Numbers

Q.

Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Q.

Express 0.237 bar on 237 in p/q form

Q.

The expression $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ when simplified reduces to $a-b\sqrt{15}$

Then a + b is

1. 10

2. 20

3. 15

4. 5

Q. Find the value of x for the given equation :

$3^x+3^{x+1}=36$

1. 
   3
2. 
   7
3. 
   2
4. 
   5

Q. If $\sqrt{13-x\sqrt{10}}$=$\sqrt{8}+\sqrt{5}$ then the value of x is

1. 
   $2$
2. 
   $-5$
3. 
   $-4$
4. 
   $6$

Q.

Question 13
Write the denominator of rational number $\frac{257}{5000}$ in the form $2^m\times 5^n$, where m, n are non - negative integers. Hence, write its decimal expansion, without actual division.

Q.

What type of number is $2\mathrm{\pi }$?

Q.

Question 26
Which of the following statements is not true?

(A) The HCF of two distinct prime numbers is 1
(B) The HCF of two co-prime numbers is 1
(C) The HCF of two consecutive even numbers is 2
(D) The HCF of an even and an odd number is even.

Q.

By Rationalising the denominator , find the value of $\frac{1}{2+\sqrt{3}}$ upto 2 significant figures.

1. 0.23

2. 0.27

3. 0.37

4. 0.72

Q.

The HCF of two distinct prime is $1$.

1. True
2. False

Q.

Find the values of $a$ and $b$

if $\frac{5+2\sqrt{3}}{7+4\sqrt{3}}=a+b\sqrt{3}$

1. $a=11,b=-6$

2. $a=9,b=-6$

3. $a=-11,b=6$

4. $a=-9,b=6$

Q.

The rational number $10.11$ in the from $\frac{p}{q}$ is ____

Q.

The HCF of all possible pairs among four numbers is $3$, and the LCM of the four numbers is $198.$ What is the product of the numbers?

1. $2673$

2. $32076$

3. $16038$

4. $5346$

Q. Write some example if p and q has no common factor other than.write the property of q.

Q.

Rational numbers can be added or multiplied in any ____

Q.

Use prime factorisation find HCF of

$45\mathrm{and}75$

Q. If $\sqrt{28-6\sqrt{3}}$ = $\sqrt{3}a+b$, (where, $a,b$ are rational numbers) find the value of $a-b$.

1. 4
2. -4
3. -3
4. 2

Q.

Every whole number is an/a ___________.

1. integer

2. irrational number

3. (a) and (b) above.
4. None of the above

Q. 1, 3, 6, 10 and so on are known as numbers.

1. odd
2. triangular
3. square

Q.

$\frac{3}{4}$ lies between $\frac{1}{2}$ and 1.

1. True

2. False

Q.

$\frac{5+\sqrt{2}}{5-\sqrt{2}}=m+n\sqrt{2}$

Find the value of m and n

1. $m=3andn=\sqrt{2}$

2. $m=9andn=\frac{10}{3}$

3. $m=27andn=10$

4. $m=\frac{10}{3}andn=9$

Q.

$x^2=11+2\sqrt{30}$, find x

1. zero is a natural number

2. 6.5 is an integer

3. -1 is a whole number

4. All of these

Q.

$\frac{19}{6}$ is a terminating decimal number.

1. True

2. False

Q.

What symbol or letter is used to represent natural numbers?

Q. Evaluate : $4^{3/2}\times {125}^{-2/3}$

1. 
   $\frac{3}{25}$
2. 
   $\frac{7}{25}$
3. 
   $\frac{11}{25}$
4. 
   $\frac{8}{25}$

Q. Question 2 (ii)
Arrange the following in descending order :
$\left(ii\right)\frac{1}{5},\frac{3}{7},\frac{7}{10}$

Q.

$..........\times \frac{-2}{5}=1$. Fill in the blanks.

Q.

Why 1 is called as triangular number.

Q.

Q. Subtraction of two whole numbers always results in a whole number.

1. False
2. True