Tag: maths

Questions Related to maths

Divide $7$  by $11$ and express the result in two significant digits.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $0.64$

  2. $0.583$

  3. $0.54$

  4. $0.67$

Show answer
Correct Option: A
Explanation:

On dividing 7 by 11, we get 0.6363636363.... .

If we have to express this in two significant digits, then it would be 0.64 as 6 is > 5  and 1 would get added to 3.

Write the number of significant digits in:

$0.07$.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $7$

  2. $1$

  3. $3$

  4. $2$

Show answer
Correct Option: B
Explanation:

Zeroes placed before other digits are not significant.
$\therefore  0.07$ has $1$ significant digit.

Write the number of significant digits in:

$0.0016$.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $2$

  2. $5$

  3. $1$

  4. $4$

Show answer
Correct Option: A
Explanation:

Zeroes placed before other digits are not significant.
$\therefore  0.0016$  has $2$ significant digits.

Write the number of significant digits in:

$805.060$.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $3$

  2. $2$

  3. $5$

  4. $6$

Show answer
Correct Option: D
Explanation:

All zeroes which  are both to the right of the decimal point and to the right of all non-zero significant digits  are themselves significant.
$\therefore  805.060$ has $6$ significant digits

For rational numbers, $x$ and $y,$ if $x > y,$ then which of the following is always a positive rational number?

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $ y - xy$

  2. $ xy-x$

  3. $ y-x$

  4. $ x- y $

Show answer
Correct Option: D
Explanation:
If $x>y$

$y-xy\rightarrow $ can be both positive and negative.

Example coside $x>1$ & $y>0$

$\left(y-xy\right)<0$

$xy-x\rightarrow $ can be both positive and negative 

$y-x\rightarrow $ always negative

$\boxed {x-y\rightarrow always\ positive\ since\ x>y}$

$0.\overline{5}$ in the form of $\frac{p}{q}$ is :

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $\dfrac{9}{5}$

  2. $\dfrac{5}{10}$

  3. $\dfrac{5}{9}$

  4. $\dfrac{10}{5}$

Show answer
Correct Option: C
Explanation:

$Let\quad x=.555....\ On\quad multiplying\quad by\quad 10\quad on\quad both\quad sides\quad \ 10x=5.555....\ On\quad subtracting\quad both\quad equations\quad \ 9x=5\ x=\dfrac { 5 }{ 9 } \ $

Hence, correct answer is option C.

If $x$ and $y$ are positive real number, then which of the following is correct?

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $x > y \Rightarrow -x > -y $

  2. $x > y \Rightarrow -x < -y $

  3. $x > y \Rightarrow \dfrac{1}{x} > \dfrac{1}{y} $

  4. $x > y \Rightarrow \dfrac{1}{x} < \dfrac{-1}{y} $

Show answer
Correct Option: B
Explanation:

If $x$ and $y$ are positive number and $x>y$, then 

$\Rightarrow -x<-y$ 
Also, $x>y$ $\Rightarrow \dfrac{1}{x}<\dfrac{1}{y}$
Hence, B is correct option.

Express $\displaystyle 9\frac{7}{20}$ as a decimal.

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $9.05$

  2. $9.53$

  3. $9.26$

  4. $9.35$

Show answer
Correct Option: D
Explanation:

$9\dfrac{7}{20}= \dfrac{187}{20}=9.35$

Hence the correct answer is option D.

In expressing a length $81.472 \ km$ as nearly as possible with three significant digits, the percent error is

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. $0.34\%$

  2. $0.034\%$

  3. $0.0034\%$

  4. $0.0038\%$

Show answer
Correct Option: B
Explanation:

$81.472 km = 81472$ meters $= 81500$ meters with three significant digits.
$\displaystyle \therefore Error\%=\frac{81500-81472}{81472}\times 100=0.034\%$

If $a, b, c$ are distinct $+ve$ real numbers and ${ a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 }=1$ then $ab + bc + ca$ is 

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding off decimals rounding of decimals

  1. less then $1$

  2. equal to $1$

  3. greater then $1$

  4. any real no.

Show answer
Correct Option: A
Explanation:

${a}^{2} + {b}^{2} + {c}^{2} = 1 \quad \left( \text{Given} \right)$


${\left( a +  b + c \right)}^{2} > 0$

${a}^{2} + {b}^{2} + {c}^{2} + 2 \left( ab + bc + ca \right) > 0$

$1 + 2 \left( ab + bc + ca \right) > 0$

$2 \left( ab + bc + ca \right) > -1$

$\Rightarrow ab + bc + ca >-\dfrac 12$