Sample Question Paper Solutions (Set-3) | Sample Papers For Class 6 PDF Download

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General Instructions

All questions are compulsory.

• Section A comprises 12 questions carrying 1 mark each.
• Section B comprises 10 questions carrying 2 marks each.
• Section C comprises 8 questions carrying 3 marks each.
• Section D comprises 2 questions carrying 5 marks each.

Q1: The perimeter of a rectangle is calculated as:   (1 mark)
(a) Length × Width
(b) 2 × (Length + Width)
(c) (Length + Width) / 2
(d) Length × Width × 2

Ans: (b)

Q2: An elevator is on the 6th floor. It moves down 10 floors. Which floor is it on now?   (1 mark)
(a) 16th floor
(b) -4th floor
(c) 4th floor
(d) -10th floor

Ans: (b)

Q3: If a shape is rotated 180° around a fixed point and looks the same, it has: (1 mark)
(a) Reflection symmetry
(b) Line symmetry
(c) Rotational symmetry of order 2
(d) No symmetry

Ans: (c)

Q4: Convert the mixed fraction into an improper fraction.  (1 mark)
(a) 15/5
(b) 16/5
(c) 17/5
(d) 14/5

Ans: (c) 

Q5: What is the prime factorization of 60?  (1 mark) 
(a) 2 × 2 × 3 × 5
(b) 2 × 3 × 5
(c) 2 × 2 × 5 × 7
(d) 3 × 3 × 5

Ans: (a) 

Q6: A triangle has a base of 10 cm and a height of 6 cm. What is its area?  (1 mark)
(a) 30 cm²
(b) 60 cm²
(c) 16 cm²
(d) 40 cm²

Ans: (a) 

Q7: Which of the following shapes has infinite lines of symmetry? (1 mark) 
(a) Square
(b) Rectangle
(c) Circle
(d) Triangle

Ans: (c)

Q8: The temperature in a city was recorded as -12°C at night and rose by 15°C in the morning. What is the morning temperature? (1 mark)
(a) -3°C
(b) 3°C
(c) -27°C
(d) 27°C

Ans: (b)

Q9: Which of the following is a straight angle?   (1 mark)
(a) 45°
(b) 90°
(c) 180°
(d) 360°

Ans: (c)

Q10: Two numbers are co-prime if they have: (1 mark) 
(a) No common factor other than 1
(b) At least one common factor
(c) Only even factors
(d) Only odd factors

Ans: (a)

Q11: Which fraction is equivalent to 3/7? (1 mark)
(a) 6/14
(b) 5/14
(c) 3/14
(d) 4/7

Ans: (a)

Q12: Which of the following statements about bar graphs is correct?   (1 mark) 
(a) They have bars of varying widths
(b) The height or length of the bars represents frequency
(c) The bars must always be horizontal
(d) Bar graphs do not require a scale

Ans: (b) 

Q13:  Why are 2, 5, 9, 14, 20, ... called pentagonal numbers? Why are 1, 6, 12, 18, 24, ... called hexagonal numbers? Why are 1, 4, 10, 20, 35, ... called tetrahedral numbers? (2 marks) 

Ans:

• Pentagonal numbers: These numbers can be arranged in the shape of a pentagon by placing dots in increasing layers.
• Hexagonal numbers: These numbers can be arranged in a hexagon shape by placing dots in expanding hexagonal patterns.
• Tetrahedral numbers: These numbers can be arranged like a tetrahedron by placing dots in three-dimensional pyramid layers.

Q14: Find the remainders obtained when each of the following numbers are divided by   (2 marks) 
(i) 85

Ans: 

• Divided by 10: Remainder = 5
• Divided by 5: Remainder = 0
• Divided by 2: Remainder = 1

(ii) 102

Ans: 

• Divided by 10: Remainder = 2
• Divided by 5: Remainder = 2
• Divided by 2: Remainder = 0

Q15: Arrange the following numbers in ascending order on a number line: 1920, 3840, 2760, 4680.   (2 marks) 

Ans: Smallest to largest: 1920, 2760, 3840, 4680.

• 1920 is closer to 2000.
• 2760 comes just after 2700.
• 3840 is slightly beyond 3800.
• 4680 is close to 4700.

The correct sequence in ascending order is: 1920, 2760, 3840, 4680.

Q16: How many pieces of length 1/5 will make a length of 2/3? (2 marks) 

Ans: Total no. of pieces =
Hence, 3 full pieces of length 1/5 will make a length close to 2/3, and a small part of the fourth piece is required.

Q17: A triangle has three sides measuring 5 cm, 6 cm, and 7 cm. Find its perimeter.  (2 marks) 

Ans: Perimeter of a triangle = sum of all sides
= 5 + 6 + 7
= 18 cm

Q18:  Do you see any Line of symmetry in the figures given below?  (2 marks) 

Ans: The diamond shape has one line of symmetry and the given flower has 4 lines of symmetry

Q19: Construct a four-digit palindrome using the digits 2, 5, and 7, and explain why it works.  (2 marks) 

Ans: 2552 is a palindrome because it reads the same forward and backward: 2-5-5-2, with the first and last digits matching (2), and the second and third digits matching (5).

​Q20: Observe the sequence: 11, 22, 33, 44, 55. Extend the pattern to the next two terms and explain. (2 marks) 

Ans: In the above pattern the numbers are increasing by 11 each time, where the digits are repeated. To extend the pattern, the next two terms would be:

• 66 (two 6's)

• 77 (two 7's)

​Q21: What is the sum of 2/3 and 5/7? (2 marks) 

Ans: Convert 2/3 to 14/21 (multiply numerator and denominator by 7).

Convert 5/7 to 15/21 (multiply numerator and denominator by 3).

Now, add the two fractions:
14/21 + 15/21 = 29/21.

So, the sum of 2/3 and 5/7 is 29/21

​Q22: A tailor wants to put lace around a square tablecloth of side 20 cm. He bought 1 m lace from the market. Find the length of lace left with him after completing the task. (2 marks) 

Ans:  Side = 20cm 

Perimeter of Square: S X 4 = 20 X 4 = 80 cm 

Length of cloth = 1m = 100 cm 

Cloth left: 100 - 80 = 20cm 

Q23: Solve the following and fill in the blanks (3 marks) 
(a) (+60) + _______________ = +300
(b) (+80) + _______________ = -250
(c) (-90) + _______________ = +150

Ans: 
(a) (+60) + _______________ = +300
Let (+60) + x = +300
⇒ x = 300 - 60 = 240
∴ (+60) + (+240) = +300
(b) (+80) + _______________ = -250
Let (+80) + x = -250
⇒ x = -250 - 80 = -330
∴ (+80) + (-330) = -250
(c) (-90) + _______________ = +150
Let (-90) + x = +150
⇒ x = 150 - (-90) = 150 + 90 = 240
∴ (-90) + (+240) = +150

Q24: Can you fill in the missing numbers in the ladder? Justify your answer. (3 marks) 

Ans: 

The given sequence is:
6, __, 12, __, 18,  __, 24, 27, __

• After 6, adding 3 gives 9.
• After 12, adding 3 gives 15.
• After 18, adding 3 gives 21.
• After 27, adding 3 gives 30.

Q25: Following are the marks obtained by 72 students in Geography. Arrange these marks in a table using tally marks. (3 marks) 

(a) students obtained more than 6 marks. 
(b) students obtained marks equal to or below 2. 

Ans: 
Step 1: To count the marks obtained by the students, look at the following tally table:

Step 2: Number of students who scored more than 6 marks Or, the number of students who scored marks 7, 8, 9 = 11 + 9 + 10 = 30 students
Step 3: Number of students who scored marks equal or less than 2 Or, the number of students who scored marks 2 = 10 = 10 students

Q26: Identify the Image (3 marks) 

Ans: Image A: Ray
Image B:  Line segment. 
Image C:  Line.

Q27: Read and Answer the Pictograph Questions  (3 marks) 

(i) How many oranges were picked on Monday?
(ii) When was the maximum number of oranges picked?
(iii) When was the maximum number of oranges picked?

Ans: 
(i) Oranges picked on Monday = 4 x 15 = 60 oranges 
(ii) Friday 
(iii) Saturday 

Q28: A lift in a building moves up and down between different floors. The basement is represented by negative numbers, and floors above the ground floor are represented by positive numbers. The ground floor is 0.  (4 marks) 
(A) A lift starts at the 5th floor and moves down 8 floors. What floor does it reach?
(B) From that floor, it moves up 6 floors. Where is the lift now?
(C) If the lift goes down 4 more floors, which floor will it stop at?

Ans: 
(A) Starting at the 5th floor and moving down 8 floors:
5−8=−3
The lift reaches the 3rd basement floor (-3).
(B) Moving up 6 floors:
−3+6=3
The lift is now on the 3rd floor.
(C) Moving down 4 floors:
3−4=−1
The lift stops at the 1st basement floor (-1).

Q29: Suppose you start with ₹0 in your bank account, and then you have debits of ₹3, ₹6, ₹12, ₹24, ₹48, ₹96, and then a single credit of ₹200. What is your bank account balance now?  (4 marks)  

Ans: Here, Debits = ₹3 + ₹6 + ₹12 + ₹24 + ₹48 + ₹96 = ₹189
∴ Balance = Credits – Debits
= ₹200 – ₹189
= ₹11
Therefore, your bank account balance is ₹11.

Q30: A farmer wants to fertilize a rectangular field that is 500 m long and 200 m wide. The cost of fertilization is ₹8 per 100 sq. m. What will be the total cost of fertilizing the entire field?  (4 marks) 

Ans:  Here, length = 500 m and breadth = 200 m
Hence, the area of the rectangular field = length × breadth
= 500 × 200
= 1,00,000 sq. m

Now, the cost of fertilizing 100 sq. m = ₹8
Total cost = (8/100) × 100000
= ₹8,000

Q31: 2032 is a leap year (as February has 29 days).     (5 marks)  
Leap years occur in years that are multiples of 4, except for those years that are evenly divisible by 100 but not 400.
(a) From the year 2015 till now, which years were leap years?
(b) From the year 2032 till 2100, how many leap years are there?

Ans: (a)  From the year 2015 till 2032, there are 5 leap years: 2016, 2020, 2024, 2028, and 2032.
(b)  The leap years from 2032 to 2099 are:
2032, 2036, 2040, 2044, 2048, 2052, 2056, 2060, 2064, 2068, 2072, 2076, 2080, 2084, 2088, 2092, 2096.
Hence, there are 17 leap years from 2032 till 2099.

Q32: Find the perimeter of the shape given : (5 marks) 

Ans: There are some missing lengths we need to work out first. We can look at the vertical lengths. The missing vertical length is 7 cm because 11−4 =7

We can then look at the missing horizontal length. The missing side is 5 cm because 7−2=5.

Starting in the top left corner and going clockwise around the shape, we can add the sides together.

2+7+5+4+7+11 = 36

Therefore, perimeter =  36cm