True False[1 Marks ]

Question 11 Mark

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

Answer

False.
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.
$HCF$ 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.
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.
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.
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.
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.
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.
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.
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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