Change in the Value of a Number by Moving Decimal

Q.

I want some explanation on number system

Conversion

Binary

Hexadecimal

Octal

Decimal......

Sry I wrote the chapter algebraic expressions because number system was not there....

Q.

0.0904 has 4 significant figures. State whether true or false.

1. False

2. True

Q.

Jack’s age is 0.27 times the age of his father. His father’s present age is 45 years. Jack’s present age correct to one decimal place will be

1. 12

2. 12.1

3. 12.2

4. 12.3

Q.

How many $60s$ are there in $48000$?

Q.

If the decimal is moved three places to the right in the number - 23.456789 , what would be the new digit at the hundredths position?

1. 9

2. 7

3. 8

4. 5

Q.

How to convert 81/500 to decimal

Q. If the decimal point in a number is shifted one place to the left, the number becomes of the original number.

1. Twice
2. Ten times
3. $\frac{1}{10}$
4. $\frac{1}{100}$

Q.

If the decimal is shifted 2 places to the left in the decimal , 312749.563738 what will be the digit at the thousand's position?

1. 4

2. 3

3. 7

4. 1

Q. If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\overrightarrow{b}=2\hat{i}-\hat{j}+\hat{k}$ and $\overrightarrow{c}=\hat{i}+x\hat{j}+y\hat{k}$, are linearly dependent and $|\overrightarrow{c}|=\sqrt{3}$ then $(x,y)$ is

1. $(-\frac{7}{5},\frac{3}{5})$
2. $(1,1)$
3. $(-2,0)$
4. $(\frac{1}{5},\frac{7}{5})$

Q.

If the vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are perpendicular to each other, then a vector $\overrightarrow{v}$ in terms of $\overrightarrow{a}$ and $\overrightarrow{b}$ satisfying the equations
$\overrightarrow{v}.\overrightarrow{a}=0,\overrightarrow{v}.\overrightarrow{b}=1and\left[\overrightarrow{v}\overrightarrow{a}\overrightarrow{b}\right]=1$ is

1. $\frac{\overrightarrow{b}}{|\overrightarrow{b}{|}^2}+\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}{|}^2}$

2. $\frac{\overrightarrow{b}}{|\overrightarrow{b}|}+\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}{|}^2}$

3. $\frac{\overrightarrow{b}}{|\overrightarrow{b}{|}^2}+\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}|}$

4. None of these

Q. If $\overrightarrow{a}=\hat{i}+\hat{j}+\hat{k},\hat{b}=4\hat{i}+3\hat{j}+4\hat{k}$ and $\overrightarrow{c}=\hat{i}+\alpha \hat{j}+\beta \hat{k}$ are linearly dependent vectors and $|\overrightarrow{c}|=\sqrt{3},$ then

1. $\alpha =1,\beta =-1$
2. $\alpha =1,\beta =\pm 1$
3. $\alpha =-1,\beta =\pm 1$
4. $\alpha =\pm 1,\beta =1$

Q. System of vectors $a_1,a_2,.......a_n$ is said to be linearly dependent if there exists a system of scalars $(c_1,c_2---c_{n}suchthat{c}_1\overline{a}+c_2\overline{a_2}+...c_n\overline{a_n}=\overline{0}$

1. True
2. False

Q.

The Decimal point shifted 5 places to the left and then 2 places to the right. What is the number now if the original number was 456789.102

1. 4567.89102

2. 45678.9102

3. 45.6789102

4. 456.789102

Q.

A student while doing a math problem , misplaced the decimal point. Due to this the digit at thousandths place became the digit at hundredths place. Identify the number which the child had written incorrectly if the actual number was 45.6547.

1. 4565.47

2. 456.547

3. 4.56547

4. 45654.7

Q. Subtract:

13.876 from 22

Q. Let $\overline{a}=2\overline{i}-3\overline{j}+\hat{k},\overline{b}=\hat{i}-\hat{j}+3\hat{k}and\overline{c}=\hat{i}+\hat{j}-\hat{k}$ Then the system of vectors $\overline{a},\overline{b}and\overline{c}$

1. Is linearly dependent
2. Is linearly independent
3. Cannot be determined
4. None of the above