Push your mathematical boundaries with our “Hard” difficulty MCQ set for Class 6. Designed for the 2026 CBSE Ganit Prakash (Poorvi) syllabus, these questions cover complex problem-solving, multi-step arithmetic, and advanced logical reasoning to ensure complete mastery of the curriculum.
Class 6 Math CBSE Hard MCQ
Question 1 of 20
The product of the predecessor of the smallest prime number and the successor of the smallest composite number is
Question 2 of 20
Find the smallest 5-digit number which is exactly divisible by 12, 15, and 18.
Question 3 of 20
The sum of two integers is -25. If one of them is 30, then the other is
Question 4 of 20
In a school, 4/7 of the students are boys. If there are 210 girls, what is the total strength of the school?
Question 5 of 20
A wire of length 7/8 m is broken into two pieces. If one piece is 1/4 m long, how long is the other piece?
Question 6 of 20
The ratio of the number of sides of a square to the number of edges of a cube is
Question 7 of 20
A room is 12 m long and 8 m wide. A square carpet of side 10 m is laid on the floor. What is the area of the floor not covered by the carpet?
Question 8 of 20
How many whole numbers are there between 32 and 53?
Question 9 of 20
If x + 5 = -2, then the value of 2x + 10 is
Question 10 of 20
The HCF of two numbers is 16 and their product is 3072. Find their LCM.
Question 11 of 20
What is the value of 1 - 2 + 3 - 4 + 5 - 6 ... + 49 - 50?
Question 12 of 20
A vessel contains 4 litres and 500 ml of curd. In how many glasses, each of 25 ml capacity, can it be filled?
Question 13 of 20
The measure of an angle which is 4 times its complement is
Question 14 of 20
If 25% of a number is 100, then the number is
Question 15 of 20
The expression for 'p is multiplied by -5 and then 7 is added to the result' is
Question 16 of 20
A pictograph shows 4 symbols representing 100 books. If a library has 350 books, how many symbols are needed?
Question 17 of 20
The side of a square is increased by 10%. The perimeter increases by
Question 18 of 20
Which of the following is the Roman numeral for 98?
Question 19 of 20
If a ribbon of length 10 m is cut into 8 equal pieces, what is the length of each piece in cm?
Question 20 of 20
In the number 9,87,65,432, the period of the digit 7 in the Indian System is
Frequently Asked Questions (FAQ)
Q1: Why are these questions categorized as “Hard”?
A: These questions involve “Higher Order Thinking Skills” (HOTS). They often combine two or more concepts—such as geometry with percentages or number properties with algebra—requiring deeper analysis than standard textbook exercises.
Q2: Are these questions relevant for the 2026 NCERT ‘Poorvi’ book?
A: Yes. While the difficulty is higher, every question remains within the scope and framework of the new Ganit Prakash (Poorvi) 2026 curriculum.
Q3: Is this set helpful for competitive exams like the Maths Olympiad?
A: Definitely. The logical reasoning and multi-step calculations used here are very similar to the patterns found in the IMO (International Mathematics Olympiad) and other talent search exams.
Q4: How should I prepare before attempting this Hard MCQ set?
A: We recommend completing the “Easy” and “Medium” sets first. Ensure you have a strong grasp of LCM/HCF applications, integer operations, and word-problem decoding.