Tag: maths

Questions Related to maths

Find the value to three places of decimal of  the following. It is given that $\sqrt{2}=1.414, \sqrt{3} = 1.732, \sqrt{5} = 2.236$ and $\sqrt{10}=3.162.$ 


$\dfrac{\sqrt{5}+1}{\sqrt{2}}$

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

  1. $2.288$

  2. $1.2845$

  3. $3.629$

  4. None of the above

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Correct Option: A
Explanation:
Given,

$\dfrac {\sqrt 5+1}{\sqrt {2}}$

$=\dfrac {2.236+1}{1.414}$

$=2.288$

What is $4,563,021 \div 10^5$, rounded to the nearest whole number?

maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

  1. 45

  2. 44

  3. 46

  4. 47

Show answer
Correct Option: C
Explanation:

To divide by a positive power of 10, shift the decimal point to the left. This yields 45.63021. To round to the nearest whole number, look at the tenths place. The digit in the tenths place, 6, is more than 5. Therefore, the number is closest to 46.

Round off each of the following as required.

$5.5493$ correct to two decimal places.

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

  1. $5.00$

  2. $5.54$

  3. $5.50$

  4. $5.55$

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Correct Option: D
Explanation:

As the third digit is greater than $5$, the second digit $4$ can be rounded to $5$.
Thus, rounding off $5.5493$ gives $5.55$.

The correct expansion of $6.\overline {46}$ in the fractional form is :

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

  1. $\dfrac{646}{99}$

  2. $\dfrac{640}{100}$

  3. $\dfrac{64640}{1000}$

  4. $\dfrac{640}{99}$

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Correct Option: D
Explanation:

$6.\overline {46} = 6+ \overline {46}= 6+\dfrac{46}{99}=\dfrac{594+46}{99}=\dfrac{640}{99}$

Multiply $4.28$ and $0.67.$ Round off the product obtained correct to three decimal places

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

  1. $2.798$

  2. $2.868$

  3. $0.85$

  4. None of these

Show answer
Correct Option: B
Explanation:

$4.28 \times 0.67 = 2.8676$

As the digit in the fourth place $(6)$ is greater than $5,$ it will get rounded.
$\therefore  2.8676$  can be written as $2.868$, correct to three decimal places.

If the straight line through the point $P(3,4)$ makes an angle $\cfrac{\pi}{6}$ with the x-axis and meets the line $3x+5y+1=0$ at $Q$, the length $PQ$ is

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $\dfrac {132}{12\sqrt {3}+5}$

  2. $\dfrac {132}{12\sqrt {3}-5}$

  3. $\dfrac {132}{5\sqrt {3}+12}$

  4. $\dfrac {132}{5\sqrt {3}-12}$

Show answer
Correct Option: D
Explanation:

The equation of straight line passing through $P(3,4)$ is $y=\tan \dfrac{\pi}{6}{x}+(4-3\tan \dfrac{\pi}{6})\implies y=\dfrac{x}{\sqrt{3}}+4-\sqrt{3}$

The point of intersection will be $\bigg(\dfrac{55-57\sqrt{3}}{5+3\sqrt{3}},\dfrac{-10+3\sqrt{3}}{5+3\sqrt{3}}\bigg)$
Length will be $30(5-3\sqrt{3})$

If $m$ and $b$ are real numbers and $mb > 0$, then the line whose equation is $y = mx + b$ cannot contain the point-

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. $(0, 2009)$

  2. $(2009, 0)$

  3. $(0, -2009)$

  4. $(20, -100)$

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Correct Option: B
Explanation:
$y= mx + b$
for (2009,0)
substituting in the given line
we get $2009m+b=0$
that is possible only if $mb < 0$
which contradicts our initial assumption mb > 0
so option is $b$

The graph of $\dfrac {7x}{2}=18+\dfrac {4}{5}x-45$ is line____

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. Parallel to $x-$axis at a distance of $10$ units from the origin

  2. Parallel to $y-$axis at a distance of $10$ units from the origin

  3. Parallel to $x-$axis at a distance of $20$ units from the origin

  4. Parallel to $y-$axis at a distance of $20$ units from the origin

  5. None of these

Show answer
Correct Option: B
Explanation:

$\cfrac { 7x }{ 2 } =18+\cfrac { 4 }{ 5 } x-45\ \Rightarrow \cfrac { 7x }{ 2 } -\cfrac { 4x }{ 5 } =-27\ \Rightarrow \cfrac { 35x-8x }{ 10 } =-27\ \cfrac { 27x }{ 10 } =-27\ \Rightarrow x=-10$

Therefore graph is a straight line parallel to y-axis at a distance of $10$ units from the origin.

Find $c$ if the line $cx+5y-3=0$ passes through $(2,1)$

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. -1

  2. -2

  3. 3

  4. 4

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Correct Option: A
Explanation:

Point is $(2,1)$

Equation is $cx+5y-3=0\c(2)+5(1)-3=0\2c+2=0\c=-1$

The graph of the equation y = mx is line which always passes through

maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

  1. (0, m)

  2. (x, 0)

  3. (0, x)

  4. (0, 0)

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Correct Option: D
Explanation:

The graph is shown in image 

$y=mx$
Given lines always passes through $(0,0)$ for any value of $m$ 
Because $(0,0)$ always satisfied the equation $y=mx$