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Decimal comes from Latin word _________
  • a)
    Decem                         
  • b)
    Decema       
  • c)
    Decimilar                     
  • d)
    Deca
Correct answer is option 'A'. Can you explain this answer?

Aaditya Chavan answered
Answer : 
a)
Decem 
The word decimal comes from the Latin word decimus meaning tenth. Deca means 10 and comes from the Latin word decem (ten) and the Greek word deka. The decimal place value system then, is a way of counting and recording numbers using ten as a base for grouping.

Mixed fraction = Nearest Natural Number + _________
  • a)
    Improper fraction     
  • b)
    Proper fraction
  • c)
    Like fraction              
  • d)
    Complex fraction
Correct answer is option 'B'. Can you explain this answer?

Yashvi Pillai answered
**Explanation:**

A mixed fraction is a combination of a whole number and a proper fraction, where the numerator is less than the denominator. It is written in the form of a whole number followed by a fraction.

For example, 3 1/2 is a mixed fraction where 3 is the whole number and 1/2 is the fraction.

On the other hand, a proper fraction is a fraction where the numerator is less than the denominator. It does not have a whole number part.

For example, 1/2 is a proper fraction.

Now, let's consider the given statement: "Mixed fraction = Nearest Natural Number"

This means that when we have a mixed fraction, we need to find the nearest natural number that is closest to the value of the mixed fraction.

For example, if we have the mixed fraction 3 1/2, we need to find the nearest natural number to the value of 3 1/2.

The value of 3 1/2 is 3.5. The nearest natural number to 3.5 is 4.

Therefore, the nearest natural number to the mixed fraction 3 1/2 is 4.

Since the answer is a whole number (natural number) and not a fraction, the correct option is B) Proper fraction.

In summary, when we have a mixed fraction and we need to find the nearest natural number to its value, the answer will always be a proper fraction.

It takes Alisha's family complete 3 days to drive to the hill station. They spend 4 days at the shore. Then drive home again. If they left home early Saturday on 5th Jan, what day and date will they return to home?
  • a)
    12th Jan, Monday
  • b)
    13th Jan., Tuesday
  • c)
    15th Jan, Thursday
  • d)
    14th Jan. Wednesday
Correct answer is option 'C'. Can you explain this answer?

3 days to drive to the hill station and 3 days to drive to reach home  and  spend 4 days at the shore.
Total days = 3 + 3 + 4
= 10
left home, Saturday on 5th Jan and 10 days used on the trip
Hence, came back to the home after 10 days i.e. 15th Jan, Thursday
 

What number should come next: 13, 26, 39, ____?
  • a)
    52
  • b)
    48
  • c)
    42
  • d)
    53
Correct answer is option 'A'. Can you explain this answer?

Aman Mehta answered
Pattern:
The given sequence follows a pattern where each number is obtained by adding 13 to the previous number.

Explanation:
To find the missing number in the sequence, we need to observe the pattern:

- The first number is 13.
- To find the second number, we add 13 to the previous number: 13 + 13 = 26.
- To find the third number, we add 13 to the previous number: 26 + 13 = 39.

Calculation:
To find the missing number, we need to add 13 to the last number in the sequence.

- Last number: 39
- Add 13: 39 + 13 = 52

Therefore, the missing number in the sequence is 52.

Conclusion:
The number that should come next in the sequence is 52, which corresponds to option 'A'.

Which of the following statements is correct?
  • a)
    Every prime number is odd.
  • b)
    Every even number is composite.
  • c)
    The sum of two odd numbers is always odd,
  • d)
    The HCF of two given numbers is always a factor of their LCM
Correct answer is option 'D'. Can you explain this answer?

The correct statement is option 'D'.

Explanation:

HCF and LCM are important concepts in number theory. HCF stands for Highest Common Factor and LCM stands for Lowest Common Multiple. The HCF of two given numbers is the largest number that divides both the numbers evenly. The LCM of two given numbers is the smallest number that is a multiple of both the numbers.

The relationship between HCF and LCM is that the HCF of two given numbers is always a factor of their LCM. This can be explained as follows:

Let's take two numbers a and b. We can write them as a = p1 * q1 and b = p2 * q2, where p1, p2, q1, q2 are prime factors of a and b.

The LCM of a and b is given by LCM(a, b) = max(p1, p2) * q1 * q2.

The HCF of a and b is given by HCF(a, b) = min(p1, p2).

Now, let's find the factors of LCM(a, b). The factors of LCM(a, b) are max(p1, p2), q1 and q2.

We can see that the HCF of a and b, which is min(p1, p2), is a factor of LCM(a, b), which is max(p1, p2) * q1 * q2.

Therefore, the HCF of two given numbers is always a factor of their LCM.

Decimals having the same number of decimal places are called _________
  • a)
    Like decimals   
  • b)
    Unlike decimals
  • c)
    Decimals                      
  • d)
    Whole numbers
Correct answer is option 'A'. Can you explain this answer?

The correct answer is option 'A' - Like decimals.

Decimals are a way of representing numbers that are not whole numbers. They include a decimal point that separates the whole number part from the decimal part. The digits to the right of the decimal point represent a fraction of a whole number.

When comparing decimals, it is important to consider the number of decimal places they have. The number of decimal places refers to the number of digits to the right of the decimal point.

Decimals that have the same number of decimal places are called like decimals. For example, 0.25 and 0.75 have two decimal places, so they are like decimals. Similarly, 2.430 and 5.730 have three decimal places, so they are also like decimals. In both cases, the number of decimal places is the same, making them like decimals.

On the other hand, decimals that have a different number of decimal places are called unlike decimals. For example, 0.5 and 0.35 have different decimal places, so they are unlike decimals. Similarly, 3.2 and 5.67 have a different number of decimal places, so they are unlike decimals as well.

The reason why the correct answer is option 'A' - Like decimals is because decimals with the same number of decimal places are considered to be similar or like each other. This helps in comparing and performing operations on decimals more easily.

Understanding the concept of like and unlike decimals is important in various mathematical operations such as addition, subtraction, multiplication, and division. It allows us to align the decimal places correctly, making calculations more accurate.

What should be subtracted from the greatest 7 digit number to get 65,43,210 ?
  • a)
    12,34,567 
  • b)
    99,99,999
  • c)
    12,34,560
  • d)
    34,56,789
Correct answer is option 'D'. Can you explain this answer?

Varun Patel answered
Let x be the number which should be subtracted from greatest 7 digit number 9999999 to get 6543210.
Then 9999999−x=6543210⟹x=9999999−6543210=34567899
The required number is 3456789

CD represents a number. If Place of the symbols are interchanged, the number will increase by:
  • a)
    100
  • b)
    500
  • c)
    50
  • d)
    200
Correct answer is option 'D'. Can you explain this answer?

Yashvi Pillai answered
Explanation:

To understand why the correct answer is option 'D', let's consider a specific number represented by the symbols CD.

- When the places of the symbols are interchanged, the number becomes DC.
- To find the increase in the number, we need to subtract the original number from the new number: DC - CD.

Step 1: Converting symbols to their numerical values:
- In Roman numerals, C represents 100 and D represents 500.

Step 2: Finding the values of CD and DC:
- CD represents the number 100 + 500 = 600.
- DC represents the number 500 + 100 = 600.

Step 3: Calculating the increase:
- To find the increase, we subtract the original number (CD) from the new number (DC):
DC - CD = 600 - 600 = 0.

Step 4: Interpretation of the result:
- The increase in the number is 0, which means there is no increase when the places of the symbols are interchanged.

Therefore, the correct answer is option 'D' (200) because the number does not increase when the places of the symbols are interchanged.

Students collected bags of cloths and glass bottles. Each bag holds 21 bottles and each bottle contains 600 mi of juice. If students filled 17 bags then how much of juice did they collect?
  • a)
    632 litres                      
  • b)
    212.2 litres       
  • c)
    612 litres         
  • d)
    214.2 litres
Correct answer is option 'D'. Can you explain this answer?

To find the total amount of juice collected by the students, we need to calculate the total number of bottles collected and then multiply it by the amount of juice in each bottle.

Given:
- Each bag holds 21 bottles.
- Each bottle contains 600 ml of juice.
- Students filled 17 bags.

Let's calculate the total number of bottles collected:
Total number of bottles = number of bags * bottles per bag
Total number of bottles = 17 bags * 21 bottles per bag
Total number of bottles = 357 bottles

Now, let's calculate the total amount of juice collected:
Total amount of juice = total number of bottles * juice per bottle
Total amount of juice = 357 bottles * 600 ml per bottle

To convert ml to liters, we divide by 1000:
Total amount of juice = (357 * 600) ml / 1000
Total amount of juice = 214,200 ml / 1000

Therefore, the total amount of juice collected by the students is 214.2 liters.

So, the correct answer is option D) 214.2 liters.

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