Numbers in General Form

Q.

If a number 'x' is divisible by another number 'y', then 'x' is also divisible by all the prime factors of 'y'.

1. True

2. False

Q.

What is the sum of any two? (a) Odd Number (b) Even Number

Q.

If $n$is a natural number then $9^{2n}-4^{2n}$is always divisible by

1. $5$

2. $13$

3. both $5$and $13$

4. None of these

Q.

The units digit of a two-digit number is 3 and seven times the sum of the digits is the number itself. Find the number.

Q.

In a two-digit number, the digit at the units place is double the digit in the tens place. The number exceeds the sum of its digits by 18. Find the number.

Q.

What is the sum of the first n positive integers? [1 MARK]

Q.

Find the difference between the greatest $6$ digit number and the smallest $5$digit number.

Q. What is the value of x/0 ?

Q. Question 10
A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the form $\frac{p}{q}$? Give reasons.

Q.

Evaluate ${\left[i^{19}+{\left(\frac{1}{i}\right)}^{25}\right]}^2$

1. $4$

2. $-4$

3. $5$

4. $-5$

Q.

Find the difference between the largest $5-$digit number and the smallest $6-$digit number.

Q.

$\begin{array}{c}AB\\ \times 6\\ BBB\end{array}$

1. 100 × 1 + 10 × 8 + 2

2. 100 × 1 + 10 × 2 + 5

3. 100 × 2 + 10 × 1 + 8

4. 100 × 1 + 10 × 2 + 8

Q.

Expand the following numbers using exponents:

a) $1029.63$

b) $1296.249$

Q. Let abc be a three-digit number. Then abc – cba is not divisible by

1. 11
2. 18
3. 9
4. 33

Q. Find the least number which must be added to 306452 to make it a perfect square. [4 MARKS]

Q. Question 3 (i)
Form the pair of linear equations for the following problems and find their solution by substitution method:
(i) The difference between two numbers is 26 and one number is three times the other. Find them.

Q.

Solve each of the following equation:
$\frac{x}{2}=5$

Q. abc is a three digit number. This three digit number is reversed and subtracted from the original number. The difference obtained is 396. Find (a-c).

1. 4
2. 9
3. 11
4. 1

Q.

How to evaluate the power ${\left(\frac{2}{3}\right)}^2$?

Q. Find the least number which must be subtracted from 18265 to make it a perfect square. [4 MARKS]

Q.

Expanded form of 432 is:

1. 4 x 100 + 3 x 10 + 1

2. 4 x 100 + 3 x 10 + 2

3. 4 x 100 + 3 x 1 + 2 x 10

4. 4 x 1000 + 3 x 100 + 2

Q.

If x and y vary inversely and x = 18 when y = 8, find x when y = 16.

Q.

Question 88:

Write the number of seconds in scientific notation.
$\begin{array}{ccc}S.N.& Units& Valueinseconds\\ 1.& 1minute& 60\\ 2.& 1hour& 3,600\\ 3.& 1day& 86,400\\ 4.& 1month& 2,600,000\\ 5.& 1year& 32,000,000\\ 6.& 10year& 3,20,000,000\end{array}$

Q.

Choose the correct option which describes the number 123 in its general form.

1. $100\times 1+100\times 2+100\times 3$

2. $10\times 1+10\times 2+10\times 3$

3. $100\times 1+10\times 2+1\times 3$

4. $1\times 1+1\times 2+1\times 3$

Q. The sum of the digits of a two digit number is 14. If 29 is substracted from the certain number, the newly formed number's digits are equal to each other. So, find the certain number.

Q.

Juhi sells a washing machine for $Rs13500$. She loses $20\%$ in the bargain. What was the price at which she bought it?

Q.

Question 67

Arrange the following exponents in descendig order.
$2^{2+3},(2^2{)}^3,2\times 2^2,\frac{3^5}{3^2},3^2\times 3^0,2^3\times 5^2$

Q.

The remainder obtained when $1!+2!+3!+.....+11!$is divided by $12$ is

1. $9$

2. $8$

3. $7$

4. $6$

Q.

Find the difference between the largest 7-digit number and the smallest 6-digit number

Q.

1A*A=9A

One A is multiplied by A

And the answer is 9A