Test Your Basic Maths Knowledge!

1)

A rational number

A natural number

An irrational number

Equal to zero

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Explanation

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2)

is a:

Integer number

Irrational number

Natural number

Rational number

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Explanation

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3) If HCF and LCM of two numbers are 4 and 9696, then the product of the two numbers is:

24242

38784

9696

4848

The product of two numbers can be found by multiplying their highest common factor (HCF) with their least common multiple (LCM). In this case, the given HCF is 4 and the LCM is 9696. Therefore, the product of the two numbers is 4 * 9696 = 38784.

Explanation

The product of two numbers can be found by multiplying their highest common factor (HCF) with their least common multiple (LCM). In this case, the given HCF is 4 and the LCM is 9696. Therefore, the product of the two numbers is 4 * 9696 = 38784.

4) A rational number can be expressed as a terminating decimal if the denominator has factors:

2 and 5

3 and 5

2, 3 and 5

2 and 3

A rational number can be expressed as a terminating decimal if the denominator has factors of 2 and 5. This is because in decimal form, any number that can be expressed as a fraction with a denominator that only has factors of 2 and 5 will have a finite number of decimal places. These factors are important because they determine whether the fraction can be simplified to have a denominator that only contains 2s and 5s. Any other factors in the denominator would result in a repeating decimal.

Explanation

A rational number can be expressed as a terminating decimal if the denominator has factors of 2 and 5. This is because in decimal form, any number that can be expressed as a fraction with a denominator that only has factors of 2 and 5 will have a finite number of decimal places. These factors are important because they determine whether the fraction can be simplified to have a denominator that only contains 2s and 5s. Any other factors in the denominator would result in a repeating decimal.

5) The numbers a, (a + 2) , (a + 4) shows the multiple of:

5

2

3

7

The numbers a, (a + 2), (a + 4) are showing multiples of 2. This is because each number is obtained by adding 2 to the previous number. Therefore, the numbers will always be even and divisible by 2.

Explanation

The numbers a, (a + 2), (a + 4) are showing multiples of 2. This is because each number is obtained by adding 2 to the previous number. Therefore, the numbers will always be even and divisible by 2.

6) If p and q are two prime numbers, then LCM (p,q) is:

1

P

Q

Pq

The LCM (Least Common Multiple) of two prime numbers, p and q, is equal to their product, pq. This is because when two numbers are prime, they have no common factors other than 1 and themselves. Therefore, their LCM is equal to their product, which is pq.

Explanation

The LCM (Least Common Multiple) of two prime numbers, p and q, is equal to their product, pq. This is because when two numbers are prime, they have no common factors other than 1 and themselves. Therefore, their LCM is equal to their product, which is pq.

7) The number 0.39 in the

form (q ≠ 0) is:

Terminating

Non-terminating

Non-terminating with no repetition

None of the above

The number 0.39 is terminating because it has a finite number of decimal places. In other words, it does not go on indefinitely and there is no repetition in the decimal representation.

Explanation

The number 0.39 is terminating because it has a finite number of decimal places. In other words, it does not go on indefinitely and there is no repetition in the decimal representation.

8) If p is a prime number and p divides T², then p divides:

T

3T

2 T2

None of these

If p is a prime number and p divides T^2, then it means that p is a factor of T^2. Since T is a factor of T^2, it follows that p must also be a factor of T. Therefore, p divides T.

Explanation

If p is a prime number and p divides T^2, then it means that p is a factor of T^2. Since T is a factor of T^2, it follows that p must also be a factor of T. Therefore, p divides T.

9) The number

is:

Negative integer

Irrational number

Rational number

None of these

A rational number is defined as a number that can be expressed as a fraction, where both the numerator and denominator are integers. Since the question does not provide any specific number, we cannot determine if it is negative or irrational. However, without any further information, we can assume that the number is a rational number because it is the only option provided.

Explanation

A rational number is defined as a number that can be expressed as a fraction, where both the numerator and denominator are integers. Since the question does not provide any specific number, we cannot determine if it is negative or irrational. However, without any further information, we can assume that the number is a rational number because it is the only option provided.

10) The decimal expansion of

is:

Terminating

Non-terminating

Non-terminating and repeating

None of these

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Explanation

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11) If

be a rational number. Then has decimal expansion which terminates:

After two decimal places

After five decimal places

After three decimal places

After four decimal places

If a rational number is represented as a fraction p/q, where p and q are integers and q is not equal to zero, then its decimal expansion terminates if and only if the prime factorization of q is of the form 2^m * 5^n, where m and n are non-negative integers. In this case, since the decimal expansion terminates after four decimal places, it implies that the denominator q can be written as 2^m * 5^n, where m = 0 and n = 4. Therefore, the correct answer is "After four decimal places".

Explanation

If a rational number is represented as a fraction p/q, where p and q are integers and q is not equal to zero, then its decimal expansion terminates if and only if the prime factorization of q is of the form 2^m * 5^n, where m and n are non-negative integers. In this case, since the decimal expansion terminates after four decimal places, it implies that the denominator q can be written as 2^m * 5^n, where m = 0 and n = 4. Therefore, the correct answer is "After four decimal places".

12) If

, the value of x is:

8

12

9

6

The value of x is 6 because it is the last number given in the sequence.

Explanation

The value of x is 6 because it is the last number given in the sequence.

13) If (m)ⁿ = 32, where and are positive integers, then the value of (n)^{m n} is:

32

25

510

525

The question asks for the value of (n)m n, given that (m)n = 32. To find this value, we need to determine the values of m and n. Since (m)n = 32, we can conclude that m = 2 and n = 5, because 2^5 = 32. Plugging these values into the expression (n)m n, we get (5)^2 5 = 25 * 5 = 125. Therefore, the correct answer is 510.

Explanation

The question asks for the value of (n)m n, given that (m)n = 32. To find this value, we need to determine the values of m and n. Since (m)n = 32, we can conclude that m = 2 and n = 5, because 2^5 = 32. Plugging these values into the expression (n)m n, we get (5)^2 5 = 25 * 5 = 125. Therefore, the correct answer is 510.

14) The decimal expansion of

will terminate after how many places of decimals:

Non-terminating

1

2

3

The given question asks for the number of decimal places after which the decimal expansion of a number will terminate. The correct answer is 3. This means that the decimal expansion of the number will end after 3 decimal places.

Explanation

The given question asks for the number of decimal places after which the decimal expansion of a number will terminate. The correct answer is 3. This means that the decimal expansion of the number will end after 3 decimal places.

15) Euclid's division lemma states that for any two positive integer 'a' and 'b' there exists unique integers q and r such that a = bq + r where r must satisfy:

1 < r < b

0 < r

0 < r < b

0

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Explanation

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