Tag: maths

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Questions Related to maths

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

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 $\sqrt{10}=3.162.$ 


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

  1. $2.288$
  2. $1.2845$
  3. $3.629$

  4. None of the above
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Given,

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

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

$=2.288$
Multiple choice maths decimal fractions rounding decimals non-terminating recurring decimals in rational numbers rounding of decimals estimation and rounding off estimations, bounds and rounding off

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

  1. 45

  2. 44

  3. 46

  4. 47
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $2.798$
  2. $2.868$
  3. $0.85$

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  1. $\dfrac {132}{12\sqrt {3}+5}$
  2. $\dfrac {132}{12\sqrt {3}-5}$
  3. $\dfrac {132}{5\sqrt {3}+12}$
  4. $\dfrac {132}{5\sqrt {3}-12}$
Reveal answer Fill a bubble to check yourself
D Correct answer
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 $30(5-3\sqrt{3})$

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

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

  1. $(0, 2009)$
  2. $(2009, 0)$
  3. $(0, -2009)$
  4. $(20, -100)$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $b$
Multiple choice maths banking and taxation reading graphs describing different situations using equations to plot lines basics of a straight line

The graph of $\dfrac {7x}{2}=18+\dfrac {4}{5}x-45$ is 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
Reveal answer Fill a bubble to check yourself
B Correct answer
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.