plus sign. To proceed, continue this sequence.
(2) The second pattern alternates between an up arrow and a down arrow. To proceed, continue this sequence.
(3) The third pattern starts with a circle, followed by four stars. To proceed, repeat this sequence of one circle and four stars.
In simple words: Look at each line and see what pictures repeat. Then, draw the next pictures in the same repeating order for each line.

🎯 Exam Tip: For multiple-row patterns, treat each row as a separate sequence unless there's a clear rule connecting the rows. Focus on the repeating elements within each individual line.

 

Question 3. Fill in the blanks by numbers, in 8, 6, 11, 11, 14, 16, ?, ?
Answer: This number pattern is made by combining two separate arithmetic patterns. The first pattern is found in the numbers at the odd positions: 8, 11, 14. Here, 3 is added each time. So the next term would be \( 14 + 3 = 17 \). The second pattern is found in the numbers at the even positions: 6, 11, 16. Here, 5 is added each time. So the next term would be \( 16 + 5 = 21 \). Thus, the missing numbers are 17 and 21.
In simple words: This pattern mixes two simpler patterns. One pattern adds 3 each time (8, 11, 14, so next is 17). The other pattern adds 5 each time (6, 11, 16, so next is 21). So the missing numbers are 17 and 21.

🎯 Exam Tip: When a single sequence seems complicated, try separating it into two interleaved sequences (numbers at odd positions and numbers at even positions). Each separate sequence might follow a simpler rule.

 

Question 4. Proceed further-
The initial table cells are given as:

Answer: This table contains multiple number patterns. We need to identify the rule for each row and fill in the missing numbers.

In simple words: Fill in the table by finding the rule for each row. The first row adds 4, the second adds 9, the third subtracts 10, the fourth shows square numbers decreasing, and the last row divides by 2.

🎯 Exam Tip: For tables with number patterns, examine each row and column separately. Common patterns include arithmetic series (constant addition/subtraction), geometric series (constant multiplication/division), or sequences of squares/cubes.

 

Question 5. Find next term of 3, 7, 16, 35, 74, .
Answer: In this pattern, each term is found by multiplying the previous term by 2 and then adding an increasing number (1, 2, 3, 4, 5...).
\( 3 \times 2 + 1 = 7 \)
\( 7 \times 2 + 2 = 16 \)
\( 16 \times 2 + 3 = 35 \)
\( 35 \times 2 + 4 = 74 \)
Following this rule, the next term will be \( 74 \times 2 + 5 = 148 + 5 = 153 \).
In simple words: To get the next number, multiply the last number by 2, then add a growing number (first 1, then 2, then 3, and so on). The next number after 74 is 153.

🎯 Exam Tip: When the differences between terms increase rapidly, consider a multiplicative pattern combined with an additive or subtractive component. Look for patterns in the multiplier or the added/subtracted value.

 

Question 6. See the given number pattern and proceed further-
\( 7 \times 7 = 49 \)
\( 67 \times 67 = 4489 \)
\( 667 \times 667 = 444889 \)
Answer: This pattern shows the squares of numbers consisting of only 6s ending with a 7. As more 6s are added to the number, the result gets more 4s at the beginning and more 8s in the middle, always ending with 89.
\( 7 \times 7 = 49 \)
\( 67 \times 67 = 4489 \)
\( 667 \times 667 = 444889 \)
\( 6667 \times 6667 = 44448889 \)
\( 66667 \times 66667 = 4444488889 \)
\( 666667 \times 666667 = 444444888889 \)
In simple words: When you square a number like 7, 67, 667, the answer always starts with a certain number of 4s, then an 8, then a certain number of 8s, and ends with 9. The number of 4s and 8s grows as the number of 6s in the input increases.

🎯 Exam Tip: For complex number patterns, observe how the number of digits and the specific digits themselves change as the input grows. Look for symmetry or repeating blocks within the result.

 

Question 7. Find next term of 4, 6, 9, 13, 18.
Answer: The terms in this sequence are increasing. The rule for this pattern is that an increasing number is added to the previous term. First, 2 is added (4 + 2 = 6), then 3 (6 + 3 = 9), then 4 (9 + 4 = 13), and then 5 (13 + 5 = 18). So, the next number to be added is 6. Therefore, the next term in the sequence is \( 18 + 6 = 24 \).
In simple words: The numbers grow by adding more each time: first 2, then 3, then 4, then 5. So, for the next number, you add 6 to 18 to get 24.

🎯 Exam Tip: Always look at the differences between consecutive terms. If those differences themselves form a pattern (like a simple arithmetic progression), you've found the underlying rule for the main sequence.

 

Question 8. Perform the following steps with any number: (i) Double the number (ii) Multiply the result by 5 (iii) Divide the result by 10. (v) Which number will you get at last? (vi) Is it the same number which was taken by you?
Answer: Let's take the number 8 as an example to see how this works:
(i) Let the starting number be 8.
(ii) Double the number: \( 8 \times 2 = 16 \).
(iii) Multiply the doubled number by 5: \( 16 \times 5 = 80 \).
(iv) Divide the obtained number by 10: \( 80 \div 10 = 8 \).
(v) The number obtained at last is 8.
(vi) Yes, the final number is the same as the number you started with. This trick always returns the original number.
In simple words: If you start with a number, double it, then multiply by 5, and finally divide by 10, you will always end up with your original number. This is a number trick!

🎯 Exam Tip: Understand that \( ((\text{Number} \times 2) \times 5) \div 10 \) simplifies to \( (\text{Number} \times 10) \div 10 \), which simply equals the original Number. This mathematical property makes the trick work for any starting number.

 

Question 9. Identify the pattern in the grid and then fill in the blanks.
The initial grid is:

Answer: In this grid pattern, the number in the middle of the row above is the sum of the two numbers below it. For example, \( 3 + 5 = 8 \), and \( 6 + 7 = 13 \). Therefore, the missing middle number in the bottom row should add up to the middle number in the row above it. The number in the top middle box is found by adding the numbers below it.

In simple words: To fill in the empty boxes, add the two numbers in the boxes right below each empty box. This makes a pyramid where each block is the sum of the two blocks under it.

🎯 Exam Tip: For pyramid-style number puzzles, the common rule is that each number is the sum or difference of the two numbers immediately below or beside it. Identify this rule first.