True False[1 Marks ]

Question 11 Mark

The product of two irrational numbers is an irrational number (True/ False).

Answer

False.Reason:
As it is not always possible that the product of two irrational number be also an irrational number, it may be a rational number.
for example,
$\sqrt{3}\times\sqrt{3}=3,\sqrt{7}\times\sqrt{7}=7$

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Question 21 Mark

Two numbers have 12 as their HCF and 350 as their LCM (True/ False).

Answer

False.Solution:
HCF of two numbers = 12
LCM of two numbers = 350
$\frac{\text{LCM}}{\text{HCF}}=\frac{350}{12}=\frac{175}{6}$
The result of $\frac{\text{LCM}}{\text{HCF}}$ is not a natural number so we can say that two number have not 12 as their HCF and 350 as their LCM.
Thus, the given statement is false.

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Question 31 Mark

Every even integer is of the form 2m, where m is an integer (True/ False).

Answer

True.
Reason:
Let the various values of m as -1, 0 and 9.
Thus, the values for 2m become -2, 0 and 18 respectively.

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Question 41 Mark

Every odd integer is of the form 2m - 1, where m is an integer (True/ False).

Answer

True.
Reason:
Let the various values of m as -1, 0 and 9.
Thus, the values for 2m - 1 become -3, -1 and 17 respectively.
These are odd integers.

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Question 51 Mark

The product of any three consecutive natural number is divisible by 6 (True/ False).

Answer

True.Reason:
Let the three consecutive natural numbers be 1,2 and 3.
Their product is 6, which is divisible by 6.
Let the other set of three consecutive natural numbers be 3, 4 and 5.
Their product is 60, which is divisible by 6.

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Question 61 Mark

HCF of two numbers is always a factor of their LCM (True/ False).

Answer

True.Reason:
The HCF is a factor of both the numbers which are factors of their LCM.
Thus the HCF is also a factor of the LCM of the two numbers.

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Question 71 Mark

The sum of two prime number is always a prime number (True/ False).

Answer

False.Reason:
Sum of two prime numbers can be a composite number.
e.g. 3 and 5 are prime numbers but their sum 3 + 5 = 8 is a composite number.

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Question 81 Mark

$\pi$ is an irrational number (True/ False).

Answer

True.Reason:
Rational number is one that can be expressed as the fraction of two integers.
Rational numbers converted into decimal notation always repeat themselves somewhere in their digits.
For example, 3 is a rational number as it can be written as $\frac{3}{1}$ and in decimal notation it is expressed with an infinite amount of zeros to the right of the decimal point. $\frac{1}{7}$ is also a rational number.
Its decimal notation is 0.142857142857…, a repetition of six digits.
However $\sqrt{2}$ cannot be written as the fraction of two integers and is therefore irrational.
Now,
$\pi=3.1415926.....$
Thus, it is irrational.

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Question 91 Mark

The sum of two irrational number is an irrational number (True/ False).

Answer

False.
Reason:
As it is not always possible that the sum of two irrational is also an irrational number, it may be rational number also.
For example,
$\big(2+\sqrt{3}\big)+\big(2-\sqrt{3}\big)=2+\sqrt{3}+2-\sqrt{3}=4.$

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Maths True False[1 Marks ]

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