Triangular Numbers Using Patterns

Q. What are square and triangular numbers?

Q. how can 1 be a triangular number? 1 cannot be a triangular number becuase when it is visualised it does not form a triangle?

Q. Which of the following can be the square of a natural number 'n'?

1. Sum of the square of first n natural numbers.
2. Sum of the first n natural numbers.
3. Sum of the first (n-1) natural numbers.
4. Sum of the first n odd natural numbers.

Q. Zach has 6 matchsticks to make as many triangles as possible. What is the maximum number of triangles he can make?
(All matchsticks are used at once.)

1. 2
2. 4
3. 8
4. 16

Q. If a number has 4 or 6 in its unit place, then its squares ends in which of the following number?

1. 4
2. 5
3. 6
4. 0

Q. What of the following do we have to add with 280 to make it a perfect square nearest to it?

1. $3$
2. $3^2$
3. $2^2$
4. $1$

Q.

The pie charts show some information about the numbers of medals won by Germany and by the Russian Federation in the 2010 Winter Olympics.

While Germany won 7 bronze medals, how many gold medals did they win?

1. 7

2. 15

3. 10

4. 20

Q.

The Value of ${4.1}^2$ is equal to

1. $1.681$

2. $168.1$

3. $16.81$

4. $18.61$

Q. Which of the following will have 9 in it's unit place?

1. ${42}^2$
2. ${23}^2$
3. ${58}^2$
4. ${16}^2$

Q. Simplify and express in exponential form:
${25}^4÷5^{-3}$

1. $5^5$
2. $3^5$
3. $5^{11}$
4. ${25}^2$

Q.

Suppose you and 7 of your friends ate a medium pizza cut into 8 equal parts. Since you all were still hungry you ordered one more pizza. This time a large pizza, which is again cut into 8 equal parts. The percentage of the full large pizza eaten by you will be _____.

1. more than that of the medium pizza.

2. less than that of the medium pizza .

3. two times more than that of the medium pizza.

4. the same as that of the medium pizza.

Q.

In 2008, approximately what percent of the world's population lived in Africa if the sector angle of Africa measured 52${}^{\circ }$?

1. 14%

2. 18%

3. 20%

4. 24%

Q.

Fill in the blanks to make the statement true: $27500000=2.75\times {10}^{\_\_\_\_\_}$.

Q. Below pie-chart shows the expenditure on household expenses of Jaya.
If her salary is ₹50, 000, then the total expenditure on health and food is

1. ₹29, 000
2. ₹31, 000
3. ₹34, 000
4. ₹43, 000

Q. A square number can be expressed as product of consecutive even / odd numbers. For $n^2$, it is represented as:

1. $(n-1)(n+1)=n^2-1$
2. $(n+1)(n+1)=n^2+1$
3. $(n-1)(n-1)=n^2-1$
4. $(n^2-1)(n^2+1)=n^2-1$

Q.

Look at the patterns made by matchsticks. Complete the tables and find a general formula.

Number of double squares (x)	1	2
Number of matchsticks (y)	7	12

Q. Expansion of -8(3a + 5b) yields :

1. -24a - 40b
2. -22a + 80b
3. 20a - 30b
4. -24a - 41b

Q. Which of the following number's square has 5 in its unit place?

1. ${18}^2$
2. ${25}^2$
3. ${11}^2$
4. ${20}^2$

Q.

Observe the graph and answer:

What percentage of people voted for either Prakash or Krish?

1. 15%

2. 7%

3. 23%

4. 8%

Q.

Some children were asked to name their favourite flavour of ice cream. The result is shown in the following pie chart.

Find the number of children who said chocolate was their favourite flavour if 12 students had said that vanilla is their favourite flavour.

1. 10

2. 16

3. 25

4. 15

Q.

Fill in the blanks to make the statement true: $340900000=3.409\times {10}^{----}$.

Q. If we add two consecutive triangular numbers, then we get _________.

1. even numbers
2. odd numbers
3. square numbers
4. rational numbers

Q. Mark (✓) against the correct answer
A number increased by 20% gives 30. The number is

(a) 150
(b) 6
(c) 25
(d) 60

Q.

Observe the dot pattern arranged in triangles. How many dots will be there in the next triangle?

Q.

Find the square root of the following

$\sqrt{\left(2025\right)}$

1. $55$

2. $65$

3. $35$

4. $45$

Q. Mark (✓) against the correct answer
If 35% of a number added to 39 is the number itself, the number is

(a) 60
(b) 65
(c) 75
(d) 70

Q. A triangle is divided into 4 parts and the area of the 4 regions are given inside the corresponding regions. Find the value of $x$ if area of triangle is 30.

Q. Which of the following will have 9 as its unit digit?

1. ${14}^2$
2. ${15}^2$
3. ${17}^2$
4. ${19}^2$

Q.

Observe the dot arranged in triangles. How many dots will be there in the SEVENTH triangle?

1. $24$

2. $27$

3. $28$

4. $21$

Q. Mark (✓) against the correct answer
If 35% of a number added to 39 is the number itself, the number is

(a) 60
(b) 65
(c) 75
(d) 105