लाइव पेपर डेमो

Q.1: What is the sum of the first 6 even numbers (2 + 4 + 6 + 8 + 10 + 12)?

A) 36 B) 42 C) 40 D) 48

Q.2: What happens when you add two consecutive triangular numbers, such as 3 and 6?

A) You always get a prime number B) You always get an even number C) You always get a square number D) You always get a cube number

Q.3: Following the shape pattern where each line segment is replaced by 4 new segments at each step, what is the number of segments in Iteration 2 if Iteration 1 has 12 segments?

A) 16 B) 24 C) 36 D) 48

Q.4: What are the first four triangular numbers in order?

A) 1, 2, 3, 4 B) 1, 4, 9, 16 C) 1, 3, 6, 10 D) 1, 2, 4, 8

Q.5: How does understanding mathematical patterns help humanity propel forward?

A) It helps only in passing school exams. B) It allows us to build complex structures, launch satellites, and diagnose diseases. C) It ensures that numbers never change. D) It eliminates the need for any scientific experiments.

Q.6: If the 7th and 8th Virahanka numbers are 21 and 34, what is the 9th Virahanka number?

A) 55 B) 50 C) 65 D) 58

Q.7: What is the 5th triangular number in the sequence?

A) 12 B) 15 C) 20 D) 25

Q.8: Following the palindromic addition pattern, what is the sum of 1 + 2 + 3 + ... + 9 + 10 + 9 + ... + 3 + 2 + 1?

A) 90 B) 100 C) 110 D) 1000

Q.9: What is the value of the pattern: 1 + 2 + 1?

A) 3 B) 4 C) 5 D) 6

Q.10: What is the rule to find the next term in the Virahanka number sequence (1, 2, 3, 5, 8, 13...)?

A) Multiply the previous term by 2 B) Add the two preceding terms together C) Add 2 to the previous term D) Square the previous term and subtract 1

Q.11: What are the first four numbers in the sequence of hexagonal numbers?

A) 1, 4, 9, 16 B) 1, 6, 12, 18 C) 1, 7, 19, 37 D) 1, 8, 27, 64

Q.12: What is the value of $4^3$?

A) 16 B) 32 C) 64 D) 128

Q.13: What is the first non-zero cube number in the sequence of cubes?

A) 1 B) 2 C) 4 D) 8

Q.14: In a shape museum exhibit, the 1st shape is a triangle (3 sides), the 2nd is a square (4 sides), and the 3rd is a pentagon (5 sides). What is the name of the 4th shape in this sequence?

A) Heptagon B) Octagon C) Hexagon D) Rectangle

Q.15: Which number less than 50 is BOTH a triangular number and a square number?

A) 16 B) 25 C) 36 D) 49

Q.16: What is the value of the 5th cube number ($5 \times 5 \times 5$)?

A) 25 B) 75 C) 100 D) 125

Q.17: If the 7th triangular number is 28, how do you find the 8th triangular number?

A) Multiply 28 by 2 B) Add 8 to 28 C) Add 7 to 28 D) Square 8 and add to 28

Q.18: For the shape exhibit sequence (triangle, square, pentagon...), what is the formula to find the number of sides of the nth shape?

A) n + 1 B) n + 2 C) 2n D) n + 3

Q.19: In the study of patterns, finding out *why* a pattern works is called finding its:

A) Iteration B) Variable C) Explanation D) Element

Q.20: Which sequence is formed by the numbers 1, 8, 27, 64, 125?

A) Triangular numbers B) Square numbers C) Hexagonal numbers D) Cube numbers

Q.21: If you want to build a large cube of side length 3 units using smaller 1-unit cubes, how many small cubes do you need?

A) 9 B) 18 C) 27 D) 36

Q.22: In the sequence of even numbers 2, 4, 6, 8, 10, ..., what is the rule to find the next number?

A) Multiply the previous number by 2 B) Add 2 to the previous number C) Subtract 2 from the previous number D) Square the previous number

Q.23: If we add the 3rd triangular number (6) and the 4th triangular number (10), which square number do we get?

A) 9 B) 16 C) 25 D) 36

Q.24: Find the missing number in the pattern: 1 = 1, 1 + 3 = 4, 1 + 3 + 5 = 9, 1 + 3 + 5 + 7 + 9 = ___.

A) 16 B) 20 C) 25 D) 30

Q.25: What is the rule for the sequence of differences between consecutive triangular numbers (3-1, 6-3, 10-6, 15-10...)?

A) The differences are all equal to 2 B) The differences form the sequence of counting numbers 2, 3, 4, 5... C) The differences are all odd numbers D) The differences decrease by 1 each time

Q.26: The sequence 1, 2, 3, 5, 8, 13, 21, ... is named after which ancient Indian mathematician in the textbook Ganita Prakash?

A) Aryabhata B) Virahanka C) Brahmagupta D) Bhaskara

Q.27: How many dots are needed to form the 12th square number pattern?

A) 24 B) 120 C) 144 D) 132

Q.28: In Section 1.5, "Patterns in Shapes," an equilateral triangle starts with 3 line segments (Iteration 0). If each segment is replaced by 4 new connected segments in Iteration 1, how many line segments are there now?

A) 7 B) 12 C) 9 D) 16

Q.29: What is the sum of the first three triangular numbers (1 + 3 + 6)?

A) 10 B) 9 C) 12 D) 14

Q.30: What is the pattern of differences between consecutive hexagonal numbers (7-1, 19-7, 37-19...)?

A) The differences increase by 4 each time B) The differences are multiples of 6 (6, 12, 18...) C) The differences are all odd numbers D) The differences remain constant

1. Patterns in Mathematics 108 (डेमो)

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